Category: Class 12

Bihar Board 12th Biology Objective Questions and Answers

Bihar Board 12th Biology Objective Answers Chapter 8 Human Health and Disease

Question 1.
Which of the following facrtors affect human health ?
(i) Infections
(ii) Silent mutation
(iii) Life style
(iv) Genetic disorders
(a) (i), (ii)and(iv)
(b) (i) and (ii)
(c) (i), (iii) and (iv)
(d) (i), (ii), (iii) and (iv)
Answer:
(c) (i), (iii) and (iv)

Question 2.
Which one of the following disease is non – communicable ?
(a) Diphtheria
(b) Flu
(c) Cancer
(d) Malaria
Answer:
(c) Cancer

Question 3.
Which of the following pairs contains an infectious and a non-infectious disease respectively ?
(a) Typhoid and AIDS
(b) AIDS and cancer
(c) Pneumonia and malaria
(d) Cancer and malaria
Answer:
(b) AIDS and cancer

Question 4.
Typhoid fever in human beings is caused by
(a) Plasmodium vivax
(b) Trichophyton
(c) Salmonella typhi
(d) Rhinoviruses.
Answer:
(c) Salmonella typhi

Question 5.
Which of the following is the bacterial disease in humans ?
(a) Dysentery
(b) Malaria
(c) Plague
(d) Both (a) & (c)
Answer:
(d) Both (a) & (c)

Question 6.
Which of the following pathogens causes whooping coough ?
(a) Legionella spp.
(b) Bordetella pertussis
(c) Vibrio cholerae
(d) Burcella melitensis
Answer:
(b) Bordetella pertussis

Question 7.
Which one of the following sets includes bacterial diseases ?
(a) Tetanus, tuberculosis, measles
(b) Diptheria, leprosy, plague
(c) Cholera, typhoid, mumps
(d) Malaria, mumps, poliomyelits
Answer:
(b) Diptheria, leprosy, plague

Question 8.
The common cold is caused by
(a) Rhino viruses
(b) Streptococcus pnemoniae
(c) Salmonella typhimurium
(d) Plasmodium vivax.
Answer:
(a) Rhino viruses

Question 9.
Hepatitis B is transmitted through
(a) sneezing
(b) female Anopheles
(c) coughing
(d) blood transfusion.
Answer:
(b) female Anopheles

Question 10.
A toxic substance, responsible for the chills and high fever recurring every three to four days in malarial fever, is
(a) interferon
(b) haemozoin
(c) hirudin
(d) colostrum
Answer:
(b) haemozoin

Question 11.
During the life cycle of Plasmodium, sexual reproduction takes place in which of the following hosts ?
(a) Human
(b) Female Anopheles mosquito
(c) Male Anopheles mosquito
(d) Both (a) and (b)
Answer:
(b) Female Anopheles mosquito

Question 12.
Amoebic dysentery (amoebiasis) is caused by
(a) Entamoeba histolytica
(b) E. coli
(c) Streptococcus pneumoniae
(d) Trichophyton.
Answer:
(a) Entamoeba histolytica

Question 13.
Which one of the following diseases cannot be cured by taking antibiotics ?
(a) Plague
(b) Amoebiasis
(c) Leprosy
(d) Whooping cough
Answer:
(b) Amoebiasis

Question 14.
An intestinal parasite which causes blockage of the intestinal passage and whose eggs are excreted along with the faeces of infected person is ______.
(a) Wuchereria bancrofti
(b) Ascaris
(c) Epidermophyton
(d) Microsporum
Answer:
(b) Ascaris

Question 15.
Elephantiasis, a chronic inflammation that results in gross deformities is caused by
(a) Ascaris
(b) E.coli
(c) Wuchereria
(d) Trichophyton
Answer:
(c) Wuchereria

Question 16.
Which of the following is affected by the infection of Wuchereria bancrofti ?
(a) Lymphatic vessels
(b) Respiratory system
(c) Nervous system
(d) Blood circulation
Answer:
(a) Lymphatic vessels

Question 17.
Which of the following diseases is transmitted by the bite of the female mosquito vector ?
(a) Filariasis
(b) Amoebiasis
(c) Typhoid
(d) Pneumonia
Answer:
(a) Filariasis

Question 18.
Which of the following pairs correctly matches a disease and a pathogen causing it ?
(a) Typhoid – Salmonella typhi
(b) Pneumonia – Haemophilus pneumoniae
(c) Malaria – Ascaris lumbricoides
(d) Ringworm – Entamoeba histolytica
Answer:
(a) Typhoid – Salmonella typhi

Question 19.
The pathogen Microsporum responsible for ringworm disease in humans belongs to the same kingdom as that of
(a) Taenia, a tapeworm
(b) Ascaris, a roundworm
(c) Rhizopus, a mould
(d) Wuchereria, a filarial worm,
Answer:
(c) Rhizopus, a mould

Question 20.
Appearance of dry, scaly lesions with itching on various parts of the body are the symptoms of _______.
(a) elephantiasis
(b) ringworm
(c) ascariasis
(d) amoebiasis
Answer:
(b) ringworm

Question 21.
Gambusia is a fish which is being introduced into the ponds in order to check the vector-borne diseases such as
(a) dengue
(b) malaria
(c) chikungunya
(d) all of these.
Answer:
(d) all of these.

Question 22.
Which one of the following pairs of diseases is viral as well as transmitted by mosquitoes ?
(a) Encephalitis and sleeping sickness
(b) Yellow fever and sleeping sickness
(c) Elephantiasis and dengue
(d) Yellow fever and dengue
Answer:
(d) Yellow fever and dengue

Question 23.
Which one of the following pairs is not correctly matched ?
(a) Dengue fever – Fiavi-ribo virus
(b) Syphilis – Trichu ris inch jura
(c) Plague – Yersinia pesris
(d) Filariasis – Wuchereria banchrofri
Answer:
(b) Syphilis – Trichu ris inch jura

Question 24.
The term ‘immunity’ refers to
(a) mutalism between host and parasite
(b) ability of the host to fight the disease-causing organism
(c) ability of the parasite to survive within a host
(d) a fatal disease.
Answer:
(b) ability of the host to fight the disease causing organism

Question 25.
A person has developed interferons in his body. He seems to carry an infection of
(a) tetanus
(b) malaria
(c) measles
(d) typhoid
Answer:
(c) measles

Question 26.
The first line of defence in the immune system is provided by
(a) skin and mucous membrane
(b) inflammatory response
(c) the complement system
(d) none of these.
Answer:
(a) skin and mucous membrane

Question 27.
Primary response produced due to first time encounter with a pathogen is of
(a) high intensity
(b) low intenisty
(c) intermediate intensity
(d) no intensity.
Answer:
(b) low intenisty

Question 28.
Which of the following components does not participate in innate immunity ?
(a) Neutrophils
(b) Macrophages
(c) B-lymphocytes
(d) Natural killer cells
Answer:
(c) B-lymphocytes

Question 29.
Antibodies are secreted by
(a) T-lymphocytes
(b) B-lymphocytes
(c) both (a) and (b)
(d) natural killer cell.
Answer:
(b) B-lymphocytes

Question 30.
The antigen binding site of an antibody is present at
(a) the constant region
(b) the C-terminal
(c) the variable region
(d) between constant and variable region.
Answer:
(c) the variable region

Question 31.
Humoral immunity is associated with
(a) T-cells
(b) B-cells
(c) macrophages
(d) both (a) and (b)
Answer:
(b) B-cells

Question 32.
The antibody which can cross placental barrier is.
(a) IgA
(b) JgE
(c) IgM
(d) IgG.
Answer:
(d) IgG.

Question 33.
The most abundant class of immunoglobulins (Igs) in the body is
(a) IgA
(b) IgG
(c) IgE
(d) IgM
Answer:
(b) IgG

Question 34.
A protein or polysaccharide molecule that stimulates antibody formation.
(a) antigen
(b) antibiotics
(c) exotoxin
(d) endotoxins.
Answer:
(a) antigen

Question 35.
Passive immunity can be conferred directly by
(a) vaccines
(b) antitoxins
(c) colostrum
(d) both (b) & (c)
Answer:
(d) both (b) & (c)

Question 36.
Which form of pathogen is used in vaccination ?
(a) Activated and strong pathogenic antigens
(b) Inactivated and weakened pathogenic antigens
(c) Hyperactive and strong pathogen
(d) Preformed antibodies
Answer:
(b) Inactivated and weakened pathogenic antigens

Question 37.
Injection of antitoxin in tetanus confers which type of immunisation ?
(a) Active immunisation
(b) Passive immunisation
(c) Auto-immunisation
(d) Humoral immunisation
Answer:
(b) Passive immunisation

Question 38.
The term ‘antitoxin’ refers to a preparation containing
(a) B-lymphoctyes and T-lymphocytes
(b) antibodies to the toxin
(c) weakend pathogen
(d) inactivated T-lymphocytes.
Answer:
(b) antibodies to the toxin

Question 39.
The injection given against the snake venom contains
(a) antigenic proteins
(b) preformed antibodies
(c) attenuated pathogen
(d) all of these.
Answer:
(b) preformed antibodies

Question 40.
Vaccine against polio viruses is an example of
(a) auto-immunisation
(b) passive immunisation
(c) active immunisation
(d) simple immunisation
Answer:
(c) active immunisation

Question 41.
Hepatitis B vaccine is produced from
(a) inactivated viruses
(b) yeast
(c) Haemophilus influenzae
(d) Salmonella typhimurium.
Answer:
(b) yeast

Question 42.
Use of vaccines and immunisation programmes have controlled which of the following infectious diseases ?
(a) Polio and tetanus
(b) Diphtheria and pheumonia
(c) Cancer and AIDS
(d) Both (a) and (b)
Answer:
(d) Both (a) and (b)

Question 43.
The most abundant antibody produced against allergens is
(a) IgE
(b) IgA
(c) IgG
(d) IgM.
Answer:
(a) IgE

Question 44.
Which of the following cells actively participate during allergy ?
(a) B-lymphocytes
(b) Liver cells
(c) Mast cells
(d) Red blood cells
Answer:
(c) Mast cells

Question 45.
The drugs used to quickly reduce the symptoms of allergy are
(a) ati-histamine and adrenaline
(b) histamine and thyroxine
(c) adrenaline and a-interferon
(d) all of these
Answer:
(a) ati-histamine and adrenaline

Question 46.
An auto-immune disease is
(a) SCID
(b) rheumatoid arthritis
(c) myasthenia gravis
(d) both (b) and (c).
Answer:
(d) both (b) and (c).

Question 47.
Which out of the following groups represent auto-immune disorders ?
(a) SCID and diphtheria
(b) Diabetes mellitus (type 1) and rheumatic fever
(c) AIDS and cholera
(d) Hepatitis and leukaemia
Answer:
(b) Diabetes mellitus (type 1) and rheumatic fever

Question 48.
The primary lymphoid organs are
(a) spleen and thymus
(b) bone marrow and thymus
(c) bone marrow and lymph node
(d) thymus and MALT.
Answer:
(d) thymus and MALT.

Question 49.
The site where lymphocytes interact with antigens and proliferate to become effector cells are
(a) spleen and lymph nodes
(b) bone marrow and thymus
(c) Peyer’s patches and tonsils
(d) both (a) and (c).
Answer:
(d) both (a) and (c).

Question 50.
Which of these glands is large at the time of birth but in adults, it reduces to a very small size ?
(a) Thyroid
(b) Adrenal
(c) Thymus
(d) Spleen
Answer:
(c) Thymus

Question 51.
MALT is
(a) Muscle Associated Lymphoid Tissues
(b) Mucosal Associated Lymphoid Tissues
(c) Mucosal and Lymphoid Tissue
(d) Memory Association Lymphoid Tissues.
Answer:
(b) Mucosal Associated Lymphoid Tissues

Question 52.
The lymphoid tissue, located within the lining of digestive tract is
(a) spleen
(b) Peyer’s pathes
(c) lymph nodes
(d) MALT
Answer:
(d) MALT

Question 53.
The abbreviation AIDS stands for
(a) Acquired immuno disease syndrome
(b) Acquired immuno deficiency syndrome
(c) Acquired immunity determining syndrome
(d) Acquired immunity delay syndrome.
Answer:
(b) Acquired immunodeficiency syndrome

Question 54.
The genetic material of HIV is
(a) dsDNA
(b) dsRNA
(c) ssDNA
(d) ssRNA
Answer:
(d) ssRNA

Question 55.
The human immunodeficiency virus is
(a) an unenveloped, RNA genome containing retrovirus
(b) an enveloped, RNA genome containing retrovirus
(c) an enveloped, DNA genome containing retrovirus
(d) an enveloped, RNA genome containing reovirus.
Answer:
(b) an enveloped, RNA genome containing retrovirus

Question 56.
Which of the following is not a cause of transmission of HIV?
(a) Multiple sexual partners
(b) Sharing infected needles
(c) Mosquito bite
(d) Transfusion of contaminated blood
Answer:
(c) Mosquito bite

Question 57.
Viral DNA after being converted from viral RNA by X, incorporates into host genome to undergo replication. What is‘X’ ?
(a) DNA polymerase
(b) Restriction endonuclease
(c) RNA polymerase
(d) Revers transcriptase
Answer:
(d) Revers transcriptase

Question 58.
The cells called ‘HIV factory’ is
(a) helper T-cells
(b) macrophages
(c) dendritic cells
(d) WBCs.
Answer:
(b) macrophages

Question 59.
HIV is a retrovirus that attacks
(a) helper T-cells
(b) cytotoxin t-cells
(c) B-cells
(d) neutrophils.
Answer:
(a) helper T-cells

Question 60.
AIDS is characterised by
(a) decrease in the number of killer T-cells
(b) decrease in the number of suppressor T-cells
(c) decrease in the number of helper T-cells
(d) increase in the number of helper T-cells
Answer:
(c) decrease in the number of helper T-cells

Question 61.
AIDS is widely diagnosed by
(a) Widal test
(b) ELISA
(c) PC
(d) Chromatography.
Answer:
(b) ELISA

Question 62.
Which of the following day is celebrated as ‘World AIDS Day’ ?
(a) 31st March
(b) 1st March
(c) Ist December
(d) 31st December
Answer:
(c) Ist December

Question 63.
Cancer cells do not exhibit the property of
(a) generating tumors
(b) metastasis
(c) contact inhibition
(d) less number of mitochondrial^cristae.
Answer:
(c) contact inhibition

Question 64.
A person suffering from leukaemia has
(a) tumors in adipose tissue
(b) increased number of plasma cells
(c) increased number of melanocytes
(d) increased number of WBCs.
Answer:
(d) increased number of WBCs.

Question 65.
A metastatic cancerous tumour is termed ‘sarcoma’ if the disorder is in
(a) fibroblasts
(b) circulatory system
(c) immune system
(d) epithelial cells.
Answer:
(a) fibroblasts

Question 66.
A chemical carcinogen present in tobacco smoke is responsible for
(a) skin cancer
(b) pancreatic cancer
(c) stomach cancer
(d) lung cancer.
Answer:
(d) lung cancer.

Question 67.
Major factors that cause cancer are
(a) oncogenes and polymorphonuclear leucocytes
(b) oncogenes and tumour suppressor genes
(c) MHC genes
(d) cellular oncogenes and a-interferons.
Answer:
(b) oncogenes and tumour suppressor genes

Question 68.
Which of the following approaches are used for the treatment of cancer ?
(a) Immunotherapy
(b) Surgery
(c) Radiotherapy & chemotherapy
(d) All of these
Answer:
(d) All of these

Question 69.
The substance given to cancer patients in order to activate their immune system and destroy the tumour is
(a) histamine
(b) interleukin
(c) a-interferon
(d) morphine.
Answer:
(c) a-interferon

Question 70.
In humans, receptors for opioids are present in
(a) central nervous system
(b) gastrointestinal tract
(c) respiratory tract
(d) both (a) and (b)
Answer:
(d) both (a) and (b)

Question 71.
Heroin is commonly called as
(a) coke
(b) crack
(c) smack
(d) charas.
Answer:
(c) smack

Question 72.
Which compound is formed by acetylation of morphine ?
(a) Heroin
(b) Cocaine
(C) Tobacco.
(d) Marijuana
Answer:
(a) Heroin

Question 73.
Marijuana is extracted from .
(a) dried leaves and flowers of hemp plant .
(b) ergot fungus
(c) roots of hemp plant
(d) cocoa plant.
Answer:
(a) dried leaves and flowers of hemp plant .

Question 74.
Charas and ganja are the drugs which affect
(a) respiratory system
(b) cardiovascular system
(c) digestive system
(d) nervous system.
Answer:
(b) cardiovascular system

Question 75.
Cocaine is obtained from
(a) Erythroxylon coca
(b) Papaver somniferum
(c) Atropa belladona
(d) Dature stramonium
Answer:
(a) Erythroxylon coca

Question 76.
Cocaine is commonly called as
(a) smack
(b) coke
(c) crack
(d) both(b)&(c)
Answer:
(d) both(b)&(c)

Question 77.
_______ is a CNS stimulant as it interferes with the trasport of the neuro-transmitter __________ .
(a) Cocaine, acetylcoline
(b) Barbituarate, glutamate
(c) Cocaine, dopamine
(d) Barbiturate, glycine
Answer:
(c) Cocaine, dopamine

Question 78.
Whihc of the following plants possess hallucinogenic properties ?
(a) Erythroxylon coca
(b) Atropa belladona
(c) Datura stramonium
(d) All of these
Answer:
(d) All of these

Question 79.
Which drug is being excessively taken by some sports persons nowadays ?
(a) Opioids
(b) Barbiturates
(c) Cannabinoids
(d) Lysergic acid diethly amides (LSD)
Answer:
(c) Cannabinoids

Question 80.
Which drug is used as medicine to help patients cope with depression and insomnia ?
(a) Morphine
(b) Amphetamines
(c) Barbiturate
(d) Both (b) and (c)
Answer:
(d) Both (b) and (c)

Question 81.
Which one of the following is an opiate narcotic ?
(a) Barbiturates
(b) Morphine
(c) Amphetamines
(d) LSD
Answer:
(b) Morphine

Question 82.
Which one of the following is a mismatched pair of the drug and its effect ?
(a) Amphetamines – CNS stimulants
(b) Lysergic acid Diethlyamide (LSD) – Psychedelic (hallucinogen)
(c) Heroin – Depressant, slows down body functions
(d) Barbiturates – Transquilliser
Answer:
(d) Barbiturates – Transquilliser

Question 83.
The addictive chemical present in tobacco is
(a) caffeine
(b) nicotine
(c) catechol
(d) carbon monoxide.
Answer:
(b) nicotine

Question 84.
Level of which hormones get elevated by the intake of nicotine ?
(a) FSH,LH
(b) Thyroxine, progesterone
(c) Oxytocine, prolactin
(d) Adrenaline, nor-adrenaline
Answer:
(d) Adrenaline, nor-adrenaline

Question 85.
The intravenous drug abusers are more likely to develop
(a) cancer
(b) AIDS
(c) malaria
(d) typhoid.
Answer:
(b) AIDS

Question 86.
The organisms which cause diseases is plants and animals are called
(a) pathogens
(b) vectors
(c) insects
(d) worms.
Answer:
(a) pathogens

Question 87.
The chemical test that is used for diagnosis of tyhpoidis
(a) ELISA-Test
(b) EST-Test
(c) PCR-Test
(d) Widal-Test.
Answer:
(d) Widal-Test.

Question 88.
The sporozoites that cause infection, when a female Anopheles mosquito bites a person are formed in
(a) liver of the person
(b) RBCs of mosquito
(c) salivary glands of mosqiot
(d) intenstine of mosquito.
Answer:
(d) intenstine of mosquito.

Question 89.
The disease chikungunya is transmitted by
(a) house flies
(b) Aedes mosquitoes
(c) cockroach
(d) female Anopheles.
Answer:
(b) Aedes mosquitoes

Question 90.
The genes causing cancer are
(a) structural genes
(b) expressor genes
(c) oncogenes
(d) regulatory genes.
Answer:
(c) oncogenes

Question 91.
AIDS is caused by HIV. Among the following, which one is not a mode of transmission of HIV ?
(a) Transfusion of contaminated blood.
(b) Sharing the infected needles.
(c) Shaking hands with infected persons.
(d) Sexual contact with infected persons.
Answer:
(c) Shaking hands with infected persons.

Question 92.
‘Smack’ is a drug obtained from the
(a) latex of Papever somniferum
(b) leaves of Cannabis saliva
(c) flowers of Datura
(d) fruits of Erythroxyl coca.
Answer:
(a) latex of Papever somniferum

Question 93.
The substance produced by a cell in viral infection that can protect other cells from further infection is
(a) serotonin
(b) colostrum
(c) interferon
(d) histamine.
Answer:
(c) interferon

Question 94.
Antibodies present in colostrum which protect the new born from certain diseases is of
(a) IgG type
(b) IgA type
(c) IgD type
(d) IgE type.
Answer:
(b) IgA type

Question 95.
Tobacco consumption is known to stimulate secretion of adrenaline and nor-adrenaline. The component causing this could be
(a) nicotine
(b) tannic acid
(c) curaimin
(d) catechin.
Answer:
(a) nicotine

Question 96.
Antivenom against snake poison contains
(a) antigens
(b) antigen-antibody complexes
(c) antibodies
(d) enzymes
Answer:
(c) antibodies

Question 97.
Which of the following is not a lymphoid tissue ?
(a) Spleen
(b) Tonsils
(c) Pancreas
(d) Thymus
Answer:
(c) Pancreas

Question 98.
Which of the following glands is large sized at birth but reduces in size with ageing ?
(a) Pineal
(b) Pituitary
(c) Thymus
(d) Thyroid
Answer:
(c) Thymus

Question 99.
Haemozoin is a
(a) precursor of haemoglobin
(b) toxin released from Streptococcus infected cells
(c) toxin released from Plasmodium infected cells
(d) toxin released from Haemophilus infected cells.
Answer:
(c) toxin released from Plasmodium infected cells

Question 100.
One of the following is not the causal organism for ringworm.
(a) Microsporum
(b) Trichophyton
(c) Epidermophyton
(d) Macrosporum
Answer:
(d) Macrosporum

Question 101.
A person with sickle cell anaemia is
(a) more prone to malaria
(b) more prone to typhoid
(c) less prone to malaria
(d) less prone to typhoid.
Answer:
(c) less prone to malaria

Bihar Board 12th Biology Objective Questions and Answers

Bihar Board 12th Biology Objective Answers Chapter 7 Evolution

Question 1.
One of the possible early sources of energy was/were
(a) CO₂
(b) chlorophyll
(c) green plants
(d) UV rays and lightning.
Answer:
(d) UV rays and lightning.

Question 2.
Abiogenesis theory of origin supports
(a) spontaneous generation
(b) origin of life from blue-green algae
(c) origin of life is due to pre-existing organisms
(d) organic evolution is due to chemical reactions.
Answer:
(a) spontaneous generation

Question 3.
Who proposed that the first form of the could have come from pre-existing non-living organic molecules ?
(a) S.L. Miller
(b) Oparin and Haldane
(c) Charles Darwin
(d) Alfred Wallace
Answer:
(b) Oparin and Haldane

Question 4.
According to one of the most widely accepted theories, earth’s atmosphere before origin of life was
(a) oxidising
(b) oxidising along with H₂
(c) reducing with free O₂ in small amount
(d) reducing with oxygen absent in O₂ form.
Answer:
(b) oxidising along with H₂

Question 5.
According to Oparin, which one of the following was not present in the primitive atmosphere of the earth ?
(a) Methane
(b) Oxygen
(c) Hydrogen
(d) Water vapour
Answer:
(b) Oxygen

Question 6.
The correct sequence for the manufacture of the compounds on the primitive earth is
(a) NH_3, CH₄, protein and carbohydrate
(b) protein, carbohydrate, water and nucleic acid
(c) NH₃, CH₄, carbohydrate and nucleic acid
(d) NH₃, carbohydrate, protien and nucleic acid.
Answer:
(d) NH₃, carbohydrate, protien and nucleic acid.

Question 7.
Early at mosphere contained methane and other hydrocarbons. They have been now replaced by
(a) nitrogen
(b) oxygen
(c) carbon dioxide
(d) hydrogen.
Answer:
(c) carbon dioxide

Question 8.
The first life originated
(a) on land
(b) in air
(c) in water
(d) all of these.
Answer:
(c) in water

Question 9.
Coacervates are
(a) colloid droplets
(b) nucleoprotein containing entities
(c) microspheres
(d) both (a) and (b)
Answer:
(d) both (a) and (b)

Question 10.
First life from on earth was a
(a) cyanobacterium
(b) chemoheterotroph
(c) autotroph
(d) photoautotroph.
Answer:
(b) chemoheterotroph

Question 11.
The ship used by Charles Darwin during the sea voyages was
(a) HMS Beagle
(b) HSM Beagle
(c) HMS Eagle
(d) HSM Eagle.
Answer:
(a) HMS Beagle

Question 12.
Fitnes according to Darwin refers to
(a) number of species in a community
(b) useful variation in population
(c) strength of an individual
(d) reproductive fitness of an organism.
Answer:
(d) reproductive fitness of an organism.

Question 13.
Alfred Wallace worked in
(a) Galapagos Island
(b) Australian Island Continent
(c) Ma lay Archipelago
(d) none of these.
Answer:
(c) Ma lay Archipelago

Question 14.
The theory of natural selection was given by
(a) Lamarck
(b) Alfred Wallace
(c) Charles Darwin
(d) Oparin and Haldane.
Answer:
(c) Charles Darwin

Question 15.
The preserved fossil remains of Archaeopteryx show that
(a) it was a flying reptile from the Permian period
(b) reptiles gave rise to birds during Jurassic period
(c) it was a flying reptile in the Triassic period
(d) reptiles gave rise to birds during Permian period.
Answer:
(b) reptiles gave rise to birds during Jurassic period

Question 16.
Which of the following isotopes is used for Finding the fossil age maximum about 35,0000 years ?
(a) ²³⁸U
(b) ¹⁴C
(c) ³H
(d) ²⁰⁶Pb
Answer:
(b) ¹⁴C

Question 17.
Which of the following statements is True ?
(a) Wings to birds and insects are homologous organs.
(b) Human hands and bird’s wings are analogous organs.
(c) Human hands and bat’s wings are analogous organs.
(d) Flipper of penguin and dolphin are analogous organs.
Answer:
(d) Flipper of penguin and dolphin are analogous organs.

Question 18.
Replacement of the lighter-coloured variety of peppered moth (Biston betularia) to its darker variety (Biston carbonaria) in England is the example of
(a) natural selection
(b) regeneration
(c) genetic isolation
(d) temporal isolation.
Answer:
(a) natural selection

Question 19.
Phenomenon of ‘industrial melanism’ demonstrates
(a) geographical isolation
(b) reproductive isolation
(c) natural selection
(d) induced mutation.
Answer:
(c) natural selection

Question 20.
Which one of the following phenomena supports Darwin’s concept of natural selection in organic evolution ?
(a) Development of transgenic animals
(b) Production of “Dolly’, the sheep by cloning
(c) Prevalence of pesticide resistant insects
(d) Development of organs from ‘stem cells’ for organ transplantation.
Answer:
(c) Prevalence of pesticide resistant insects

Question 21.
The phenomenon ‘ontogeny repeats phylogeny’ is explained by
(a) recapitualtion theory
(b) Inheritcance theory
(c) mutation theory
(d) natural selection theory.
Answer:
(a) recapitualtion theory

Question 22.
The presence of gill slits, in the embryos of vertebrates, supports the theory of
(a) metamorphosis
(b) biogenesis
(c) organic evolution
(d) recapitulation
Answer:
(d) recapitulation

Question 23.
Which is not a vestigial organ in man ?
(a) Nictitating membrane
(b) Tail vertebrae
(c) Vermiform appendix
(d) Nails
Answer:
(d) Nails

Question 24.
Which one is not a vestigia organ ?
(a) Wings of kiwi
(b) Coccyx in man
(c) Pelvic girdle of python
(d) Flipper of seal
Answer:
(d) Flipper of seal

Question 25.
By the statement ‘survival of the fittest’, Darwin meant that
(a) the strongest of all species survives
(b) the most intelligent of the species survives
(c) the cleverest of the species survives
(d) the species most adaptable to changes survives.
Answer:
(d) the species most adaptable to changes survives.

Question 26.
Which of the following are the two key concepts of Darwinian theory of evolution ?
(a) Genetic drift and mutation
(b) Adaptive radiation and homology
(c) Mutation and natural selection
(d) Branching descent and natural selection
Answer:
(d) Branching descent and natural selection

Question 27.
According to Lamarckism, long necked giraffes evolved because
(a) nature selected only long necked ones
(b) humans preferred only long necked ones
(c) short necks suddenly changed into long necks
(d) of stretching of necks over many generations by short necked ones.
Answer:
(d) of stretching of necks over many generations by short necked ones.

Question 28.
Which of the following evidences does not favour the Lamarckian concept of inheritance of acquired characters ?
(a) Lack of pigment in cave-dwelling animlas
(b) Melanisation in peppered moth
(c) Absence of limbs in snakes
(d) Presence of webbed toes in aquatic birds
Answer:
(b) Melanisation in peppered moth

Question 29.
“Human population grows in geometric ratio while food materials increase in arithmetic proportion”. It is a statement from
(a) Darwin
(b) Bateson
(c) AmartyaSen
(d) Malthus.
Answer:
(d) Malthus.

Question 30.
Which one of the following scientist’s name is correctly matched with the theory put forth by him ?
(a) de Vries – Theory of natural selection
(b) Darwin – Theory of pangenesis
(c) Weismann – Theory of continuity of germplasm
(d) Pasteur – Theory of inheritance of acquired charcters
Answer:
(c) Weismann-Theory of continuity of germplasm

Question 31.
Single step large mutation leading to speciation is also called
(a) founder effect
(b) saltation
(c) branching descent
(d) natural selection
Answer:
(b) saltation

Question 32.
At a particular locus, frequency of allele A is 0.6 and that of allele a is 0.4. What would be the frequency of heterozygotes in a random mating population at equilibrium ?
(a) 0.36
(b) 0.16
(c) 0.24
(d) 0.48
Answer:
(d) 0.48

Question 33.
Hardy-Weinberg equilibrium is known to be affected by gene flow, genetic drift mutation, genetic recombination and
(a) evolution
(b) limiting facrtors
(c) saltation
(d) natural selection.
Answer:
(d) natural selection.

Question 34.
The Hardy-Weinberg principle cannot operate if
(a) a population does not migrate for a longtime to a new habitat.
(b) frequent mutations occur in the population
(c) the population has no chance of interaction with other populations
(d) free interbreeding occurs among all members of the population.
Answer:
(b) frequent mutations occur in the population

Question 35.
Genetic drift operates only in
(a) larger populations
(b) Mendelian populations
(c) island populations
(d) smaller populations.
Answer:
(d) smaller populations.

Question 36.
Which of the following is most important for speciation ?
(a) Seasonal isolation
(b) Reproductive isolation
(c) Behavioural isolation
(d) Tropical isolation
Answer:
(b) Reproductive isolation

Question 37.
The factors involved in the formation of new species are
(a) Isolation and competition
(b) gene flow and competition
(c) competition and mutation
(d) isolation and variation.
Answer:
(d) isolation and variation.

Question 38.
Stabilising selection favours
(a) both extreme forms of a trait
(b) intermediate forms of a trait
(c) environmental differences
(d) one extreme form over the other extreme form and over intermediate forms of a trait.
Answer:
(b) intermediate forms of a trait

Question 39.
The different forms of interbreeding species that live in different geographical regions are called
(a) sibling species
(b) sympatric species
(c) allopatric species
(d) polytypic species.
Answer:
(c) allopatric species

Question 40.
Which of following represents correct order of evolutiton ?
(a) Amoeba → Leucosolenia → Hydra → Ascaris
(b) Leucosolenia → Hydra → Amoeba → Ascaris
(c) Ascaris → Amoeba → Leucosolenia → Hydra
(d) None of these
Answer:
(a) Amoeba → Leucosolenia → Hydra → Ascaris

Question 41.
Presence of gills in the tadpole of frog indicated that
(a) fishes were amphibious in the past
(b) fishes evolved from frog-like ancestors
(c) frogs will have gills in future
(d) frogs evolved from gilled ancestors.
Answer:
(d) frogs evolved from gilled ancestors.

Question 42.
The character that proves that frogs have evolved from fishes is
(a) their ability to swim in water
(b) tadpole larva in frogs
(c) similarity in the shape of the head
(d) their feeding on aquatic plants.
Answer:
(b) tadpole larva in frogs

Question 43.
Identify the correct arrangement of periods of Palaeozoic era in ascending order in geological time scale.
(a) Cambrian → Devonian → Ordovician → Silurian → Carboniferous → Permian
(b) Cambrian → Ordovician → Silurian → Devonian→Carboniferous → Permian
(c) Cambrian → Ordovician → Devonian → Silurian → Carboniferous → Permian
(d) Silurian → Devonian → Cambrian → Ordovician → Permian → Carboniferous
Answer:
(b) Cambrian → Ordovician → Silurian → Devonian → Carboniferous → Permian

Question 44.
Which is the correct order of increasing geological time scale for a hypothetical vertebrate evolution ?
(a) Cenozoic, Mesozoic, Palaeozoic, Proterozoic
(b) Cenozoic, Palaeozoic, Mesozoic, Proterozoic
(c) Proterozoic, Cenozoic, Palaezoic, Mesozoic
(d) Proterozoic, Palaeozoic, Mesozoic, Cenozoic
Answer:
(d) Proterozoic, Palaeozoic, Mesozoic, Cenozoic

Question 45.
The ‘Devonian period’ is considered to be as
(a) age of fishes
(b) age of amphibians
(c) age of reptiles
(d) age of mammals.
Answer:
(a) age of fishes

Question 46.
Amphibians were dominant during _______ period.
(a) Carboniferous
(b) Silurian
(c) Ordovician
(d) Cambrian
Answer:
(a) Carboniferous

Question 47.
The primate which existed 15 mya was
(a) Homo habilis
(b) Australopithecus
(c) Ramapithecus
(d) Homo erectus
Answer:
(c) Ramapithecus

Question 48.
The extinct stone ancestor, who ate only fruits and hunted with stone weapons was
(a) Ramapithecus
(b) Australophecus
(c) Dryopithecus
(d) Homo erectus
Answer:
(b) Australophecus

Question 49.
One of the oldest, best preserved and most complete hominid fossil commonly known as ‘Lucy’ belongs to the genus
(a) Austraolopithecus
(b) Oreopithecus
(c) Dryopithecus
(d) Pithecanthropus
Answer:
(a) Austraolopithecus

Question 50.
The brain capacity of Homo eractus was about
(a) 650 c.c.
(b) 900 c.c.
(c) 1500 c.c.
(d) 1400 c.c.
Answer:
(b) 900 c.c.

Question 51.
The extinct human who lived 1,00,000 to 40,000 years ago, in East and Central Asia, used hides to protect their bodies and had brain capacity of 1400 c.c. were
(a) Homo habilis
(b) Neanderthal man
(c) Cro-Magnon man
(d) Ramapithecus.
Answer:
(b) Neanderthal man

Question 52.
Which of the following statements is correct ?
(a) Australopithecus has large brain around 900 c.c.
(b) Neanderthal man lived in East Africa and the fruits.
(c) Homo erectus had brain capacity 900 c.c.
(d) Homo sapiens arose in Central Asia and moved to other continuents and developed into distinct races.
Answer:
(c) Homo erectus had brain capacity 900 c.c.

Question 53.
Which of the following statements js correct regarding evolution of mankind ?
(a) Homo erectus is preceded by Homo habilis.
(b) Neanderthal man and Cro-Magnon man were living at the same time.
(c) Australopithecus was living in Australia.
(d) None of these
Answer:
(a) Homo erectus is preceded by Homo habilis.

Question 54.
The cranial capacity was largest among the
(a) Peking man
(b) Java ape man
(c) African man
(d) Neanderthal man.
Answer:
(d) Neanderthal man.

Question 55.
The most apparent change during the evolutionary history oiHomo sapiens is traced in
(a) loss of body hair
(b) walking unright
(c) sortening of the jaws
(d) remarkable, increase in the brain size.
Answer:
(d) remarkable, increase in the brain size.

Question 56.
What kind of evidences suggested that man is more closely related with chimpanzee than with other hominoid apes ?
(a) Evidence from DNA of sex chromosomes only
(b) Comparison of chromosome morphology and number
(c) Evidence from fossil remains, and the fossil mitochondrial DNA alone
(d) Evidence from banding pattern of chromosome 3 and 6
Answer:
(d) Evidence from banding pattern of chromosome 3 and 6

Question 57.
Which of the following eras, in geological time scale, corresponds to the period when life had not orginated upon the earth ?
(a) Azoic
(b) Palaeozoic
(c) Mesozoic
(d) Archaeozoic
Answer:
(a) Azoic

Question 58.
Homo sapiens arose during which epoch ?
(a) Pleistocene
(b) Pliocene
(c) Oligocene
(d) Holocene
Answer:
(d) Holocene

Question 59.
Study the human evolution is called
(a) archaeology
(b) anthropology
(c) pedigree analysis
(d) chronobiology.
Answer:
(b) anthropology

Question 60.
Which of the following is used as an atmospheric pollution indicator ?
(a) Lepidoptera
(b) Lichens
(c) Lycopersicon
(d) Lycopodium
Answer:
(b) Lichens

Question 61.
The theory of spontaneous generation stated that
(a) life arose from living forms only
(b) life can arise from both living and non-living
(c) life can arise from non-living things only
(d) life arises spontaneusly, neither from living nor from the non-living.
Answer:
(c) life can arise from non-living things only

Question 62.
Animal husbandry and plant breeding programmes are the examples of
(a) reverse evolution
(b) aritifical selection
(c) mutation
(d) natural selection.
Answer:
(d) natural selection.

Question 63.
Palaentological evidences for evolutaion refer to the
(a) development of embryo
(b) homologous organs
(c) fossils
(d) analogous organs.
Answer:
(c) fossils

Question 64.
The bones of forelimbs of whale, bat, cheeah and man are similar in structure, because
(a) one organism has given rise to another
(b) they share a common ancestor
(c) they perform the same function.
(d) the have biochemical similarities.
Answer:
(b) they share a common ancestor

Question 65.
Analogous organs arise due to
(a) divergent evolution
(b) artificial selection
(c) genetic drift
(d) convergent evolution.
Answer:
(d) convergent evolution.

Question 66.
(p+q)² = p² + 2pq + q² = 1 represents an equation used in
(a) population genetics
(b) Mendilian genetics
(c) biometircs
(d) molecular genetics.
Answer:
(a) population genetics

Question 67.
Appearnace of antibiotic-resistant bacteria is an example of
(a) adaptive radiation
(b) transduction
(c) pre-existing variation in the population
(d) divergent evolution.
Answer:
(c) pre-existing variation in the population

Question 68.
Fossils are generally found in
(a) sedimentasry rocks
(b) igneous rocks
(c) metamorphic rocks
(d) any type of rock.
Answer:
(a) sedimentasry rocks

Question 69.
Which type of selection is industrial melanism observed in moth, Biston betularia?
(a) Stabilising
(b) Directional
(c) Disruptive
(d) Artificial
Answer:
(b) Directional

Question 70.
Which of the following is an example for link species ?
(a) Lobe fish
(b) Dodo bird
(c) Seaweed
(d) Chimpanzee
Answer:
(a) Lobe fish

Question 71.
Variations during mutations of meiotic recombinations are
(a) random and directionless
(b) random and directional
(c) random and small
(d) random small and directional
Answer:
(a) random and directionless

Bihar Board 12th Maths Model Papers

Bihar Board 12th Maths Model Question Paper 3 in English Medium

Time : 3 Hours 15 Min
Full Marks: 100

Instructions for the candidates :

1. Candidates are required to give their answers in their own words as far as practicable.
2. Figure in the right-hand margin indicates full marks.
3. While answering the questions, the candidate should adhere to the word limit as far as practicable.
4. 15 Minutes of extra time has been allotted for the candidate to read the questions carefully.
5. This question paper is divided into two sections. Section-A and Section-B
6. In Section A, there are 1-50 objective type questions which are compulsory, each carrying 1 mark. Darken the circle with blue/black ball pen against the correct option on the OMR Sheet provided to you. Do not use Whitener/Liquid/ Blade/Nail on OMR Sheet otherwise result will be invalid.
7. In section-B, there are 25 short answer type questions (each carrying 2 marks), out of which only 15 (fifteen) questions are to be answered.
   A part from this there is 08 Long Answer Type questions (each carrying 5 marks), out of which 4 questions are to be answered.
8. Use of any electronic device is prohibited.

Objective Type Questions

There are 1 to 50 objective type questions with 4 options, choose the correct option which is to be answered on OMR Sheet. (50 × 1 = 50)

Question 1.
Let R be the relation in the set N given by R = {(a, b): a = b – 2, b > 6}. Which of the following is correct answer.
(a) (2,4) ∈ R
(b) (3,8) ∈ R
(c) (6,8) ∈ R
(d) (8,7) ∈ R
Answer:
(c) (6,8) ∈ R

Question 2.
Let f: R → R be defined as f(x) = x⁴. Choose the correct answer ?
(a) f is one-one and onto
(b) f is many one onto
(c) f is one-one but not onto
(d) f is neither one-one nor opnto
Answer:
(d) f is neither one-one nor opnto

Question 3.
Let a binary operation on N defined as L.C.M. of a * b = a and b. Then (20 * 16) – (16 * 20) is equal to
(a) 4
(b) 60
(c) 0
(d) 1
Answer:
(c) 0

Question 4.
The value of \(\sin \left(\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right)\) is
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{1}{4}\)
(d) 1
Answer:
(d) 1

Question 5.
The principle value of \(\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)\) is
(a) \(\frac{2 \pi}{3}\)
(b) \(\frac{\pi}{6}\)
(c) \(\frac{\pi}{4}\)
(d) \(\frac{\pi}{3}\)
Answer:
(d) \(\frac{\pi}{3}\)

Question 6.
tan^-1 =
(a) cos^-1x
(b) \(\frac{1}{\cot ^{-1} x}\)
(c) \(\cot ^{-1} \frac{1}{x} 0\)
(d) -cot^-1x
Answer:
(b) \(\frac{1}{\cot ^{-1} x}\)

Question 7.
The number of all possible matrices of order 3 x 3 with each entry 0 or 1.
(a) 27
(b) 18
(c) 81
(d) 512
Answer:
(d) 512

Question 8.
If A = \(\left[\begin{array}{cc}
\alpha & \beta \\
\gamma & -\alpha
\end{array}\right]\) such that A² = I,
(a) 1 + α² + βγ = 0
(b) 1 – α²+ βγ = 0
(c) 1 – α² – βγ = 0
(d) 1 + α² – βγ = 0
Answer:
(c) 1 – α² – βγ = 0

Question 9.
The value of determinant \(\left|\begin{array}{lll}
\frac{1}{a} & 1 & b c \\
\frac{1}{b} & 1 & c a \\
\frac{1}{c} & 1 & a b
\end{array}\right|\) is
(a) 0
(b) abc
(c) 1/abc
(d) None of these
Answer:
(a) 0

Question 10.
The value of determinant is \(\left|\begin{array}{lll}
2 & 7 & 65 \\
3 & 8 & 75 \\
5 & 9 & 86
\end{array}\right|\) is
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(a) 0

Question 11.
\(\left|\begin{array}{lll}
1 & x & x^{2} \\
1 & y & y^{2} \\
1 & z & z^{2}
\end{array}\right|=\)
(a) (x – y) (y + z) (z + x)
(b) (x+y) (y – z) (z – x)
(c) (x – y)(y – z) (z + x)
(d) (x – y)(y – z) (z – x)
Answer:
(d) (x – y)(y – z) (z – x)

Question 12.
If , \(\left[\begin{array}{cc}
2 x-y & 5 \\
3 & y
\end{array}\right]=\left[\begin{array}{cc}
6 & 5 \\
3 & -2
\end{array}\right]\) then x =
(a) 3
(b) 4
(c) 5
(d) 8
Answer:
(b) 4

Question 13.
If \(f(x)=\left\{\begin{array}{l}
x, \text { if } x \geq 0 \\
0, \text { if } x<0
\end{array}\right.\) then the function is
(a) Continuous
(b) Discontinuous
(c) well defined
(d) None of these
Answer:
(b) Discontinuous

Question 14.
In how many points the function f(x) = \(\frac{1}{\log |x|}\) is discontinuous
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(c) 3

Question 15.
The differential of sin (x² + 5) is
(a) 2 sin (x + 5)
(b) 2 cos (x² + 5)
(c) 2x cos (x² + 5)
(d) None of these
Answer:
(c) 2x cos (x² + 5)

Question 16.
If y = log x then the value of \(\frac{d y}{d x}\) is
(a) x log x
(b) \(\frac{1}{x \log x}\)
(c) \(\frac{1}{\log x}\)
(d) \(\frac{1}{ x }\)
Answer:
(d) \(\frac{1}{ x }\)

Question 17.
If y = (3x² – 9x + 5)⁹ then \(\frac{d y}{d x}\) is equal to :
(a) 27 (3x² – 9x + 5)⁸ (2x – 3)
(b) 27 (3x² – 9x + 5)
(c) 27 (2x – 3)
(d) None of these
Answer:
(a) 27 (3x² – 9x + 5)⁸ (2x – 3)

Question 18.
The rate of change the area of circle w.r.t.r, when r = 5 cm.
(a) 10πcm²/cm
(b) 12πcm²/cm
(c) 8π cm²/cm
(d) 11πcm²/cm
Answer:
(a) 10πcm²/cm

Question 19.
The function f(x) = sin x is strictly increasing in the interval
(a) (0,1)
(b) \(\left(\frac{\pi}{2}, \pi\right)\)
(c) \(\left(0, \frac{\pi}{2}\right)\)
(d) None of these
Answer:|
(c) \(\left(0, \frac{\pi}{2}\right)\)

Question 20.
The function f(x) = e^2x is
(a) strictly increasing
(b) strictly decreasing
(c) neither incrasing nor decreasing
(d) None of these
Answer:
(a) strictly increasing

Question 21.
The slope of tangent to the curve y = x² + 3r + 4 at (1,1) is
(a) 5
(b) \(-\frac{1}{5}\)
(c) 8
(d) None of these
Answer:
(b) \(-\frac{1}{5}\)

Question 22.
The line y = mx is a tangent to the curve y² = 4r if the value of m is
(a) 1
(b) 2
(c) 3
(d) \(\frac{1}{2}\)
Answer:
(a) 1

Question 23.
If f(x) = 3x² + 15x + 5, then approximate value of f(3.02) is
(a) 47.66
(b) 57.66
(c) 67.66
(d) 77.66
Answer:
(d) 77.66

Question 24.
The antiderivative of (ax + b)² is

Answer:
\(\frac{1}{3 a}(a x+b)^{3}+C\)

Question 25.
\(\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x\) is equal to
(a) tan x + cot x + C
(b) tan x + cosec x + C
(c) – tan x + cot x + C
(d) tan x + sec x + C
Answer:
(a) tan x + cot x + C

Question 26.
∫ log xdx is equal to
(a) xlogx + x + C
(b) xlogx – x + C
(c) log x + x + C
(d) logx – x + C
Answer:
(b) xlogx – x + C

Question 27.
If f(a + b – x) = f(x) then \(\int_{a}^{b} x f(x) d x\) is equal to

Answer:
\(\frac{a+b}{2} \int_{a}^{b} f(x) d x\)

Question 28.
The value of \(\int_{0}^{1} \tan ^{-1}\left(\frac{x}{1+x^{2}}\right) d x\) is
(a) 1
(b) \(\frac{\pi^{2}}{32}\)
(c) -1
(d) \(\frac{\pi}{4}\)
Answer:
(b) \(\frac{\pi^{2}}{32}\)

Question 29.
\(\int_{0}^{1} \tan ^{-1}\left(1-x+x^{2}\right) d x\) is equal to
(a) log 2
(b) \(\log \frac{1}{2}\)
(c) πlog2
(d) \(\frac{\pi}{2} \log \frac{1}{2}\)
Answer:
(c) πlog2

Question 30.
The area enclosed by circle x² + y² = a² is
(a) 4
(b) πa²
(c) 2
(d) 1
Answer:
(b) πa²

Question 31.
The order and degree of \(\left(\frac{\mathrm{ds}}{\mathrm{dt}}\right)^{4}+3 \mathrm{s} \frac{\mathrm{d}^{2} \mathrm{s}}{\mathrm{dt}^{2}}=0\) is
(a) 1, 2
(b) 2, 1
(c) 2, 4
(d) 4, 2
Answer:
(b) 2, 1

Question 32.
Which of the following is linear differential equation ?
(a) (4x + 6y + 5) dy – (3y + 2x + 4)dx = Q
(b) xydx – (x³ + y³) dy = 0
(c) (x³ + 2y²) dx + 2xydy = 0
(d) y²dx + (x² – xy – y²) dy = 0
Answer:
(d) y²dx + (x² – xy – y²) dy = 0

Question 33.
The integrating factor at the diff eqⁿ (1 – y²) \(\frac{d x}{d y}\) + yx = ay (-1 < y < -1) is

Answer:
(d) \(\frac{1}{\sqrt{1-y^{2}}}\)

Question 34.
The general solution of diff eq \(\frac{y d x-x d y}{y}=0\) is
(a) xy = C
(b) x = cy²
(c) y = cx
(d) y = cx²
Answre:
(c) y = cx

Question 35.
The generval solution of diff. eqⁿ e^xdy + (ye^x + 2x)dx = 0 is
(a) xe^x + x² = C
(b) xe^y + y² = C
(c) ye^x + x² = C
(d) ye^x + x² = C
Answer:
(c) ye^x + x² = C

Question 36.
If the adjacent side of parallelogram are \(\vec{a}\) and \(\vec{b}\) then its area is

Answer:
(a) \(|\vec{a} \times \vec{b}|\)

Question 37.
If a + b + c = 0 then
(a) \(\vec{a} \cdot \vec{b}=0\)
(b) \(\vec{a}=\vec{b}\)
(c) \(\vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a}\)
(d) None of these
Answer:
(c) \(\vec{a} \times \vec{b}=\vec{b} \times \vec{c}=\vec{c} \times \vec{a}\)

Question 38.
If \(\vec{a}\) and \(\vec{b}\) are two vectors then \((\vec{a}+\vec{b}) \cdot(\vec{a}-\vec{b})\) is equal to

Answer:
(d) \(2(a \times b)\)

Question 39.
The angle between the vectors 2î – 3ĵ + 2k̂ and î + 4ĵ + 5k̂ is
(a) 30°
(b) 90°
(c) 45°
(d) 60°
Answer:
(b) 90°

Question 40.
If θ be the angle between the vectors \(\vec{a}\) and \(\vec{b}\) then sin θ is

Answer:
(a) \(\frac{\vec{a} \cdot \vec{b}}{|\vec{a} \| \vec{b}|}\)

Question 41.
The mean and variance of a binomial distribution are 6 and 1 respectively. Then the value of parameter n is
(a) 18
(b) 12
(c) 10
(d) 9
Answer:
(a) 18

Question 42.
The plane x = 0,y = 0 is
(a) Parattel
(b) Perpendicular
(c) Intersect z-axis
(d) None of these
Answer:
(c) Intersect z-axis

Question 43.
Linear programming problem is with
(a) One objective function
(b) Two objective function
(c) No objective function
(d) None of these
Answer:
(a) One objective function

Question 44.
If P(A) = 0.8, P(B) = 0.5 and P(B/A) = 0.4 then P(A/B) =
(a) 0.32
(b) 0.64
(c) 0.16
(d) 0.25
Answer:
(b) 0.64

Question 45.
The mean and variance of a random X are 4 and 2 respectively P(X = 1) is
(a) 1/32
(b) 1/16
(c) 1/8
(d) 1/4
Answer:
(b) 1/16

Question 46.
The pair of dice are rolled. The probability of obtaining an even prime number on each die is
(a) 1/36
(b) 1/12
(c) 1/6
(d) 0
Answer:
(a) 1/36

Question 47.
If P(A∪B) = 0.8 and P(A∩B) = 0.3 then P(Ā) + P(B̄) =
(a) 0.3
(b) 0.5
(c) 0.7
(d) 0.9
Answer:
(a) 0.3

Question 48.
Let the binary operation * on R defined by x *y = 1 + 12x + xy ∀ x,y ∈ R then 2 * 3 is
(a) 31
(b) 41
(c) 43
(d) 51
Answer:
(a) 31

Question 49.
Which of the following is the equation of ary – plane
(a) x = 0
(b) y = 0
(c) x = k
(d) z = 0
Answer:
(a) x = 0

Question 50.
In a hostel 60 % of the students read Hindi news paper, 40% read. English news paper and 20% read both Hindi and English news paper. Then what is probability that reads neither Hindi nor English news paper
(a) 0.2
(b) 0.3
(c) 0.4
(d) 0.5
Answer:
(a) 0.2

Non – Objective Type Questions

Short Answer Type Questions

Q. No. 1 to 25 are of Short Answer type carry of 2 marks each. Answer any 15 questions. (15 × 2 = 30)

Question 1.
Let N be the set of natural numbers and relation R define one N. as R = {(x,y); x,y ∈ N and x divide y} Verify that the whether R is reflexive, symmetric and transitive.
Answer:
Let.x, y, z, ∈ N
(i) xR.x ⇒ x divide x i.e. xRx. ∀ x ∈ N. So R is reflexive.
(ii) x divide y ⇒ xRy ⇒ (x, y) ∈ R but (y, x) ∉ R. Since .x divide y therefore it is not possible y divide x due to x, y ∈ N.SoR is not symmetric
(iii) x divide y, y divide z ⇒ x divide z i.e. .xRy, yRz ⇒ yRz So R is transitive.

Question 2.
Show that the function f: N → N defined as f(x) = 2x is one-one but not onto.
Answer:
we have f(x) = 2x ⇒ f(x₁) = f(x₂) ⇒ 2x₁ = 2x₂
⇒ x₁ = x₂ so, f is one-one
Further,f is not onto, as for 1 ∈ N, there does not exist any x in N such that f(x) = 2x = 1 ∈ N.
Thus f is one-one but not onto

Question 3.
Prove that the binary opeation * on the set N such that a * b = \(\frac{a+b}{2}\) ∀ a,b,∈ N is commutative but not associative.
Answer:

Thus the binary operation * is commutative but not associative

Question 4.
Find the value of cot [tan^-1 a + cot^-1 a]
Answer:

Question 5.
Prove that \(\sin ^{-1} \frac{2 \sqrt{2}}{3}+\sin ^{-1} \frac{1}{3}=\frac{\pi}{2}\)
Answer:

Question 6.
Find the value of x if \(\left[\begin{array}{ll}
x & 4 \\
2 & 2 x
\end{array}\right]=0\)
Answer:
\(\left[\begin{array}{ll}
x & 4 \\
2 & 2 x
\end{array}\right]=0\)
⇒ 2x² = 8 ⇒ x² = 4 ⇒ x = ±2

Question 7.
If A = \(\left[\begin{array}{lll}
3 & \sqrt{3} & 2 \\
4 & 2 & 0
\end{array}\right]\) then prove that (A’)’ = A
Answer:

Question 8.
Find the value at x if \(\left|\begin{array}{ll}
3 & x \\
x & 1
\end{array}\right|=\left|\begin{array}{ll}
3 & 2 \\
4 & 1
\end{array}\right|\)
Answer:
\(\left|\begin{array}{ll}
3 & x \\
x & 1
\end{array}\right|=\left|\begin{array}{ll}
3 & 2 \\
4 & 1
\end{array}\right|\)
Answer:
⇒ 3 – 2x² = 3- 8 ⇒ x² = 8
∴ x = ±2√2

Question 9.
Find the value of x and y if \(\left|\begin{array}{ll}
2 & 3 \\
y & x
\end{array}\right|=4\) and \(\left|\begin{array}{ll}
x & y \\
2 & 1
\end{array}\right|=\frac{7}{2}\)
Answer:

⇒ y = -3
Multiplying (2) by 2 and subtract (1), we get Putting the value of y in (2), we get

Question 10.
If a matrix has 24 elements. What are the possible orders it can have ? what, if has 13 element.
Answer:
The possible order of matrices for 24 elements are :
1 × 24, 24 × 1,2 × 12, 12 × 2, 3 × 8,8 × 3, 4 x 6 and 6 × 4
Again, possible order of matrices for 13 elements are 1 × 13 and 13 × 1.

Question 11.
Verify the Rolle’s theorem of the function f(x) = x³ (x – 1)² for the interval [0,1)
Answer:
Given, f(x) = ³(x – 1)²
⇒ f'(x) = 3x² (x-1)² + x³ 2(x – 1) = x² (x – 1) (3 (x – 1) + 2x) or, f'(x) = x² (x – 1) (5x – 3)
clearly f(x) is differentiable and continuous for each x.
(ii) f(x) is differentiable in (0, 1)
(iii) f(0) = 0 and f(1) = 0, ∴ f(0) =f(1)
So, all the condition of the Rolles theorem are satisfies for the function f(x) in (0, 1). Then f'(c) = 0
⇒ c²(c – 1)(5c – 3) = 0 c = 0,1,3/5
But 0< c < 1 ∴ c = 3/5

Question 12.
If x = at², y = 2at. then find that dy/dx
Answer:

Question 13.
Find the anti derivative F off defined by f(x) = 4x³ – 6, where F(0) = 3.
Answer:
one anti-derivative of f(x) is x⁴ – 6x since
\(\frac{d}{d x}\) (x⁴-6x) = 4x³ – 6
Therefore, the anti derivative F is given by
F(x) = x⁴ – 6x + C, where C is constant
Given that F(0) = 3, which gives 3 = 0 – 6 × 0 + C
⇒ C = 3
Thus, the required anti-derivative is the unique function F defined by F(x) = x⁴ – 6x + 3

Question 14.
Evaluate: \(\int_{0}^{1} x(1-x)^{23} d x\)
Answer:
Let z = 1 – x, then dz = -dx and x = 1 – z
when x = 0, z = 1 and when x = 1, z = 0

Question 15.
Evaluate: \(\int_{a}^{b} \frac{\log x}{x} d x\)
Answer:

Question 16.
Find the differential equation of the curve y = Ae^x + Be^-x; where A and B are constant.
Answer:
y = Ae^x + Be^-x
Differentiating both side w.r.t. x, we get
\(\frac{d y}{d x}\) = Ae^x + Be^-x
Again, differentiating w.r.t we get

or, \(\frac{d^{2} y}{d x^{2}}-y=0\) which is required, differential equation.

Question 17.
Find the particular solution of the differential equation \(\frac{d y}{d x}\) = ytanx when y = 1 if x = 0
Answer:

⇒ logy = -logcos x+ logC
⇒ log y + logcosx = log C
⇒ log (ycosx) = logC ⇒ ycosx = C …….(1)
Now, putting y= I and x = 0 in (1), we get
cos 0 = C ⇒ C = 1 ∴ y cos x = 1
y = \(\frac{1}{\cos x}\) ⇒ y = sec x

Question 18.
Find the unit vector in the direction of the vector \(\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
Answer:

Question 19.
If \(\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathbf{b}}=3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}\) then find the \(|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|\)
Answer:

Question 20.
Find the equation of the planes parallel to the plane dr -3y + 2z + 9 = 0 and at distance 5 from the origin.
Answer:
Let the plane 6x – 3y + 2z + k = 0 is the parallel, to the plane 6x – 3y + 2z + 9 = 0. Now, the distance of plane 6x – 3y + 2z + 9 = 0 from the origin is

Thus the plane is 6x – 3y + 2k ± 35 = 0

Question 21.
A Player has 7 cards in hand of which 5 arc red and of these five 2 are kings. A card is drawn at random. Find the probability that it is a king, it is known that it is red.
Answer:
Let A = The event of red card and B = The event of king.
Then n(A) = 5 and the events are red and king is = A ∩ B
∴ n(A) = 5 and the events of red and king – A∩B

Question 22.
Find the probability of the occurrence of a number greater than 1 if it is known that only odd numbers can occur in a die.
Answer:
Let A = The event of occurrence odd number and B = the event of occurrence the odd number greater Then
Then A = {1, 3,5} ⇒ n(A) = 3 and B = {3,5)
then A ∩ B = {3,5} ⇒ n(A∩B) = 2

Question 23.
Verify the continuity of the function f(x) = 2x² – 1 at x = 3.
Answer:

Question 24.
The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference when r = 4.9 cm ?
Answer:
Let c and r be the circumference and radius of circle. Then

Question 25.
Find the slope of the tangent to the curvey = x³ – x + 1 at the point whose x-co-ordinate is 2.
Answer:
Given the curve y = x³ – x + 1

Long Answer Type Questions

Questions No. 26 to 33 are Long Answer Type Questions. Each question carry 5 marks. Answer any 4 question. (4 × 5 = 20)

Question 26.
Prove that of all the rectangles inseribed in a given circle the square has the maximum area.
Answer:
Let ABCD be a rectangle inscribed in a given circle of centre O and radius r.
Let AB = 2x and BC = 2y,
∴∆ AOAM be a right angled triangle. Then
OA² = AM² + OM²
or, a² = x² + y²



Hence area is maximum when x = y
or, 2x = 2y Thus the rectangle is square.

Question 27.
Verify Lagrange’s mean value theorem when the function f(x) = (x – 1) (x – 2) (x – 3) in the interval [0,4].
Answer:
The given function, f(x) = (x – 1)(x – 2)(x – 3) in interval [0,4]
⇒ f(x) = (x² -x -2x + 2) (x – 3)
⇒ f(x) = (x² – 3x + 2) (x – 3) = x³ – 3x² + 2x – 3x² + 9x – 6
⇒ f(x) = x³ -6x² + 11x – 6
Since f(x) is a polynomial function and polynomial function is continuous, i.e. f(x) is continuous in [0, 4]
Also, f'(x) = 3x² – 2x +11, exists in interval ]0, 4[.
So, f(x) is differentiable in ]0,4[. Thus Lagrange’s theorem are satisfied
∴ c ∈] 0,4 [ exist.

Clearly, the both value of c lie between ] 0, 4 [. Thus theorem is verified.

Question 28.
Find area enclosed by the ellipse \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\)
Answer:
We have, The equation of ellipse

Putting x = 3sinθ ⇒ dx = 3cosθ. Also,
when x = 0, then θ = 0 and when A = 3 then θ = π/2
∴ Required area of the ellipse

Question 29.
Evaluate: \(\int_{0}^{\pi / 2} \log \sin x d x\)
Answer:

Question 30.
Prove that
\(\overrightarrow{[a} \times \vec{b}, \vec{b} \times \vec{c}, \vec{c} \times \vec{a}]=[\vec{a}, \vec{b}, \vec{c}]^{2}\)
Answer:

Question 31.
Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane 2r – 3y + 4z – 6 = 0.
Answer:
Let the co-ordinates of the foot of the perpendicular P from the origin to the plane is P (x₁, y₁, z₁).
Then the direction ratios of the line OP are x₁y₁, z₁.
Now the direction ratio of the plane is 2, – 3, 4. So direction cosines are

Now, since the direction cosines and direction ratios of the line are proportional. Then



Thus the co-ordinates of foot of perpendicular is

Question 32.
Solve the LPP: Minimize Z = – 3x + 4x
under the constraints x + 2y ≤ 8, 3x + 2y ≤ 12, x ≥ 0, y ≥ 0.
Answer:
Minimize Z = -3x + 4. under the costraints
A + 2y ≤ 8 ⇒ x + 2y = 8 …..(1)
3x + 2y ≤ 12 ⇒ 3x + 2y = 12 …(2)
x ≥ 0, y ≥ 0 ⇒ x = 0, y = 0 …(3)

First of all draw the graph of the equations (1) to (3) corresponds to the inequations. It is clear from figure, that (1) and (2) are intersect each other at the point (2,3). So, we get a feasible region OABC, which is bounded. The co-ordinates of the corner points of the feasible region are 0(0, 0) A(4,0), B(2, 3) and C (0, 4). Lastly, applying corner point method to find the value of the objective function Z are as follows :

It is clear from the above table that the minimum value of Z at the point (4,0) is – 12. Thus the minimum value of Z is -12

Question 33.
A furniture dealer deals in only two items tables and chairs. He has Rs. 5000/- to invest and a space to store at most 60 pices. A table costs him Rs. 250 and a chair Rs. 50. He can sell a table at a profit to Rs. 50 and a chair at a profit of Rs. 15. Assuming that he can sell all the items that he buys how should he invest his money in order that he may maximize his profit.
Answer:
Let x and y represents tables and chairs respectively. Now, by question costs of x tables = 250 x and the chair = 50y ∴ Total costs (250x + 50y)
Since the dealer has invest Rs. 5000
∴ 250x + 50v ≤ 5000 =>5y + y ≤ 100
Again, the dealer has a space to store at most 60, so
x + y ≤ 60
Also, non-negative constraints : x ≥ 0, y ≥ 0.
Further, profit from x table = 50.v and y chair = 15y
Objective Function Z = 50x + 15y
So. the mathematical form of the problem are as follows
Maximize Z = 50x + 15y
Subject to constraints 5x + y ≤ 100 ⇒ 5x + y = 100 .. .(1)
v + y ≤ 60 ⇒ x + y = 60 .. .(2)
x ≥ 0, y ≥ 0 ⇒  x = 0, y = 0 …(3)
First of all draw the graph of equations (1) to (3) corresponds to inequations. On joining the points (20, 0),

(0,100) and (60,0), (0,60) we get two straight line, which intersects at the point (10, 50). The point of intersection (10, 50) can be obtained from solving equations (1) and (2). It is clear from figure OABC be the feasible region, which is bounded. Lastly, by the using comer points of feasible region 0(0, 0), A(20,0), B(10,50) and C(0, 60) to find the maximum values of Z :

It is clear from the table that the maximum value of Z is Rs. 1250. Thus the maximum profit to the dealer for buying 10 tables and 50 chairs.

Bihar Board 12th Chemistry Model Papers

Bihar Board 12th Chemistry Model Question Paper 2 in English Medium

Time : 3 Hours 15 Min
Full Marks: 70

Instructions for the candidates

1. Candidates are required to give answers in their own words as far as practicable.
2. Figures in the right hand margin indicates full marks.
3. While answering the questions, candidate should adhere to the words limit as far as practicable.
4. 15 Minutes of extra time has been allotted for the candidates to read the questions carefully.
5. This question paper is divided into two sections : Section -A and Section-B
6. In Section A, there are 35 objective type questions which are compulsory, each carrying 1 mark. Darken the circle with blue/black ball pen against the correct option on OMR Sheet provided to you. Do not use Whitener/Liquid/Blade/ Nail on OMR Sheet otherwise your result will be treated as invalid.
7. In section-B, there are 18 short answer type questions (each carrying 2 marks), out of which only 10 (ten) questions are to be answered Apart from this there are 06 Long Answer type questions (each carrying 5 marks), out of which 3 questions are to be answered.
8. Use of any electronic device is prohibited.

Objective Type Questions

In the following questions no. from 1 to 35, there is only one correct answer against each question. For each question, mark (darken) the correct answer on the OMR Sheet provided to you. (1 x 35 = 35)

Question 1.
Which among the following will show anisotropy ?
(a) Glass
(b) NaBr
(c) Plastic
(d) Rubber
Answer:
(b) NaBr

Question 2.
Study the figure of a solid given below depicting the arrangement of particles. Which is the most appropriate term used for the figure ?

(a) Isotropy
(b) Anisotropy
(c) Irregular
(d) Amorphous nature
Answer:
(b) Anisotropy

Question 3.
Which of the following forms a molecular solid when solidified ?
(a) Calcium fluoride
(b) Silicon dioxide
(c) Carbon dioxide
(d) Sodium chloride
Answer:
(c) Carbon dioxide

Question 4.
Ionic solids conduct electricity in molten state but not in solid state because ……………..
(a) in molten state free ions are furnished which are not free to move
(b) in solid state in solid state ionic are hard, brittle and become soft in molten state
(c) all solids conduct electricity in molten state
(d) in solid state ions are converted to atoms which are insulators.
Answer:
(a) in molten state free ions are furnished which are not free to move

Question 5.
The major binding force in diamond, silicon and quartz is ………………
(a) electrostatic force
(b) electrical attraction
(c) covalent bond force
(d) van der Waals force
Answer:
(c) covalent bond force

Question 6.
Homogeneous mixture of two or more than two components is called …………….
(a) solute
(b) solvent
(c) both (a) and (b)
(d) solution
Answer:
(d) solution

Question 7.
Which of the following is an example of gaseous solution ?
(a) Camphor is nitrogen gas
(b) Solution of hydrogen, in palladium
(c) Chloroform mixed with nitrogen gas .
(d) Both (a) and (c)
Answer:
(d) Both (a) and (c)

Question 8.
In a Daniell cell,
(a) the chemical energy liberated during the redox reaction is converted to electrical energy
(b) the electrical energy of the cell is converted to chemical energy
(c) the energy of the cell is utilised in conduction of the redox reaction
(d) the potential energy of the cell is converted into electrical energy.
Answer:
(a) the chemical energy liberated during the redox reaction is converted to electrical energy

Question 9.
Which of the following is the correct cell representation for the given cell reaction ?
Zn H₂SO₄ → ZnSO₄ + H2
(a) Zn|Zn²⁺||H⁺|H,
(b) Zn |Zn²⁺||H⁺, H,|Pt
(c) Zn |ZnSO₄||H₂SO₄|Zn
(d) Zn|H₂SO₄||ZnSO₄|H₂
Answer:
(b) Zn |Zn²⁺||H⁺, H,|Pt

Question 10.
When a chemical reaction takes place, during the course of the reaction the rate of reaction
(a) keeps on increasing with time
(b) remains constant with time
(c) keeps on decreasing with time
(d) shows irregular trend with time
Answer:
(c) keeps on decreasing with time

Question 11.
For a reaction P + Q → 2R + S. Which of the following statements is incorrect ?
(a) Rate of disappearance of P = Rate of appearance of S
(b) Rate of disappearance of Q = 2 x Rate_of appearance of R
(c) Rate of disappearance of P = Rate of disapearance of Q
(d) Rate of disappearance of Q= -1/2 x Rate of appearance of R
Answer:
(b) Rate of disappearance of Q = 2 x Rate_of appearance of R

Question 12.
After the reaction is over between adsorbed reactants, it is important to create space for the other reactant molecules to approach the surface and react. The process responsible for this is known as ………….
(a) sorption
(b) desorption
(c) physisorption
(d) chemisorption
Answer:
(b) desorption

Question 13.
Powdered substances are more effective adsorbents than their crystalline form because
(a) adsorption is an exothermic process
(b) they become inert and do not react with the adsorbate
(c) the extent of adsorption increases with increase in surface area of the adsorbent
(d) adsorption is more if the size of adsorbent is small
Answer:
(c) the extent of adsorption increases with increase in surface area of the adsorbent

Question 14.
Which of the following example is not correctly matched ?
(a) Two most abudant elements-Fe, AI
(b) Two metals which occur in native state-Au, Pt
(c) Two metals which can occur in combined and native state both-Zn,Fe.
(d) None of these
Answer:
(c) Two metals which can occur in combined and native state both-Zn,Fe.

Question 15.
Which of the following is not the correct name of the formula of the ore given with it ?
(a) MgSO₄.7H₂O – Epsom salt
(b) CuCO₃.Cu(OH)₂ – Malachite
(c) KAlSi₃O_g– Feldspar
(d) MgCl₂.6H₂O – Dolomite
Answer:
(d) MgCl₂.6H₂O – Dolomite

Question 16.
Nitrogen shows different oxidation states ranging from
(a) -3 to +5
(b) -5 to + 5
(c) 0 to -5
(d) -3 to +3
Answer:
(a) -3 to +5

Question 17.
The oxidation state of nitrogen is highest in ……………….
(a) N₃H
(b) NH₃
(c)NH₂OH
(d) N₂H₄
Answer:
(a) N₃H

Question 18.
General electronic configuration of transition metals is ………………….
(a) (n-1)d^1_10ns²
(b) nd^wns²
(c) (n-1)d¹⁰ns²
(d) (n-1)d1⁵ns²
Answer:
(a) (n-1)d^1_10ns²

Question 19.
Which one of the following is a ‘d-block element’ ?
(a)Gd
(b)Hs
(c) Es
(d) Cs
Answer:
(b)Hs

Question 20.
Copper sulphate dissolves in ammonia due to the formation of
(a) Cu₂O
(b) [Cu(NH₃)₄]SO₄
(c) [Cu(NH₃)₄]OH
(d) [Cu(H₂O)₄]SO₄
Answer:
(b) [Cu(NH₃)₄]SO₄

Question 21.
The numberofions given by [Pt(NH₃)₆]Cl₄ inaqueous solution wil be ………………….
(a) two
(b) three
(c) five
(d) eleven
Answer:
(c) five

Question 22.
Which of the following is a primary halide ?
(a) iso-Propyl iodide
(b) sec-Butyl iodide
(c) tert-Butyl bromide
(d) neo-Hexyl   chloride
Answer:
(d) neo-Hexyl   chloride

Question 23.
Which of the following is not an allylic halide ?
(a) 4-Bromopent-2-ene
(b) 3-Bromo-2-methylbut-l-ene
(c) 1-Bromobut-2-ene
(d) 4-Bromobut-1-ene
Answer:
(d) 4-Bromobut-1-ene

Question 24.
C₅H₁₂O is a monohydric alcohol. How many isomers of this alcohol are possible ? How many of these contain chiral centres as well as can exhibit enantiomerism ?
(a) 8 and 3
(b) 6 and 2
(c) 4 and 2
(d) 12 and 4
Answer:
(a) 8 and 3

Question 25.
IUPAC name of

(a) 3-propylbutan-1-o1
(b) 2-ethylpentan-1-o1
(c) 3-methyl hydroxyhexane
(d) 2-ethyl-2-propyl ethanol
Answer:
(b) 2-ethylpentan-1-o1

Question 26.
Which of the following structures is not correctly matched ?

Answer:
(c)

Question 27.
Which of the following carbonyl compounds is most , polar ?

Answer:
(d)

Question 28.
Nitrogen atom of amino group is……
(a) sp
(b)sp²
(c) sp³
(d) sp³d
Answer:
(c) sp³

Question 29.
C₃H₉N cannot represent
(a) 1° amine
(b) 2° amine
(c) 3° amine
(d) quaternary ammonium salt
Answer:
(d) quaternary ammonium salt

Question 30.
The general formula of carbohydrates is……………….
(a) C_nH_2n+10
(b) C_nH_2nO
(c) C_n(H₂O)_n
(d)C_n(H₂O)_2n
Answer:
(c) C_n(H₂O)_n

Question 31.
Which of the following compounds is found abundantly in nature ?
(a) Fructose
(b) Starch
(c) Glucose
(d) Cellulose
Answer:
(d) Cellulose

Question 32.
Glycogen, a naturally occuring polymert stored in animals is a
(a) Monosaccharide
(b) Disaccharide
(c) Trisaccharide
(d) Polysaccharide.
Answer:
(d) Polysaccharide.

Question 33.
Which of the following is a homopolymer ?
(a) Bakelite
(b) Nylon 6, 6
(c) Neoprene
(d) Buna -S
Answer:
(c) Neoprene

Question 34.
The use of chemicals for treatment of disease is called ………………….
(a) chemotherapy
(b) Physiotherapy
(c) angiotherapy
(d) polytherapy.
Answer:
(a) chemotherapy

Question 35.
Which of the following is a criteria to classify drugs ?
(a) Chemical structure
(b) Molecular targets
(c) Drug action
(d) All of these.
Answer:
(d) All of these.

Non-Objective Type Questions

Short Answer Type Questions

In this Section, there are 18 Short answer type questions (each carrying 2 marks), out of which answer any 10 questions.  2 x 10 = 20

Question 1.
How will you distinguish between Lyophobic colloid and Lyophilic colloid ?
Answer:
Lyophobic Colloids:

• They are irreversible in nature
• They are easily precipitated by addition of a small amount of suitable electrolyte.

Lyophilic Colloids :

• They are. reversible in nature.
• They are completely stable and do not easily precipitated.

Question 2.
Calculate the osmotic pressure of 5% solution of urea at 273 K.
Answer:
If the pressure applied on the solution in greater than osmotic pressure then solvent starts passing from solution into solvent. This is called reverse osmosis. The Phenomenon of reverse osmosis is generally used for purification of sea water or hare water.

Question 3.
Write IUPAC names of the following :
(a) K₂[Ni(CN)4]
(b) [CoCl₂(NH₃)₄]CI
Answer:
K₂ [Ni(CN)₄] → Potassium Tetra Cyanonicilet (III)
CoCl₂ (NH₃)₄ Cl → Tetramine Dichloride Cobalt (III) Chloride.

Question 4.
How would you convert
(a) aniline to bromobenzene
(b) ethanal to methanamine ?
Answer:
(a) Aniline to Bromobenzene :

(b) Ethanol to methanamine :

Question 5.
Given reasons for the following :
(a) Formic acid is stronger than acetic acid.
(b) Aniline is less basic than methylamine.
Answer:
(a) Formic acid is stronger than acetic acid – In every acid its acidity depends upon donation of proton from the solution .

If the value of Ka is maximum, the acidity will be max^m-
HCOOH → Ka – 1.77 x 10⁵
CH₃COOH → Ka- 1.75 x 10⁵
So, by the above equations it is clear that formic acid is more acidic than acetic acid.

(b) Aniline is less basic than methylamine -In aniline one pair of electron is present on nitrogen atom which is overlapped with n – electron in the ring. So, nitrogen atom is positively charged or there in lack of electrons due to this it is not in the state that it can give paired electrons to acid, in comparision with methylamine, due to this there in no overlaping. Thus, aniline is a weak base than methylamine.

Question 6.
Account for the following :
(a) The boiling point of ether is much lower than that of alcohol.
(b) Phenol is more acidic than alcohol.
Answer:
(a) The boiling point of other is much lower than that of alcohol-In the case of alcohol hydrogen bond is present between the molecules, whereas in ether there is no hydrogen bond present between their molecules. nDue to this reason, the boiling point of ether is much lower than alcohol.

(b) Phenol is more acidic than alcohol-Phenol is generally a weak acid, but it has acidic property because it gives phenoscide ion in the solution.

In the above reaction the negative charge gives stability to the phenoscide ion.

Question 7.
Write down the half cell reaction and cell reaction for the Daniel cell.
Zn(s) | Zn⁺²(aq) (1M) || Cu⁺²(aq) (1M) | Cu(s)
Answer:
Zn (s) → Zn²⁺ (aq) + Ze (half cell reaction)
Cu⁺⁺ (aq) + 2e^– → Cu (s) (half cell reaction)
———
Zn + Cu⁺⁺ (1M) → Zn⁺⁺ (1M) + Cu (Complete Cell reaction)

Question 8.
Account for the following .
(a) HI is stronger acid than HF
(b) The electron affinity of fluorine is less than that of chlorine.
Answer:
(a) HI is stronger acid than HF – The bond length between HF is very small and since Fluorine is the most electronegative element of the periodic table Due to this reason HF is more electronegative which catches hydrogen strongly. On the other hand, bond-length between HI is very big because T is less electronegative than F. Due to this reason H⁺ ion comes out easily after Alteration.

(b) Since we know that the bond distance increases from I₂ to I₁ So the bond dissociation enthalpy should decrease, because of the increase in size of atom as we move from F to The F-F bond dissociation enthalpy is smaller than that of Cl-Cl and smaller than that of Br-Br. This is due to the reaseon than that of the F atom in very small and the there lone pairs of electrons on each f-atom repel the bond pair holding the F- atoms F₂ molecule. I₂< F₂< Br₂ < Cl₂

Question 9.
Give definitions of the following with examples :
(a) Calcination
(b) Roasting
Answer:
(a) Calcination → The process of heating a metal- rich arc to a high temperature to convert the metal into its oxide either in absence or insufficient supply of air is called calcination.
eq: Al₂ O₃ . 2H₂O → Al₂ O₃ + 2H₂O
2 Al (OH)₃ → Al₂ O₃ + 3 H₂O

(b) Roasting →The process of heating a finely ground arc to a high temperature in excess of air in called roasting.
Roasting converts the metal present in the ore to its oxide.
4FeS₂ -110₂ → 2Fe₂d₃ +8SO₂
2Cu₂S + 3O₂ → 2Cu₂O + 2SO₂

Question 10.
Complete the following reactions :
(a) CHCl₃ + ale. KOH + C₆H₅NH₂ →
(b) CH₃CH₂OH + I₂ + NaOH →
Answer:
(a) CHCl₃ + KOH+C₆H₅NH₂ → C₆H₅NC+3KCl+3H₂0.
(b) CH₃CH₃OH + 41₂ + NaOH → CHI₃ + NCOONa + 5Hl.

Question 11.
Differentiate between adsorption and absorption.
Answer:
Adsorption :

• In this phenomenon, the concentration on the surface of adsorbent is different from that in the bulk.
• It occurs only at the surface of adsorpent.

Absortion :

• In this phenomenon, the concentration is same through out the material.
• It occurs throughtout the body of the material.

Question 12.
What is the difference between Schottky defect’ and ‘Frenkel defect’ ?
Answer:
The difference between ‘Schottky defect’ and ‘Frenkel defect’ is stated below
Schottky defect :

• This type of defect is created when one positive ion and one negative ion are missing from their respective positions, leaving behind a pair of holes
• Maximum no. of Schottky defects in crystal minimizes the density
  Ex-NaCl, kCl, CsC12KBr

Frenkel defect:

•  This type defect is created when an ion leaves its correct lattice site & occupies an intersitial site.
• It does not give any charge in density. eg-Zns, AgCl, AgBr and Agl M

Question 13.
When 10 gm of a non-volatile solute is dissolved in 100 gm of benzene, its boiling point is raised by 1°. What is the molecular mass of the solute ? (K₄ for benzene – 2-53 Km^-1)
Answer:
Mass of solution (M_B) = 100 g
Mass of solution (M_A) = 100 g .
Mass of solution (N_A) = 100 g
Raise in B.P. = AT_b = 1°
Molecular mass of soluted (M_B) = ?
Benzene (solution) K_h = 253 km^-1 .
∵ ΔT_b = K_h-m = 253 x \(\frac{10}{m_{B} \times 100} \times 1000\)
m_B = 253g

Question 14.
Define the following terms :
(a) Order of reaction
(b) Threshold energy.
Answer:
Define the following terms
(a) Order of reaction – It is. an important parameter for every chemical reaction, which refers to the number of reacting particles.
Order of reaction – It is defined ass the sum of powers or exponents to which the concentration terms are raised in the rate law expression.
e.g. αA + bB → Products
Rate = K[A]^m[B]^m then, order of reaction is = (m + n)

(b) Threshold energy—The minimum amount of energy which the colliding particles must possess in order to bring about chemical reaction is called thresholod energy.

Question 15.
Define electrochemical equivalent.
Answer:
Faraday’s 1st law of electrolysis – This law states that the mass of a substance produced at an electrode is directly proportional to the quantity of electricity passed.
m α Q  where,
m α I x t Q → quantity of elecricity.
m =Z x I x t
I → current in amperes.
t → time
Z → Electrochemical equivalent
Electrochemical – The amount of substance liberated at the electrode, when current of one ampere is passed through the electrolyte for one second.

Question 16.
If in a chemical reaction A+B product, rate law is given by R = K [A]^1/2 [ B ]^3/2, find the order of reaction.
Answer:
A + B → production
\(\frac{d n}{d t}=R=K[A]^{1 / 2}[B]^{3 / 2}\)
So, order of reaction \(=\frac{1}{2}+\frac{3}{2}=\frac{4}{2}=2\)

Question 17.
What is Tyndall effect ? Discuss.
Answer:
When a beam of light is passed through a colloidal solution, the beam is illuminated, such phenomena is not observed in true solution. Tyndall effect is observed when a beam of sunlight enter a earth room. Illuminating dust particles in beam scatter light.

Question 18.
Give the name of two copper ores.
Answer:

• CuFe S₂
• Cu₂ O

Long Answer Type Questions

There are 06 long answer type questions (each carrying 05 marks), out of which answer any there questions.             (5 x 3 = 15)

Question 19.
(a) A first order reaction is 75% completed in 60 min. Find the half-life period of the reaction.
(b) Given one example each of zero order and first order reactions.
Answer:
(a) We know that half life period \(t_{1 / 2}=\frac{0.693}{K}\)
Also, the first order expression is 2.303

Now, by putting the values of K in above equation.

(b) Examples of Zero-order reaction

Question 20.
Describe the general characteristics of transition elements with special reference to the following :
(i) Formation of colour salt
(ii) Variable oxidation state.
Answer:
(i) Formation of clour salt- Majority of transition metal compounds and cloured both in solid state as well as in aqeous solution. This is contrast to the compounds of respective (s and p-block) elements wich are usually colourless.

In a transition metal atom or oil, all the five d-orbits have the same energy i. e. these are degenerate orbitals. However three out of these (dxy, dyz, dzx) orbitals differ in shape from the other two (dx²y¹dz²). When ligands both neutral or anionic approach these, species, the orbital no longer degenerate, and split into two sets of orbitals. This is called crytal field splitting one set with lower energy has three orbitals (dxy, d, dzx), where as the other set with slightly higher energy has two orbitals (dx²y², dz²).

This, Promotion of one more electrons from a set of lower energy orbitals to a set of higher energy orbitals with in the same subshell is possible in case of transition elements with partly filled (n – 1) d-subshell. Since these two sets of d-orbital belonging to the same subshell. Have slightly different energy, the energy required to promote one or more electrons is small. Radiations of light corresponding to such a small amount of energy are available with it in the visible region of the spectrum.

Thus, when white light falls on such a transition element, some radiation corresponding to certain colour are absorbed and one are more electrons are raised from lower energy set of orbitals to higher energy set of orbitals. With the abosorption or radiations corresponding to specific colour from the white light a colour known as the complementary colour is observed or is transmitted. It may be noted the transmitted colour depends upon the colour which is observed for the electronic transition.

(ii) The oxoanions of metals have co-valent mature in which oxygen is involved in the multiple bonding with the metal atom. This is responsible for the high oxidation state of the metal in oxoamine. For example-The elements Mn exibibits +7 oxidation state in permaganate ion (MnO₄^_)

Question 21.
Write IUPAC names of the following :
(i) CH₃CONH₂
(ii) (CH₃)₂CHCH₂COCl
(iii) CH₃ – O – C₂H₅
(iv) Ch₃CH₂CN

Answer:
(i) CH₃ CONH₂ → Ethanamide
(ii) (CH₃)₂ CHCH₂ CoCl -3-Methyl butanoil Chloride.
(iii) CH₃ – O – C₂H₅ – Methoxy ethane.
(iv) CH₃CH₂CN — Ethyl isocyanide

Question 22.
What is polymerisation ? Define the terms addition polymerisation and condensation polymerisation. Give one example of each.
Answer:
Polymerisation-Polymerization is a Process of reacting monomer molecules together in a chemical reaction to form polymer chains or three dimensional networks. Polymerisation occurs via a variety of reaction mechanisms that vary in colexity due to functional groups presnt in reacting compounds and their inherent steric effects.

There are following two types of polarization.

• Additional Polymerization
• Condensation Polymerization.
• Additional Polymerization-It is formed by the repeated addition of a large number of same or different monomers processing double and triple bonds.

(b) Condensation Polymerization- Condensation Polymers are formed by repeated condensation reaction between two bifunctional or trifunctional monomer units usually with the elimination of small molecules like water, alcohol, ammonia, Carbondioxide, hydrogen chloride, etc. and process by which condensation Polymers are formed is called condensation polymerization.

Question 23.
A element A (atomic mass = 100) having 100 structure has unit cell edge length of 400 pm. Calculate the density of A and number of unit cells in 10 cm of A.
Answer:
a (edge length) = 400 pm
N_a = 6.02 x 10²³
M = 100 gm / mole.

Question 24.
Write the following giving chemical equations :
(i) Carbylamine reaction
(ii) Wurtz reaction.
(iii) Nitration of benzene
Answer:
(i) Carbylamine reaction – Chloroform when heated with primary amine in presence of alcoholic KOH. forms a derivative called isocyanide.

(ii) Wurtz reaction – When two moles of alkyl halide is heated with Na in the presence of ether goes higher alkane.

(iii) In the presence of concentration H₂SO₄ benzenes reacts with cone HNO₃ and it is found into benzene.

Bihar Board 12th Maths Model Papers

Bihar Board 12th Maths Model Question Paper 5 in English Medium

Section – I

Time : 3 Hours 15 Min
Full Marks: 100

Instructions for the candidates

1. Candidates are required to give their answers in their own words as far as practicable.
2. Figure in the right-hand margin indicates full marks.
3. While answering the questions, the candidate should adhere to the word limit as far as practicable.
4. 15 Minutes of extra time has been allotted for the candidate to read the questions carefully.
5. This question paper is divided into two sections. Section-A and Section-B.
6. In Section A, there are 1-50 objective type questions which are compulsory, each carrying 1 mark. Darken the circle with blue/black ball pen against the correct option on the OMR Sheet provided to you. Do not use Whitener/Liquid/ Blade/Nail on OMR Sheet otherwise result will be invalid.
7. In section-B, there are 25 short answer type questions (each carrying 2 marks), out of which only 15 (fifteen) questions are to be answered. A part from this there is 08 Long Answer Type questions (each carrying 5 marks), out of which 4 questions are to be answered.
8. Use of any electronic device is prohibited.

Objective Type Questions

There are 1 to 50 objective type questions with 4 options, choose the correct option which, is to be answered on OMR Sheet. (50 × 1 = 50)

Question 1.
If the function f : N → N defined as f(x) = 4x + 3, then f^-1(x) = _________
(a) 4x – 3
(b) \(\frac{4 x-3}{2}\)
(c) \(\frac{x+3}{2}\)
(d) \(\frac{x-3}{4}\)
Answer:
(d) \(\frac{x-3}{4}\)

Question 2.
The set natural numbers defined, as the relation less than is
(a) only reflexive
(b) only symmetric
(c) equivalence
(d) only transitive
Answer:
(d) only transitive

Question 3.
The operation * defined as a* b such that a² + b² then (1*2) *5 is
(a) 3125
(b) 625
(c) 125
(d) 50
Answer:
(d) 50

Question 4.
If the function f : R → R defined as f(x) = \(\left(3-x^{3}\right)^{1 / 3}\) then fof(x) is
(a) \(x^{1 / 3}\)
(b) x³
(c) (3 – x³)
(d) x
Answer:
(d) x

Question 5.
\(\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)=\) = _______
(a) \(\frac{2 \pi}{3}\)
(b) \(\frac{\pi}{6}\)
(c) \(\frac{4 \pi}{3}\)
(d) \(\frac{\pi}{3}\)
Answer:
(d) \(\frac{\pi}{3}\)

Question 6.
tan^-1 √3 – cot^-1(-√3) = _______
(a) π
(b) 0
(c) 2√3
(d) \(-\frac{\pi}{2}\)
Answer:
(d) \(-\frac{\pi}{2}\)

Question 7.
\(\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)\) is equal to
(a) \(\frac{7 \pi}{6}\)
(b) \(\frac{5 \pi}{6}\)
(c) \(\frac{\pi}{3}\)
(d) \(\frac{\pi}{6}\)
Answer:
(b) \(\frac{5 \pi}{6}\)

Question 8.
A matrix A = [a_ij]_n×n is symmetric if
(a) a_ij = 0
(b) a_ij = -a_ji
(c) a_ij = a_ji
(d) a_ij = 1
Answer:
(c) a_ij = a_ji

Question 9.
\(\int { \frac { { sec }^{ 2 }x }{ { cosec }^{ 2 }x } } dx\quad =\) ___________
(a) x – tan x + c
(b) tan x + x + c
(c) tan x – x + c
(d) -tan x – x + c
Answer:
(c) tan x – x + c

Question 10.
\(\int \frac{\cos 2 x}{(\sin x+\cos x)^{2}} d x=\) _______
(a) \(\frac{1}{\sin x+\cos x}+c\)
(b) log (sinx + cosx) + c
(c) log |sinx – cosx| + c
(d) \(\frac{1}{(\sin x+\cos x)^{2}}+c\)
Answer:
(b) log (sinx + cosx) + c

Question 11.
q11
(a) \(\frac{-y}{x}\)
(b) \(\frac{y}{x}\)
(c) \(\frac{-x}{y}\)
(d) \(\frac{x}{y}\)
Answer:
(a) \(\frac{-y}{x}\)

Question 12.
If √x + √y = 5 then \(\frac{d y}{d x}\) = ? at (4, 9).
(a) \(\frac{2}{3}\)
(b) \(\frac{3}{2}\)
(c) \(\frac{-3}{2}\)
(d) \(\frac{-3}{3}\)
Answer:
(b) \(\frac{3}{2}\)

Question 13.
\(\int \tan ^{2} \frac{x}{2} d x=\) __________
(a) \(\tan \frac{x}{2}-x+c\)
(b) \(\tan \frac{x}{2}+x+c\)
(c) \(2 \tan \frac{x}{2}+x+c\)
(d) \(2 \tan \frac{x}{2}-x+c\)
Answer:
(a) \(\tan \frac{x}{2}-x+c\)

Question 14.
qim 14
(a) \(\frac{\pi}{4}\)
(b) \(-\frac{\pi}{4}\)
(c) 0
(d) \(\frac{\pi}{2}\)
Answer:
(a) \(\frac{\pi}{4}\)

Question 15.
Let A be a square matrix of order 3 × 3 then |KA| is equal to.
(a) K|A|
(b) K² |A|
(c) K³ |A|
(d) 3K|A|
Answer:
(c) K³ |A|

Question 16.
If \(A=\left|\begin{array}{lll}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
a_{31} & a_{33} & a_{33}
\end{array}\right|\) and cofactor of a_ij is A_ij then which of following is the value of Δ
(a) a₁₁ A₃₁ + a₁₂ A₃₂ + a₁₃ A₃₃
(b) a₁₁ A₁₁ + a₁₂ A₂₁ + A₁₃ A₃₁
(c) a₂₁ A₁₁ + a₂₂ A₂₂ + a₂₃ A₁₃
(d) a₁₁ A₁₁ + a₂₁ A₂₁ + a₃₁ A₃₁
Answer:
(d) a₁₁ A₁₁ + a₂₁ A₂₁ + a₃₁ A₃₁

Question 17.

(a) Continuous
(b) Discontinuous
(c) Well defined
(d) None of these
Answer:
(b) Discontinuous

Question 18.
If y = log (log x) then the value of \(\frac{d y}{d x}\) is:
(a) x log x
(b) \(\frac{1}{x \log x}\)
(c) \(\frac{1}{\log x}\)
(d) \(\frac{1}{x}\)
Answer:
(b) \(\frac{1}{x \log x}\)

Question 19.
If y = sec (tan^-1 x) Then \(\frac{d y}{d x}\) is equl to
(a) \(\frac{x}{\sqrt{1+x^{2}}}\)
(b) \(\frac{-x}{\sqrt{1+x^{2}}}\)
(c) \(\frac{x}{\sqrt{1-x^{2}}}\)
(d) None of these
Answer:
(a) \(\frac{x}{\sqrt{1+x^{2}}}\)

Question 20.
If f(x) = sin(x²) Then \(\frac{d f}{d x}\) is equal to
(a) 2x sin x²
(b) 2x cos x²
(c) 2cos x
(d) 2x sin x
Answer:
(b) 2x cos x²

Question 21.
The rate of change of the area of the circle with respect to r = 7 cm is
(a) 42 cm²/cm
(b) 44 cm²/cm
(c) 28 cm²/cm
(d) 22 cm²/cm
Answer:
(b) 44 cm²/cm

Question 22.
The function f(x) = x³ – 6x² + 12x – 18 is:
(a) Strictly decreases for each x ∈ R
(b) Strictly increasing ∀ x ∈ R
(c) Increasing in ] -∞, 0 [ and decreasing in [0, ∞[
(d) None of these
Answer:
(b) Strictly increasing ∀ x ∈ R

Question 23.
The total revenue in Rupees received from the sale of x units of a product is given by R (x) = 3x² + 36x + 5. The marginal revenue, when x = 15 is:
(a) Rs. 116
(b) Rs. 96
(c) Rs. 90
(d) Rs. 126
Answer:
(d) Rs. 126

Question 24.
What is the slope of the tangent to the curve y = x³ – x + 1 at the point whose x-coordinate is 2?
(a) 11
(b) 21
(c) 31
(d) 41
Answer:
(a) 11

Question 25.
\(\int \frac{10 x^{9}+10^{x} \log e^{10}}{x^{10}+10^{x}}\) is equal to
(a) 10^x – x¹⁰ + C
(b) 10^x + x¹⁰ + C
(c) (10^x – x¹⁰)^-1 + C
(d) log (10^x + x¹⁰) + C
Answer:
(d) log (10^x + x¹⁰) + C

Question 26.

Answer:
(b) \(\log \left|\frac{(x-2)^{2}}{x-1}\right|+C\)

Question 27.

(a) 2
(b) \(\frac{3}{4}\)
(c) 0
(d) -2
Answer:
(c) 0

Question 28.
If f(a + b – x) = f(x) then \(\int_{a}^{b} x f(x) d x\) is equal to

Answer:
(d) \(\frac{a+b}{2} \int_{a}^{b} f(x) d x\)

Question 29.
Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0, and x = 2 is:
(a) π
(b) \(\frac{\pi}{2}\)
(c) \(\frac{\pi}{3}\)
(d) \(\frac{\pi}{4}\)
Answer:
(a) π

Question 30.
The value of \(\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x\) is equal to
(a) tan x + cot x + C
(b) tan x + cosec x + C
(c) -tan x + cot x + C
(d) tan x + sec x + C
Answer:
(a) tan x + cot x + C

Question 31.
The value of \(\int_{0}^{\pi / 2} \cos 2 x d x\) is:
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(a) 0

Question 32.
The degree of diff. eqn.

(a) 3
(b) 2
(c) 1
(d) None of these
Answer:
(d) None of these

Question 33.
The degree and order of the differential equation

(a) 4, 2
(b) 2, 4
(c) 3, 4
(d) 4, 3
Answer:
(b) 2, 4

Question 34.
The general solution of diff. eqn \(\frac{y d x-x d y}{y}=0\) is:
(a) xy = c
(b) x = cy²
(c) y = cx
(d) y = cx²
Answer:
(c) y = cx

Question 35.
The number of arbitrary constant in the solution of diff. eqn of fourth-order is
(a) 0
(b) 2
(c) 3
(d) 4
Answer:
(d) 4

Question 36.
The general solution of diff. eqn \(\frac{d y}{d x}=e^{x+y}\) is
(a) e^x + e^y = c
(b) e^x + e^-y = c
(c) e^-x + e^y = c
(d) e^-x + e^-y = c
Answer:
(b) e^x + e^-y = c

Question 37.
Let the vectors \(\vec{a}\) and \(\vec{b}\) be such that \(|\vec{a}|=3\) and \(|\vec{b}|=\frac{\sqrt{2}}{3}\), then \(\vec{a} \times \vec{b}\) is a unit vector if the angle between \(\vec{a}\) and \(\vec{b}\) is
(a) \(\frac{\pi}{6}\)
(b) \(\frac{\pi}{4}\)
(c) \(\frac{\pi}{3}\)
(d) \(\frac{\pi}{2}\)
Answer:
(b) \(\frac{\pi}{4}\)

Question 38.
If \(\vec{a}=2 \hat{j}-5 \hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}+2 \hat{j}-\hat{k}\) Then
(a) \(\vec{a} \cdot \vec{b}=0\)
(b) \(\vec{a} \cdot \vec{b} \neq 0\)
(c) \(\vec{a} \cdot \vec{b}=-9\)
(d) \(\vec{a}+\vec{b}\)
Answer:
(c) \(\vec{a} \cdot \vec{b}=-9\)

Question 39.
l² + m² + n² is equal to
(a) 0
(b) 1
(c) -1
(d) None of these
Answer:
(b) 1

Question 40.
The Dr’s of any line is 2, -1, -2 then dc’s is:
q40
Answer:
(a) \(\frac{1}{3}, \frac{2}{3},-\frac{2}{3}\)

Question 41.
The direction ratios of the line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is:
(a) 3, 2, 7
(b) 3, 7, 2
(c) 2, 3, 7
(d) 7, 3, 2
Answer:
(b) 3, 7, 2

Question 42.
The lines with dr’s a₁, b₁, c₁ and a₂, b₂, c₂ are parallel if
(a) a₁a₂ – b₁b₂ – c₁c₂ = 0
(b) a₁a₂ + b₁b₂ + c₁c₂ = 0
(c) a₁b₁ + a₂b₂ + a₁b₂ = 0
(d) \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)
Answer:
(d) \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)

Question 43.
The angle between the two lines with direction cosines are l₁, m₁, n₁ and l₂, m₂, n₂ is θ. Then θ is equal to
(a) l₁l₂ + m₁m₂ + n₁n₂
(b) l₁l₂ – m₁m₂ – n₁n₂
(c) l₁m₁n₁ + l₂m₂n₂
(d) None of these
Answer:
(a) l₁l₂ + m₁m₂ + n₁n₂

Question 44.
Which of the following equations correponds to inequations ax + by ≥ c, ax + by > c, ax + by ≤ c and ax + by < c is:
(a) ax + by = c
(b) ax + by = 0
(c) bx + ay = c
(d) None of these
Answer:
(a) ax + by = c

Question 45.
Which of the following is non-negative constraints
(a) x ≤ 0, y ≤ 0
(b) x ≤ 0, y ≥ 0
(c) x ≥ 0, y ≥ 0
(d) None of these
Answer:
(c) x ≥ 0, y ≥ 0

Question 46.
If P(A) = \(\frac{3}{8}\), P(B) = \(\frac{1}{2}\), P(A∩B) = \(\frac{1}{4}\), then P(A/B) = _______
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{2}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{3}{8}\)
Answer:
(b) \(\frac{1}{2}\)

Question 47.
If A and B are two independent events then
(a) P(AB’) = P(A) P(B)
(b) P(AB’) = P(A) P(B’)
(c) P(AB’) = P(A’) + P(B)
(d) P(AB’) = P(A) + P(B’)
Answer:
(b) P(AB’) = P(A) P(B’)

Question 48.
If A and B are two envents such that P (A) = \(\frac{1}{3}\), P(B) = \(\frac{1}{4}\), P (A∩B) = \(\frac{1}{5}\) thenP(A/B) is:
(a) \(\frac{1}{5}\)
(b) \(\frac{2}{5}\)
(c) \(\frac{3}{5}\)
(d) \(\frac{4}{5}\)
Answer:
(d) \(\frac{4}{5}\)

Question 49.
If P(A) = \(\frac{3}{8}\), P(B) = \(\frac{5}{8}\) and P(A∪B) = \(\frac{3}{4}\), then P(B/A) is:
(a) \(\frac{1}{4}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{1}{2}\)
Answer:
(c) \(\frac{2}{3}\)

Question 50.
If A and B are two events such that P(A) + P(B) – P(A and B) = P(A) then
(a) \(P\left(\frac{B}{A}\right)=1\)
(b) \(P\left(\frac{B}{A}\right)=0\)
(c) \(P\left(\frac{A}{B}\right)=1\)
(d) \(P\left(\frac{A}{B}\right)=0\)
Answer:
(c) \(P\left(\frac{A}{B}\right)=1\)

Section – II

Time : 2 Hours 5 Minutes
Total Marks: 50

Non-Objective Type Questions

Short Answer Type Questions

Q. No. 1 to 25 are of Short Answer type carry of 2 marks each. Answer any 15 questions. (15 × 2 = 30)

Question 1.
If \(A=\left[\begin{array}{rr}
-1 & 2 \\
3 & 4
\end{array}\right]\) and \(B=\left[\begin{array}{ll}
3 & -2 \\
1 & 4
\end{array}\right]\) suchthat 2A + B + X = 0, then find X.
Solution:
Given, 2A + B + X = 0 ⇒ X = -(2A + B)

Question 2.
Consider f : R → R given by f(x) = 4x + 3. show that f is invertible. Find the inverse of f also.
Solution:
Given f: R → R and f(x) = 4x + 3
f(x₁) = f(x₂)
or, 4x₁ + 3 = 4x₂ + 3
or, x₁ = x₂
f is one-one
Again, let y = 4x + 3
\(x=\frac{y-3}{4}\)
Each element in co-domain of y is a image of any one element in domain.
f is onto
since f is one-one and onto then f is invertible
Hence \(f^{-1}(x)=g(y)=\frac{y-3}{4}\)

Question 3.
Prove that

Solution:

Question 4.
For what value of x is:
\(\left[\begin{array}{lllll}
1 & 2 & 1
\end{array}\right]\left[\begin{array}{lll}
1 & 2 & 0 \\
2 & 0 & 1 \\
1 & 0 & 2
\end{array}\right]\left[\begin{array}{l}
0 \\
2 \\
x
\end{array}\right]=0\)
Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.

Answer:

Question 8.
If x = a(θ + sinθ), y = a(1 – cosθ), then find \(\frac{d y}{d x}\)
Answer:

Question 9.
Find the point at which the tangent to the curve \(y=\sqrt{4 x-3}-1\) has its slope \(\frac{2}{3}\)
Solution:
Given curve \(y=\sqrt{4 x-3}-1\)
Differentiating both sides w.r.t. x, we get

Question 10.
If A = tan^-1 2, and B = tan^-1 3 then prove that C = \(\frac{\pi}{4}\)
Solution:
Let A = tan^-1 2 = tan A = 2 and B = tan^-1 3 ⇒ tan B = 3

Question 11.
Using differential, find the approximate value of √25.3 up to three places of decimal.
Solution:
Let y = √x

Question 12.
Find the integral \(\frac{e^{\tan -1} x}{1+x^{2}}\)
Solution:

Question 13.
Integrate: \(\int \tan ^{4} x d x\)
Solution:

Question 14.
Evaluate: \(\int_{0}^{1} \frac{e^{x}}{1+e^{x}} d x\)
Solution:

Question 15.
Find the area enclosed by the circle x² + y² = a²
Solution:
x² + y² = a²
⇒ y² = a² – x²
⇒ y = \(\sqrt{a^{2}-x^{2}}\)
Area enclosed by the circle = 4 × (Given curve, A-axis and ordinates x = 0, x = a)

Hence the area of a circle is πa² sq. units

Question 16.
Solve: y dx – x dy = xy dx
Solution:
y dx – x dy = xy dx
⇒ x dy = y (1 – x) dx

Question 17.
Solve: \(\frac{x d y}{d x}-y=x^{2}\)
Solution:

Question 18.
Find the value of λ, which the planes \(\vec{r} \cdot(\hat{i}+2 \hat{j}+3 \hat{k})=13\) and \(\vec{r} \cdot(\lambda \hat{i}+2 \hat{j}-7 \hat{k})=9\) perpendiular to each other.
Solution:

Question 19.
Find the area of the parallelogram whose adjacent sides are \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathbf{b}}=3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\)
Solution:

Question 20.
Find the internally intercepts of the plane 2x + y – z = 5
Solution:
Given plane 2x + y – z = 5

Hence the intercepts of the plane are \(\frac{5}{2}\), 5 and -5 respectively

Question 21.
Find the shortest distance between the lines

Solution:
Let PQ be the distance between the lines AB and CD.
If direction cosines of PQ is l, m, n. then 3l – m + n = 0 and -3l + 2m + 4n,
Now, 3l – m + n = 0

Again, the coordinates of the point R and S on. the lines AB and CD are R(3, 8, -3) and (-3, -7, 6)
Now, PQ = Projection of RS

Question 22.
The probabilities of solving a problem by three students are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\); find the probability that the problem will be solved.
Solution:
Let A, B and C are the events for solving the problem by 1st, 2nd and 3rd students.

Question 23.

Solution:

Question 24.
Find the value of x, y and z if \(\left[\begin{array}{cc}
x+y & 2 \\
5+z & x y
\end{array}\right]=\left[\begin{array}{ll}
6 & 2 \\
5 & 8
\end{array}\right]\)
Solution:
Given, \(\left[\begin{array}{cc}
x+y & 2 \\
5+z & x y
\end{array}\right]=\left[\begin{array}{ll}
6 & 2 \\
5 & 8
\end{array}\right]\)
x + y = 6, 5 + z = 5, xy = 8
⇒ y = 6 – x
⇒ xy = x(6 – x) = 8
⇒ 6x – x² = 8
⇒ x² – 6x + 8 = 0
⇒ x² – 4x – 2x + 8 = 0
⇒ (x – 4) (x – 2) = 0
⇒ x – 4 = 0 or x – 2 = 0
⇒ x = 2, 4
y = 4, 2 and z = 0
Thus x = 2, 4, y = 4, 2, and z = 0

Question 25.
Prove that

Solution:

Long Answer Type Questions

Questions No. 26 to 33 are Long Answer Type Questions. Each question carries 5 marks. Answer any 4 questions. (4 × 5 = 20)

Question 26.
A rectangular sheet of 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is maximum.
Solution:
Let each side of the square cut-off from each comer be x cm.
Sides of the rectangular box are (45 – 2x), (24 – 2x) and x cm.
Then volume of the box.
V = (45 – 2x) (24 – 2x) (x) = 2x (45 – 2x) (12 – x) = 2 (2x³ – 69x² + 540x)
\(\frac{d V}{d x}\) = 2(6x² – 138x + 540) = 12(x² – 23x + 90)
For max. and min. value. \(\frac{d V}{d x}\) = 0
or 12(x² – 23x + 90) = 0

or, (x – 5) (x – 18) = 0
But x is not greater than 12.
x = 5
\(\frac{d^{2} V}{d x^{2}}\) = 12(2x – 23) = 12(10 – 23) = -156 = -ve [∵ x = 5]
Hence V is maximum at x = 5 i.e. square of sides 5 cm is cut off from.

Question 27.
Find the absolute maximum and minimum values of functions f given by f(x) = 2x³ – 15x² + 36x + 1 at [1, 5]
Solution:
f(x) = 2x³ – 5x² + 36x + 1
⇒ f'(x) = 6x² – 30x + 36
⇒ f(x) = 6(x² – 5x + 6) = 6(x – 3)(x – 2)
If f'(x) = 0 then x = 2, x = 3
Now, evaluate the value off at interval [1, 5] i.e. x = 1, x = 2 and x = 3
f(x) = 2x³ – 15x² + 36x + 1
⇒ f(1) = 2 – 15 + 36 + 1 = 39 – 15 = 24
⇒ f(2) = 2 × 2³ – 15 × 2² + 36 × 2 + 1 = 16 – 60 + 72 + 1 = 80 – 60 = 29
⇒ f(3) = 2 × 3³ – 15 × 3² + 36 × 3 + 1 = 54 – 135 + 108 + 1 = 163 – 135 = 28
⇒ f(5) = 2 × 5³ – 15 × 5² + 36 × 5 + 1 = 250 – 375 + 180 + 1 = 56
Thus the absolute maximum value of f on [1, 5] is 56 at x = 5 and minimum is 24 at x = 1

Question 28.
Find the area of the curve bounded by x² = 4y and the line x = 4y – 2.
Solution:
Given curve x² = 4y …(1 )
Which is an upward parabola with vertex (0, 0) and is symmetrical about y-axis and equation of the line.
x = 4y – 2 …(2)
Solving (1) and (2), we get,
(4y – 2)² = 4y
⇒ 16y² – 16y + 4 = 4y
⇒ 16y² – 20y + 4 = 0
⇒ 4y² – 5y + 1 = 0
⇒ (4y – 1) (y – 1) = 0
⇒ y = \(\frac{1}{4}\), 1
From(2), when y = \(\frac{1}{4}\), then x = 1 – 2 = -1
and when y = 1, then x = 4 – 2 = 2
The intersection of (1) and (2) is A(-1, \(\frac{1}{4}\)) and B (2, 1)
Clear from figure, shaded, region. OBDA be the required area.
Required Area = Area of region LOMBDA – Area of region LMBOA …(3)

Question 29.
Evaluate: \(\int_{0}^{\pi / 2}(\sqrt{\tan x}+\sqrt{\cot x}) d x\)
Solution:

Question 30.
The two adjacent sides of parallelogram are \(\mathbf{2} \hat{\mathbf{i}}-\mathbf{4} \hat{\mathbf{j}}+\mathbf{5} \hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}-\mathbf{3} \hat{\mathbf{k}}\). Find the unit vector parallel to its diagonal. Also find its area.
Solution:
Let the adjacent sides of a prallelogram are

Question 31.
Find the image of the point (1, 6, 3) in the line \(\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}\)
Solution:
Let P (1, 6, 3) be any point and AB be the given line.
Draw perpendicular PM from P to AB such that PM = P’M, where P’ be the image of P.

Question 32.
Minimize Z = 200x + 500y subject to constraints; x + 2y ≥ 10, 3x + 4y ≤ 24, x ≥ 0, y ≥ 0.
Solution:
Minimize Z = 200x + 500y
x + 2y ≥ 10 ⇒ x + 2y = 10 ……. (1)
3x + 4y ≤ 24 ⇒ 3x + 4y = 24 …….. (2)
x ≥ 0, y ≥ 0 ⇒ x = 0, y = 0 ……… (3)
First of all draw the graph of the equations (1) to (3) corrsponds to inequations.

On joining the points (10, 0), (0, 5) and (8, 0), (0, 6) we get two mutually lines which intersects at the point (4, 3). It is clear from figure shaded region ABC is feasible and bounded. The coordinates of the feasible region ABC are A (4, 3), B(0, 6) and C(0, 5)
Lastly, applying corner point method to find, the minimum value of objective function as follows.
Corner point – Z = 200x + 500y
(0, 5) ⇒ Z = 0 + 5000 × 5 = 2500
(4, 3) ⇒ Z = 200 × 4 + 500 × 3 = 2300
(0, 6) ⇒ Z = 200 × 0 + 500 × 6 = 3000
We see from the above table that the minimum value of Z is 2300 at the point (4, 3).
Thus minimum value of Z is 2300.

Question 33.
Solve the following LPP problem graphically: Maximize Z = 4x + y subject to constraints: x + y ≤ 50, 3x + y ≤ 90, x ≥ 0, y ≥ 0.
Solution:
Maximize Z = 4x + y
Subject to constraints: x + y ≤ 50 ⇒ x + y = 50 …… (1)
3x + y ≤ 90 ⇒ 3x + y = 90 …… (2)
x ≥ 0, y ≥ 0 ⇒ x = 0, y = 0 ….. (3)
First of all draw the graph of the equations (1) to (3) corresponds to inequations. It is clear from the figure shaded region OABC. be the feasible region and is bounded. The co-ordinate of the point B obtain by solving equation (1) and (2).

It is clear from figure the co-ordinates of the comer points of the feasible region OABC are O(0, 0), A (30, 0), B (20, 30) and C(0, 50).
Lastly applying corner point method to find the maximum value of Z as follows:
Corner point – z = 4x + y
O(0, 5) ⇒ z = 4 × 0 + y
A(30, 3) ⇒ z = 4 × 0 + 0 = 0
B(20, 30) ⇒ z = 4 × 30 + 0 = 120
C(0, 50) ⇒ z = 4 × 20 + 30 = 110
We see from table that the maximum value of Z is 120 at the point A(30, 0).
Thus maximum value of Z is 120.

Bihar Board 12th Chemistry Model Papers

Bihar Board 12th Chemistry Model Question Paper 5 in English Medium

Time : 3 Hours 15 Min
Full Marks: 70

Instructions for the candidates

1. Candidates are required to give answers in their own words as far as practicable.
2. Figures in the right hand margin indicates full marks.
3. While answering the questions, candidate should adhere to the words limit as far as practicable.
4. 15 Minutes of extra time has been allotted for the candidates to read the questions carefully.
5. This question paper is divided into two sections : Section -A and Section-B
6. In Section A, there are 35 objective type questions which are compulsory, each carrying 1 mark. Darken the circle with blue/black ball pen against the correct option on OMR Sheet provided to you. Do not use Whitener/Liquid/Blade/ Nail on OMR Sheet otherwise your result will be treated as invalid.
7. In section-B, there are 18 short answer type questions (each carrying 2 marks), out of which only 10 (ten) questions are to be answered Apart from this there are 06 Long Answer type questions (each carrying 5 marks), out of which 3 questions are to be answered.
8. Use of any electronic device is prohibited.

Objective Type Questions

In the following questions no. from 1 to 35, there is only one correct answer against each question. For each question, mark (darken) the correct answer on the OMR Sheet provided to you. (1 x 35 = 35)

Question 1.
The coordination number of metal crystallising in a hexagonal close packing is ………….
(a) 12
(b) 4
(c) 8
(d) 6
Answer:
(a) 12

Question 2.
A crystalline structure has radius ratio (r, / r) in the range of 0.225 – 0.414. The coordination number and arrangement of anions around the cations are
(a) 3, plane triangular
(b) 6, octahedral
(c) 4, tetrahedral
(d) 8, cubic
Answer:
(c) 4, tetrahedral

Question 3.
A crystal lattice with alternative +ve and -ve ions has radius ratio 0.524. The coordination number of lattice is
(a) 4
(b) 6
(c) 8
(d) 12
Answer:
(b) 6

Question 4.
A solid AB has a rock salt structure. If radius of cation A⁺ is 120 pm, what is the minimum value of radius of B^–anion ?
(a) 120 pm
(b) 240 pm
(c) 290 pm
(d) 360 pm
Answer:
(c) 290 pm

Question 5.
A crystal is formed by two elements X and Y in cubic structure. X atoms are at the comers of a cube while Y atoms are at the face centre. The formula of the compound will be ………..
(a) XY
(b) XY₂
(c) X₂Y₃
(d) XY₃
Answer:
(d) XY₃

Question 6.
What will be the mole fraction of ethanol in a sample of spirit containing 85% ethanol by mass ?
(a) 0.69
(b) 0.82
(c) 85
(d) 0.60
Answer:
(a) 0.69

Question 7.
What is the molarity of a solution containing 10 g of NaOH in 500 mL of solution ?
(a) 0.25 mol L^-1
(b) 0.75 mol L^-1
(c) 5 mol L^-1
(d) 1.25 mol L^-1
Answer:
(c) 5 mol L^-1

Question 8.
In a cell reaction,

If the concentration of Cu²⁺ ions is doubled then Ep_ell will be
(a) doubled
(b) halved
(c) increased by four times
(d) unchanged
Answer:
(d) unchanged

Question 9.
A standard hydrogen electrode thas a zero potential because
(a) hydrogen can be most easily oxidised
(b) hydrogen has only one electron
(c) the electrode potential is assumed to be zero
(d) hydrogen is the lightest element.
Answer:
(c) the electrode potential is assumed to be zero

Question 10.
In a reaction 2X → Y, the concentration of X decreases from 3.0 moles/litre to 2.0 moles/litre in 5 minutes. The rate of reaction is …………
(a) 0.1 mol L^-1 min ¹
(b) 5 mol L^-1 min^-1
(c) 1 mol L^_1 min^-1
(d) 0.5 mol L^-1 min^-1
Answer:
(a) 0.1 mol L^-1 min ¹

Question 11.
For the reaction, 2N₂O₅ → 4NO₂+O rate and rate constant are 1,02 x 10^-4 mol Lr¹ s^-1 and 3.4 x 10^-5 s^-1  The
concentration of N₉O₅ in mol L^-1 will be ………….
(a) 3.4 x 10⁴
(b) 3.0
(c) 2
(d) 3.2 x 10~⁵
Answer:
(b) 3.0

Question 12.
The incorrect statement about physical adsorption is
(a) it lacks specificity
(b) it is generally reversible
(c) porous surfaces are good adsorbent
(d) heat of adsorption is quite high
Answer:
(d) heat of adsorption is quite high

Question 13.
Which is correct in case of vander Waals adsorptions ?
(a) High temperature, low pressure
(b) High temperature, high pressure
(c) Low temperature, low pressure
(d) Low temperature, high pressure
Answer:
(d) Low temperature, high pressure

Question 14.
Which of the following is not an ore of magnesium ?
(a) Carnal lite
(b) Magnesite
(c) Dolomite
(d) Gypsum
Answer:
(d) Gypsum

Question 15.
Which of the following is not an oxide ore ?
(a) Corundum
(b) Zincite
(c) Calamine
(d) Chromite
Answer:
(c) Calamine

Question 16.
Nitrogen is relatively inactive element because
(a) its atoms has a stable electronic configuration
(b) it has low atomic radius
(c) its electronegativity is fairly high
(d) dissociation energy of its molecule is fairly high
Answer:
(d) dissociation energy of its molecule is fairly high

Question 17.
Nitrogen combines with metals to form
(a) nitrites
(b) nitrates
(c) nitrosyl chloride
(d) nitrides
Answer:
(d) nitrides

Question 18.
Reactivity of transition elements decreases almost regularly from Sc to Cu because of
(a) lanthanoid contraction
(b) regular increase in ionisation enthalpy
(c) regular decrease in ionisation enthalpy
(d) increase in number of oxidation states.
Answer:
(b) regular increase in ionisation enthalpy

Question 19.
The first ionisation energies of the elements of the first transition series (Ti to Cu)
(a) increases as the atomic number increases
(b) decreases as the atomic number increases
(c) do not show any change as the addition of electrons takes place in the inner (n – 1) d-orbitals
(d) increases from Ti to Mn and then decreases from Mn to Cu
Answer:
(a) increases as the atomic number increases

Question 20.
The ligand N(CH₂ CH₂ NH₂)₃ is
(a) bidentate
(b) tridentate
(c) tetradentate
(d) pentadentate
Answer:
(c) tetradentate

Question 21.
Which of the following is a tridentate ligand ?
(a) EDTA^4-
(b) (COO)₂^2-
(c) dien
(d)  NO^–₂
Answer:
(c) dien

Question 22.
Which of the following is not correctly matched with its IUPAC name ?         .
(a) CHF₂CBrClf : l-Bromo-l-chloro-1,2, 2 – trifluoro- ethane
(b) (CC1₃)₃ CC1: 2-(Trichloromethyl)-l, 1,1,2,3,3,3 – heptachloropropane
(c) CH₃C(p-ClC₆H₄)₂CH(Br)CH₃ : 2-Bromo-3,3-bis (4- chlorophenyl) butane
(d) o-BrC₆H₄CH(CH₃)CH₂CH₃ : 2-Bromo-l-methyl- propropyl benzene
Answer:
(d) o-BrC₆H₄CH(CH₃)CH₂CH₃ : 2-Bromo-l-methyl- propropyl benzene

Question 23.
Halogen acids react with alchols to form alkyl halides. The reaction follows a nucleophilic substitution mechanism. What will be the major product of the folowing reaction ?

Answer:
(c)

Question 24.
The best method to prepare 3-methylbutan-2-ol from 3- methylbut-l-ene is
(a) addition of water in presence of dil. H₂SO₄ .
(b) addition of HCl followed by reaction with dil. NaOH
(c) hydroboration-oxidation reaction
(d) Reimer-Tiemann reaction
Answer:
(a) addition of water in presence of dil. H₂SO₄ .

Question 25.
An alkene CH₃CH = CH₂ is treated with B₂H₆ in presence of H₂O₂. The final product formed is
(a) CH₃CH₂CHO
(b) CH₃CH(OH)CH₃
(c) CH₃CH₂CH₂OH
(d) (CH₃CH₂CH₂)₃B
Answer:
(c) CH₃CH₂CH₂OH

Question 26.
Benzoyl chloride on reduction with H₂/Pd – BaSO₄ produces
(a) benzoic acid
(b) benzyl alcohol
(c) benzoyl sulphate
(d) benzaldehyde
Answer:
(d) benzaldehyde

Question 27.
The oxidation of toluene to benzaldehyde by chromyl chloride is called
(a) Etard reaction
(b) Riemer-Tiemann reaction
(c) Wurtz reaction
(d) Cannizzaro’s reaction
Answer:
(a) Etard reaction

Question 28.
When excess of ethyl iodide is treated with ammonia, the product is
(a) ethylamine
(b) diethylamine
(c) triethylamine
(d) tetraethylammonium iodide
Answer:
(d) tetraethylammonium iodide

Question 29.
Secondary amines can be prepared by
(a) reduction of nitro compounds
(b) reduction of amides
(c) reduction of isonitriles
(d) reduction of nitriles
Answer:
(c) reduction of isonitriles

Question 30.

(a) 2-Iodoheptane
(b) Heptane-2-ol
(c) 2-lodohexane
(d) Heptanoic acid
Answer:
(d) Heptanoic acid

Question 31.
On oxidation with a mild oxidising agent like Br₂/H₂O, the glucose is oxidised to …………..
(a) saccharic acid
(b) glucaric acid
(c) gluconic acid
(d) valeric acid
Answer:
(c) gluconic acid

Question 32.
Which factor imparts the crystalline nature to a polymer like nylon ?
(a) Strong intermolecular farces the hydrogen bonding between chains.
(b) vander Walls forces between the polymeric chains.
(c) Close packing of the chains due to ionic bonding between the chains.
(d) Three-dimensional network of chains.
Answer:
(a) Strong intermolecular farces the hydrogen bonding between chains.

Question 33.
Arrange the following polymes in an increasing order of intermolecular forces; fibre, plastic, elastomer.
(a) Elastomer < Fibre < Plastic
(b) Elastomer < Plastic < Fibre
(c) Plastic < Elastomer < Fibre
(d) Fibre < Elastomer < Plastic
Answer:
(b) Elastomer < Plastic < Fibre

Question 34.
Antihistamines are not helpful
(a) in curing nasal allegries
(b) in treating rashes caused by itching
(c) in bringing down acute fever
(d) in vasodilation.
Answer:
(c) in bringing down acute fever

Question 35.
The drugs which are given to the patients suffering from anxiety and mental tension are known as
(a) tranquilizers
(b) analgesics
(c) antimicrobials
(d) antibiotics
Answer:
(a) tranquilizers

Short Answer Type Questions

In this Section, there are 18 Short answer type questions (each carrying 2 marks), out of which answer any 10 questions.  2 x 10 = 20

Question 1.
Which methods are usually employed for purifying the following metals ?
(i) Nickel
(ii) Iron. Mention the principles.
Answer:
(i) Silesion process
(ii) Pudding process, cementation process, Bessemer’s rocess, siemens martin open heart process, Linz Donawitz process.

Question 2.
Cl, Br, I or halogens are members of which group in the periodic table ?
Answer:
Group-(ViiA)

Question 3.
Explain, why the valency of inert gases is zero.
Answer:
It is because since the valence shell is saturated with 8 electrons. The hoble gases have so a valence equal to zero as in principle can not make chemical bands with other – atoms.

Question 4.
Explain standard electrode potential.
Answer:
Standard electrode potential : It is the measure of individual potential of a reversible electorde at standard state which is with solutes at an effective concentration of 1 mol dm^-3 and gases at a pressure of 1 atm.

Question 5.
What is carbocation ? Explain.
Answer:
Carbocation : A carbocation is an ion with positively-charged carbon atom. Among the simplest example methenium CH⁺₃ ethanium C₂H⁺₂ . Some carbocations may have two or more positive charges, on the same carbon atom or on different atom such as ethylene dictation (C₂H₄⁺). It is classified in two categories according to the valence of the charged carbon.

Question 6.
What do you mean by acid rain ? Explain.
Answer:
Acid rain : It is a rain or any other form of precipitation that usually acidic, meaning that it possesses elevated levels of hydrogen ions (low pH). It can have harmful effects on plants aquatic animals and infrastructure. Acid rain is caused by emissions of sulphur dioxide and nitrogen oxide, which react with water molecules in the atmosphere to produce acids. In chemical acid rain can cause point to peel, corrosion of steel structures such as bridges and erosion of stone statues.

Question 7.
Explain two important uses of formalin.
Answer:
Two use of formaline are following:

• It is used as preservative
• It is also used as a disinfectation and an antibacterial.

Question 8.
How will you convert Aniline into Benzoic acid ?
Answer:

Question 9.
Any transition series contains only ten elements. Why?
Answer:
There are only 10 members because in period left to right atomic number increases and hence after a certain number when the D subshell is fully filled the electron has to go in S and P sub shell, hence it ends and P blocks

Question 10.
Explain mole fraction.
Answer:
Mole fraction : It is defined as the amount of a constituent n divided by the total amount of all constituents
in a mixture n_total It is also called amount fraction i.e  \(\left(x_{i}=\frac{h_{i}}{n_{\text {total }}}\right)\)

Question 11.
What is salt bridge ? What are its uses ?
Answer:
Salt bridge : In electro chemistry, it is a laboratory device used to connect the oxidation and reduction half-cells of a galvanic cell (voltaic cell, a type of electrochemical cell. Salt bridge usually comes into two types : glass tube and filter paper.
Uses : It is used in voltaic cell. Purpose of salt bridge is only to move electrons from electrotype solution to the other.

Question 12.
(a) Write the IUPAC name of the following compound :
Answer:

(b) Name the product formed when ethyne is oxidised with cold alkaline solution of KMnO₄.
Answer:
(a) 2, 3 -Dimethyl butane
(b) Ethane – 1, 2 – diol
(CH₂OH – CH₂OH)

Question 13.
If 20 g of calcium carbonate is added to a solution containing 20 g of HCl. What substances will be present when the reaction is over and what quantity of each of them will be present there?
Answer:

Thus, HCl will be present when the reaction is over. Rest amount of HCl = 20 – 14.8 = 0.56 g.

Question 14.
Write chemical reaction to obtain the following :
(i) Methane to chloroform
(ii) Chloroform to ethyne.
Answer:

Question 15.
Give reasons for the following:
(i) Ethyne is more acidic than ethane,
(ii) Lower members of aldehyde are more soluble in water.
Answer:
(i) Ethyne contains SP hybridized carbons, while ethane contain SP³ hybridized carbons. Th SP hybrid orbitals have greater S character than SP³ which allows negative charge to be held closer to the nucleus and increasing the acidic character that is why ethyne is more acidic than ethane.

(ii) Because, lower member of aldehyde have capability of forming H-bond with water molecule.

Question 16.
Transition elements form coloured compound. Explain.
Answer:
The value of electrods potential depends upon the heat of sublimation and ionisation energy AH – AH_sib + IE + AH_hyd. Due to.the influence of ligand d-or-bitals of transition metals divided into two unequal energy containing sets, unpaired electrons obsorb sunlight and jumps from one orbit into another orbit and oen colour is reflected.

Question 17.
Why is the bond angle of PH₄ more than PH ₃ ?
Answer:
Because CH₄ has no lone pair of electrons, while PH₃ has so bond angle of CH₄ (1095°) is more than PH₃.

Question 18.
Give I.U.P.A.C. names of the following :

Answer:
(a) Butane-1,4 dioic acid
(b) 2-hydroxy propan-1- oic acid.

Long Answer Type Questions

There are 06 long answer type questions (each carrying 05 marks), out of which answer any there questions.
(5 x 3 = 15)

Question 19.
How does nitric acid react with the following ? Give equation.
(i) Copper
(ii) Iron.
Answer:
(i) Reaction of HNO₃ with copper : (A) With not and concentrated HNO₃, copper reacts to give nitrogen peroxide, copper nitrate and water
Cu + 4HNO₃ → Cu(NO₃ ) + 2NO₂+H₂O.

(ii) With 50% concentrated nitric acid copper reacts to give copper nitrate, nitric oxide and water
3Cu+ HNO₃ → Cu(NO₃)₂ +2NO + 4H₂O

(iii) With 20 – 25% dilute. HNO₃ copper reacts to give copper nitrate, nitrous oxides and water.
4Cu + 10HNO₃ → 4Cu(NO₃)₂ +N₂O + 5H₂O

(iv) On passing vapour of nitric acid on heated copper nitrogen gas and water vapour are obtained
5Cu + 2HNO₃ → 4CuO + N₂+H₂O

(v) Reaction of HNO₃ with Iron : (A) With cold and dilute HNO₃ Iron reacts to give ferrous nitrate and ammonium nitrate
4Fe +10HNO₃ → NH₄NO₃ +4Fe(NO₃)₂ + 3H₂O

(B) Hot & dil nitric acid reacts with iron and gives ferric Nitrate & No gas.
2Fe + SHNO₃ → 2Fe(NO₃)₂ +2NO↑+H₂O
Fe + 6HNO₃ → Fe(NO₃)₃ +3NO₂ +3H₂O

(C) With hot and cone. HNO₃ Iron reacts to give ferric nitrate and nitrogen dioxide gas.
Fe + 6HNO₃ → Fe(NO₃)₃ + 3NO₂ + 3H₂O

Question 20.
What are the main sources of iodine ? How is iodine extracted from sea weeds ?
Answer:
Natural sources of Iodine : Due to its reactivity Iodine is not found in nature in free state its main sources are

• sea weeds
• chile salt puter
• Natural brine.

Extraction of Iodine from sea weeds : Sea weeds lamineria contains iodine, Sea weed is well dried and burnt in deep pite carefully so that iodine donot get destroyed. The obtained ash is called kelp which contains 0.4 to 1.3% Iodine kelp is dissolved in water and solution is partially crystallised when less. Soluble KI and Nal remain in the mother liquor,

cone H₂SO₄ is added when basic sulphides despositeat the bottom, when is filtered and removed Now the filtrate is mixed with MnO₂ and H₂SO₄ and heated iron vessel. Iodine vapourises due to the reaction and is collected Aludel. Iodine is new collected as solid after condensation.

2Nal + MnO₂ +3H₂SO₄ -4 2NaHSO₄ + MnSO₄ + 2H₂O+I₂ ↓

Iodine obtained by this method contains CI₂ and Br₂ as impurifies. It is treted with KI to obtained pure Iodine

Question 21.
(a) Write only the principle for the manufacturing of sulphuric acid by contact process.
(b) Complete the following reactions-
(i) KBr + Cl₂ →…………….. +……….
(ii) I₂ + H₂O + CI₂→………….. +………..
(iii) NaOH + Cl₂ → …………..+…………. +………… (Cold and dilute)
Answer:
(a) Principle-(i) The process involves the oxidation of sulphur dioxide by air in the presence of catalyst V₂O₅.

(ii) Sulphur trioxide is dissolved in 98% sulphuric acid, forms oleum.

(iii) Sulphuric acid of any desire concentration is prepared from oleum with water.
H₂S₂O₇ + H₂O→2H₂SO₄
The oxidation of SO₂ is reversible process, contraction in volume and exochermic.
Hence applying i.e., Chatelier’s principle to obtained greater yield of SO₃.

• Reaction is carried out high pressure.
• At low temperature production of SO₃ should increase. But at lower temperature SO₂ does not oxidise. Hence at optimum temperature 450°C catalyst V₂O₅ is applied.

(b)

• KCI, Br₂
• HIOj, HCl
• NaCl, NaClO₃

Question 22.
(a) State Werner’s coordination theory.
(b) What are ligands ? Classify them with examples.
Answer:
(a)

• In co-ordination compounds metals show two types of linkages (valencies) primary and secondary.
• The primary valencies are normally ionisable and are satisfied by negative ions.
• The secondar valencies are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the co-ordination number and is fixed for a neutral.
• The ions/groups bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to different numbers.
• In the modem formulations, such spatial arrangements are called co-ordination polyhedra. The species with the square brackets are co-ordination entities or complexes and the ions out side the square bracket are called counter ions.
• He further postulated that octahedral, tetrahedral and square planar geometrical shapes are more common in co­ordination compounds of transition metals. Thus [Co(NH₃)₆]^{3 +}, [CoCl(NH₃)₅]²⁺and [CoCl₂(NH₃)₄]⁺ are octahderal entities, while [Ni(CO)₄] and [PtCl₄]^2- are tetrahedral and square planar respectively.

(b) The atoms or molecules or ions which donate pair of electrons to the central metal atom and thus forms co-ordinate bond with the central metal atom. Common ligands are – NH3, CO, CN-, Cl”, Br, I”, H₂O etc. Ligands which can attach themselves (called ligating) through two different atoms of the same molecule are called ambident ligands or group, e.g., NO₂ , SCN^–. They introduce linkage isomerism in the complexes.

Question 23.
Explain why
(i) Aniline dissolves in HCl.
(ii) Amines are stronger base than Ammonia
(iii) Ethylamine is more basic than Aniline
(iv) Cyclohexamine is more basic than Aniline
(v) Phenol is acidic in nature.
Answer:
(i) Aniline is somewhat basic. It is not as basic as amonia, since protonation destroys the interaction between the ring aind the lone pair on the nitrogen atom but even still it is sufficiently basic (PKb ~ 9.4) to dissolve in HCl.

(ii) The inductive effect of attached carbon chain to an amine will raise the energy of the lone pair on the nitrogen. On amines carbon will withdraw less electron density from an atom of interest that hydrogen (in amonia). That explain why alkyl amine are stronger bases than amonia.

(iii) Therefore, less electron is available in the nitrogen atom in C₆H₅NH₂. It can easily dissociate to denote a proton, H⁺ by breaking -N-H bond in the amine group that attach to phenyl group. Hence aniline is a stronger acid than ethylamine.

(iv) In cyclohexamine, the electron donating group is attached to SP³ hybridized cyclohexane ring while in case of aniline it is attached with SP² hybridized carbon containing benzene ring. Due to more S-character in benzene ring, here becomes the de localization of 7t-electrons in the ring and further the NH₂– group donates more electron to the ring so that it reduces the -i-ve charge centers and stablizes the ring and moves it less acidic means basicity increases while in case of cyclohexamine, the lone pair of electron donating NH,- group is not de localised over cyclohexane ring and is available for donation, which makes the compound more basic than anile.

(v) Phenol loses its H⁺ when kept in an acidic medium. Due to which phenote ion is formed. This ion formed is more stable than phenol due to its resonating character. Hence phenote formation is favoured and releases of H⁺ make phenol acidic.

Question 24.
Explain the main points in the extraction of zinc from zinc blende.
Answer:
Explain the main points in the extraction of zinc from zinc blende.
Answer:
Extraction of zinc : Reduction process involves the steps.
(i) Concentration of the ore : The ore is Crushed and made to powder. The crushed ore is concentrated by Froth floation process. The concentrated ore goes to the surface along with the froth. This is removed and dried.

(ii) Roasting: The concentrated ore is roasted in a furnace at high temp. (900°C) in presence of excess of air. In this process zinc blends is converted into ZnO.

There is chance of formation of ZnSO₄ if the reaciton temperature remains low. The ZnSO₄ thus formed is decomposed to give ZnO, SO₂ and O₂

If calamine ore (ZnCO₃) is used then it is converted to ZnO by calcination.
ZnCO₃ → ZnO + CO₂ ↑

(iii) Reduction: ZnO thus formed as a result of roasting or calcination is reduced by carbon. As a result at reduction Zn metal in molten state is formed.

(iv) Purification: Impure Zn is purified by the process of electrolysis, for this impure zinc rod is made anode and a rod of pure zinc is made cathode. These rods are dipped in an electrolytic cell containing ZnSO₄ Zn in deposited at cathode on electrolysis. The following cell reactions occur
Zn Zn⁺⁺ +2e (At anode),Zn⁺⁺ +2e → Zn (At cathode)

Bihar Board 12th Economics Model Papers

Bihar Board 12th Economics Model Question Paper 3 in English Medium

Time : 3 Hour 15 Min
Full Marks : 100

Instructions

1. Candidates are required to give their answers in their own words as far as practicable.
2. Figures in the right hand margin indicate full marks.
3. 15 minutes of extra time has been allotted for the candidate to read the questions carefully.
4. This question paper has two sections : Section-A and Section-B.
5. In Section-A, there are 50 objective type questions which are compulsory, each carrying 1 mark. Darken the circle with black/blue ball pen against the correct option on OMR Sheet provided to you Do. not use Whitener/Liquid/Blade/Nail on OMR Sheet, otherwise the result will be treated as invalid.
6. In Section-B, there are Non-objective type questions. There are 25 Short answer type questions, out of which any 15 questions are to be answered. Each question carries 2 marks. Apart froms this, there are 08 Long answer type questions, out-of which any 04 of them are to be answered. Each questions carries 5 marks.
7. Use of any electronic device is prohibited.

Objective Type Questions

Question No. -1 to 50 have four options provided, out of which only one is correct. You have to mark, your selected option, on the OMR-Sheet. Each questiion carries 1 (one) mark. [50 x 1 = 50]

Question 1.
Who was the father of Economics ?
(a) J. B. Say
(b) Mai thus
(c) Asam Smith
(d) Joan Robinson
Answer:
(c) Asam Smith

Question 2.
How many types of elasticity of demand are these ?
(a) Three
(b) Five
(c) six
(d) seven
Answer:
(b) Five

Question 3.
Which of following is a source of prodution ?
(a) Land
(b) Labour
(c) Capital
(d) All of these
Answer:
(d) All of these

Question 4.
According to whom, Economics is a science of human welfare ?
(a) Marshall
(b) samuelson
(c) J. S’. Mill
(d) Adam Smith
Answer:
(a) Marshall

Question 5.
Market price is found is ___________
(a) Long period market
(b) Short period market
(c) Very long period market
(d) None of these
Answer:
(a) Long period market

Question 6.
For Giffin goods price elasticity of demand is ___________
(a) Negative
(b) Positive
(c) Zero
(d) None of these
Answer:
(b) Positive

Question 7.
Long-run production funtion is related to ___________
(a) Law of demand
(b) Law of returns to scale
(c) Elasticity of demand
(d) Law of increasing returns
Answer:
(a) Law of demand

Question 8.
If the price of goods rises by 60% but supply increases by only 5%, the supply of goods will be ___________
(a) Elastic
(b) Inelastic
(c) Highly elastic
(d) perfectly inelastic
Answer:
(b) Inelastic

Question 9.
Which is the central problem of economy ?
(a) Distribution of resources
(b) effective utilisation of resources
(c) Economic development
(d) All of these
Answer:
(a) Distribution of resources

Question 10.
In which economy decision is taken on the basis of price mechanism ?
(a) Socialist
(b) Capitalist
(c) Mixed
(d) All of these
Answer:
(b) Capitalist

Question 11.
The cycle which increases first and after being constant starts to reduce is called?
(a) APP
(b) MPP
(c) TPP
(d) All of these
Answer:
(b) MPP

Question 12.
The quantity of goods which seller is ready to sell in a market at fixed price and time is called ?
(a) Supply
(b) Demand
(c) Elasticity of supply
(d) Elasticity of demamd
Answer:
(a) Supply

Question 13.
Central bank of India is ___________
(a) Reserve Bank
(b) State Bank
(c) Public Bank
(d) Shere market
Answer:
(a) Reserve Bank

Question 14.
Which of the following is not a fixed cost ?
(a) Insurance Premium
(b) Interest
(c) Cost of raw material
(d) Rent of the factory
Answer:
(c) Cost of raw material

Question 15.
Which of the following is a component of budget receipts?
(a) Revenue Receipts
(b) Capital receipts
(c) Both a and b
(d) None of these
Answer:
(c) Both a and b

Question 16.
Which one of the following services is included in secondary sector ?
(a) Insurance
(b) Banking
(c) Trade
(d) Manufacturing
Answer:
(d) Manufacturing

Question 17.
Demand curve generally slopes ___________
(a) Upward from left to right
(b) Downward from left to right
(c) Parallel to X-axis
(d) None of these
Answer:
(b) Downward from left to right

Question 18.
On which factor does Keynesian theory of employment depend ?
(a) Effective demamd
(b) Supply
(c) Production
(d) None of these
Answer:
(a) Effective demamd

Question 19.
Financial year in India is ___________
(a) April 1 to March 31
(b) January 1 to December 31
(c) October 1 to September 30
(d) None of these
Answer:
(a) April 1 to March 31

Question 20.
Credit money is increased when CRR ___________
(a) Falls
(b) Rises
(c) Both a and b
(d) None of these
Answer:
(a) Falls

Question 21.
Narsimham committee is related to ___________
(a) Tax reforms
(b) Banking reforms
(c) Agriculture
(d) Infrastucture reforms
Answer:
(b) Banking reforms

Question 22.
Which type of currency is issued by central bank ?
(a) Currency notes
(b) Credit money
(c) Coin
(d) All the above
Answer:
(a) Currency notes

Question 23.
In which year Reserve Bank of India was established ?
(a) 1947
(b)1935
(c)1937
(d)1945
Answer:
(b)1935

Question 24.
The expenditiure which do not create assets for the government is called ___________
(a) Revenue Expenditure
(b) Capital Expenditure
(c) Both a and b
(d) None of these
Answer:
(a) Revenue Expenditure

Question 25.
For a change in which of the following there is no change in demamd ?
(a) Change in price
(b) Change in Income
(c) Change in Taste and Fashion
(d) none of these
Answer:
(a) Change in price

Question 26.
With an increase income consumers decrease the consumption of which goods ?
(a) Inferior goods
(b) Normal goods
(c) Giffin goods
(d) Both A and B
Answer:
(b) Normal goods

Question 27.
The ability of satisfying human want in goods is called its ___________
(a) Productivity
(b) Satisfaction
(c) Utility
(d) Profitability
Answer:
(a) Productivity

Question 28.
Mention the name of the curve which shows economic problem ___________
(a) Production curve
(b) Demand curve
(c) Indifference curve
(d) production possibility curve
Answer:
(d) production possibility curve

Question 29.
Consumer behaviour is studied in ___________
(a) Micro Economics
(b) Income Analysis
(c) Macro Economics
(d) None of the above
Answer:
(a) Micro Economics

Question 30.
Which of the following is studied under Micro Economics ?
(a) Individual unit
(b) Economic Aggregate
(c) National Income
(d) None of the above
Answer:
(a) Individual unit

Question 31.
Utility is related to ___________
(a) Usefulness
(b) Morality
(c) Satisfaction of human wants
(d) All of above
Answer:
(d) All of above

Question 32.
For luxury good the demand is ___________
(a) Inelastic
(b) Elastic
(c) Highly elastic
(d) perfectly inelastic
Answer:
(c) Highly elastic

Question 33.
In production function, production is a function of ___________
(a) Price
(b) Factors of production
(c) total expenditure
(d) None of these
Answer:
(b) Factors of production

Question 34.
At which time all the factors of production may be changed ?
(a) Short run
(b) Long run
(c) Very long run
(d) All the three
Answer:
(b) Long run

Question 35.
Banking Ombudsmen scheme was announced in the year ___________
(a) 1990
(b)1995
(c)1997
(d)2000
Answer:
(b)1995

Question 36.
The alternative name of opportunity cost is ___________
(a) Economic cost
(b) Equilibrium price
(c) Marginal cost
(d) Average cost
Answer:
(a) Economic cost

Question 37.
Central bank controls credit through ___________
la) Bank Rate
(b) Open market operations
(c) CRR
(d) All the above
Answer:
(d) All the above

Question 38.
Who regulates money supply ?
(a) Government of India
(b) Reserve Bank of India
(c) Commercial Banks
(d) Planning commission
Answer:
(b) Reserve Bank of India

Question 39.
For keynes, investment implies ___________
(a) Financial Investment
(b) Real Investment
(c) Both a and b
(d) None of the above
Answer:
(c) Both a and b

Question 40.
What is the duration of a Budget ?
(a) Annual
(b) Two years
(c) Five years
(d) Ten years
Answer:
(a) Annual

Question 41.
The factor(s) of the production is/are ___________
(a) Land
(b) Labour
(c) Capital
(d) All of these
Answer:
(d) All of these

Question 42.
Who invented the economic science ?
(a) Kautilya
(b) Carlyle
(c) William Morris
(d) Charles Dickens
Answer:
(a) Kautilya

Question 43.
Who said ” Economics is the science of scarcity” ?
(a) Robbins
(b) Adam Smith
(c) Marshall
(d) J.S. Mill
Answer:
(b) Adam Smith

Question 44.
Who said “Economics is the science of material welfare” ?
(a) Robbins
(b) Marshall
(c) J.B.Say
(d) Senior
Answer:
(c) J.B.Say

Question 45.
On which basic has structure of economic problem been installed ?
(a) Unlimited wants
(b) Limited resources
(c) Both (a) and (b)
(d) None of these
Answer:
(c) Both (a) and (b)

Question 46.
ForGiffen goods price elasticity of demand is ___________
(a) Negative
(b) Positive
(c) Zero
(d) none of these
Answer:
(b) Positive

Question 47.
The main reason of operating the Law of Diminishing Return is ___________
(a) Scarcity of factors
(b) Imperfect substitution between factors
(c) Both (a) and (b)
(d) none of these
Answer:
(a) Scarcity of factors

Question 48.
When supply increases more with a result of small increase in price,the nature of supply will be ___________
(a) elastic
(b) inelastic
(c) perfectly elastic
(d) perfectly inelastic
Answer:
(a) elastic

Question 49.
Which of the following is the formula for measuring the elasticity of demand ?
(a) Proportionate change in demand /Proportionate change in price
(b) Proportionate change in price/ Proportionate change in demand
(c) Change in demand/Change in price
(d) None of these
Answer:
(a) Proportionate change in demand /Proportionate change in price

Question 50.
To which factor are economic problems basically related ?
(a) Choice
(b) Consumer’s selection
(c) Firm selection
(d) None of these
Answer:
(a) Choice

Non-Objective Type Questions

Short Answer Type Questions

Question no. 1 to 25 are Short answer type questions. Answer any 15 out of them. Each question carries 2 marks. (15 x 3 = 30)

Question 1.
Explain any two factors that affect price elasticity of demand.
Answer:
Factors affecting elasticity of demand are discussed below:

1. Substitutes : When substitute of any goods is available, then demand elasticity of such goods is highly elastic because when price of these goods increases, substitutes are used in place of it. In the same way, on decrease in price of these goods, use of substitutes decrease. Tea, coffee, gas, sugar etc. are examples of subsitutes.
2. Alternative uses : When goods could be used in only one way, its demand will be in elastic and when it would be used in many ways, its demand will be elastic, eg. coal has so many used-it can be used industries houses ralways etc. Demand of coal for railways in in elastic but for house purpose, its cheeper alternative goods like wood cooking gas etc. could be used in place of it.

Question 2.
What is mean by law of increasing returns ?
Answer:
Law of increasing returns : Increasing returns to scale occurs when a given percentage increase in all factor inputs (in some constant ratio) causes proportionately greater increase in output. In this way, if factors of production are increased by 10%, then production increases more than 10%.

Percentage incress in all factors

Increasing returns to scale occur due to division of labour and Percentage increase in all factors (Factor ratio remains constant) specialisation. Division of labour and specialisation increases productivity of labour. Due to increasing in size of the scale more efficient and specialised machines are used which give increasing returns to scale.

Question 3.
Where is the equilibrium price determined ?
Answer:
Commodity Price : Demand-Supply Equilibrium : Buyer wants to give the least price while the seller wants to take the maximum price of the commodity. Bargaining takes price between both the parties and at last, the price of the commodity is determined at the price where both demand for and supply of the commodity become equal. This price is called equilibrium price.

In following Fig. price determined of the commodity by demand and supply forces has been shown. Demand curve DD and supply curve is cuts each other at point E where price OP is determined. This price OP (or EQ) shows the equilibrium price.

Question 4.
What is the difference between Micro¬Economics and Macro-Economics ?
Answer:
Micro Economics :

1. In Micro Economics economic problems at individual level are studied e.g., one consumer, one producer, one firm
2. Individual and individual behaviour is studied of Macro Economics.
3. Micro economic analysis assumes macro parameter as constant.

Macro Economics :

1. Macro Economics studies the economic units of the entire economy, e.g., national income, total consumption, general price level.
2. Society as a whole and its behavior is studied in Macro Economics.
3. Macro Economic analysis assumes parameters as constant.

Question 5.
State the qualities of good money.
Answer:
Follwoing are the qualities of good money :

1. Utility : The metal with which coin is made, must bear the feature of utility. The metal must easily be accepted. Gold and silver are such metals which possess utility.
2. Port ability: The metal with which coin is made, can easily be transferred from one place to antother. Gold and silver coins bear this feature also.
3. Durable : Money is saved by people and hence coin should be made of such metal which is durable from saving purpose.
4. Divisibility : Money metal should be divisible without my loss in its value. Gold and silver are such metals having the feature of divisibility.
5. Homogeneity : All units of money should be homogeneous.
6. Economy : Minting cost of coin should be minimum and the depreciation in the coin should be least.
7. Stability of Value: Money metal should be stable in value i.e. price fluctuation in the metal of coin should be minimum.
8. Liquidity: Money metal should be liquid in nature, metal should easily be converted into coins and coins can again be converted into metal on easily
9. Cognisibility: Metal should easily be identified. Take coins on easily be traced out if metal of money is cognisible. Gold and silver are such metals having full cognisibility.

Question 6.
State the merits & demerites of Direct Taxes.
Answer:
Merits of Direct Takes :

1. Direct takes ensure certainity. The government and the tax payer both know fairly definitely what amount are to be paid.
2. Direct taxes are elastic whenever the government needs more revenue it may raise the rate of direct taxes.
3. Direct taxes are progressive in nature. It increases with the increases in money income.
4. Direct Taxes are supposed to have on educative elfect. The tax payer is concious that provides funds to the

government and is interested in seeing that they are properly used.
Demerits of Direct Taxes :

1. Tax evasion is possible in case of direct taxes.
2. It has narrow base or limited area of functioning.
3. Directed taxes are numerious accounting and other formalities, have to be observed and partly, because large lump sum tax payment have to be made.

Question 7.
What is meant by Balance of Trade ?
Answer:
Balance of Trade : It is defined as the difference between exports and imports of goods. It takes into account only those transactions arising out of exports and imports of goods (the visible items). It does not consider the exchange of services between the countries.
Symbolically, BOT = Vx – Vm where Vx = value of exports.
VOT = value of imports.

Question 8.
What are the different types of economic system ?
Answer:
Economic system is a structure of such institutions with which all economic activities are operated in the society. Every economy is based on an economic system which can be divided into three categories :

1. Capitalist Economy or market Economy
2. Socialist Economy or planned Economy
3. Mixed Economy.

Question 9.
What is Indifference Curve ?
Answer:
Indifference curve explains the consumer’s behaviour related with the combination of two goods and this consumer’s behaviour is explained with the help of “Indifference schedule or Indifference set.” various combinations of two goods giving equal satisfactions to the consumer become the component of ‘Indifference schedule’. When indifference schedule is represented on a graph paper, we get indifference curve.

In the words of watson “An indifference schedule is the list of combination of two commodities, the list being so arranged that a consumer is indifferent to the combinations preferring more of any other”.

Question 10.
What is elasticity of demand ?
Answer:
Elasticity of Demand : Elasticity means tendency of increasing or decreasing elasticity depends on two factors-‘Nature of Goods’ and the ‘pressure on it’, when goods undergoes greater changes in response to less pressure, it is said to be ligaly elastic and when it produces less change in response to high pressure, it is said to be less elastic.

According to Marshall. “The Elasticity of demand in a market is great or small according as the amount demanded increases much or little for a given fall in price, or diminishes much or little for a given rise in price.”

Elasticity of Demand (ed) = \(\frac { Proportionate changes in quality demanded }{ Proportionate Change in price }\)

Question 11.
What do you mean by Giffen goods ?
Answer:
Giffin Goods : Giffin goods are those inferrior goods whose income effect is negative and price effect is positive. Law of demand is not applicable in case of Giffin Goods.

Question 12.
Explain the static and dynamic functions of money.
Answer:
Static Functions: Static functions are those which help the operation of the economy but those do not create movement in the economy. In this respect, the functions of money like medium of exchange, measure of value, store of value and measure of deferred payment are the static functions of money because these functions do not create any movement in economy.

Dynamic functions: The dynamic functions are those by which money acheively influences the economic system through its impact on price level interest rates, value of production distribution of wealth and income.

Question 13.
How is central bank different from commercial bank ?
Answer:
Distinction between central bank and commercial bank.
Central Bank :

1. It is an apex bank in the country which controls all other banks.
2. Its main objective is to operate banking system in national interest. It does not work with profit earning profit.
3. Leaving USA where 12 central Banks are working every country has only one central Bank.
4. It is subordinate to the government.
5. Apart from a few specific situation, it has no direct dealing with public.

Commercial Bank :

1. It is a part of banking and works under the control of central Bank.
2. Its main objective is to earn maximum profit with banking operations.
3. A country has a number of commercial banks.
4. These banks are basically banks of share holders. It may or may not be state owned.
5. It directly deals with general public.

Question 14.
What do you mean by Returns to Scale ?
Answer:
Returns to scale refers to long run production function when none of the factors of production remains fixed. All factors of production become variable and they can be changed also. Scale production can be changed in the long run. Internal and external economies are obtained in production due to technical improvement, division of labour, specialisation etc. These economics are not permanent and they get converted to diseconomies in the continuous process of production.

In the initial stage of production, these internal and external economics give ‘Increasing Returns to scale’ but when they get converted to diseconomies at later stage of production law of diminishaing returns comes into existence. According to watson Returns to scale refers to the behaviour of total output as all inputs are varied in the same proportion and is a long run concept”.

Question 15.
What is the shape of demand curve of a firm in perfect competition ?
Answer:

When a demand schedule is graphically represented, we get a demand curve. It shows the inverse relationship between price and quantity demanded. Due to this inverse relationship, demand curve slopes downward from left to right. It shows that higher the price, lower will be the quantity demanded and vice versa.

Question 16.
What is the difference between trade balance and balance of payments ?
Answer:
Difference between Balance of trade and Balance of payments.
Balance of Trade :

1. Balance of trade refers to the difference between exports and imports of goods by a country in a year.
2. It is a narrow concept as it is a component of balance of payments.
3. It is only a partial record. Hence, it is not a true indicator of economic relations with other countries.
4. It may be favorably or unfavorable.

Balance of payments :

1. Balance of payments is a statement of all economic transactions between die residents of a country and rest of the world during a year
2. It is a wider concept
3. It is a complete record of economic transactions with the rest of the world. Hence, it provides a true picture of the economy of a country with the rest of the world.
4. From accounting viewpoint; it is always balanced.

Question 17.
What is equilibrium price ?
Answer:
Equilibrium price is the price at which demand and supply of a commodity are equal. It determined by the interaction of the forces of demand and supply.

Question 18.
What is the difference between substitute goods and complementary goods ?
Answer:

1. Substitute goods : Substitute goods means is that goods which is used for each other for very one object, e.g. Tea-coffee.
2. Complementary goods : Complementary goods means that goods which used together to fullfil a particular object, e.g. scooter petrol.

Question 19.
By which percentage method elasticity of demand is measured ?
Answer:
Percentage method :

Question 20.
Expain the concept of Average Revenue.
Answer:
Average revenue is found by deviding the total revenue by total number of production
AR = \(\frac { TR }{ Q }\) , Where AR = Average Revenue
TR = Total Revenue, Q = Quantity

Question 21.
What are the causes of change in supply ?
Answer:
The law of supply states the there is direct relation between price and supply of a commodity other things remaining the same. The assumptin other things remaining the same means that factors other price of the goods, determining supply remains unchanged.
Causes of changes in supply :

1. Extention of supply
2. Contraction supply.

Question 22.
Explain different types of market.
Answer:
There are mainly three types of market :

1. Perfect competition : Perfect competition refers to a market situation in which there are large number of buyers and sellers. The seller sell homogenous product at single uniform price through out the market.
2. Monopoly: Monopoly refers to a market situation in which there are no close substitute of the commodity sold by the monopolist.
3. Monopolistic competition : Monopolistic competition refers to a market situation in which there are large number of buyers and sellers. The sellers sells closely related but not identical.

Question 23.
Why is short run average cost curve U- shaped ?
Answer:
The total revenue curve of a price taking firm is an upward-slopping straight line because it changed at a constant rate. The total revenue curve of a price-taking firm passes through the origin (point U) because the total revenue of the firm becomes zero at zero output.

Question 24.
Explain firm’s equilibrium in Non-perfect competition.
Answer:
A consumer is said to be in equalibrium when he is spending his given income on various goods in such a way that maximases his satisfaction.

Question 25.
Explain the causes of downward sloping in demand curve.
Answer:
Negative slope of demand curve is due to following reasons :-

1. Law of diminishing marginal utility Law of demand is based on law diminishing marginal utility. According to it marginal utility of a goods diminishes as an individual consumes-more units of a goods.
2. Increase in purchasing power or Income Effect When price of a goods power of consumer increases due to which he can maintain his previous level of consumption with less expenditure. In this way, at lower prices, more goods could be purchase. On the contrary, when price of a goods increase real income of consumer decreases due to which his consumption decreases.
3. Substitution effect Substitution effect is due to inverse relation between price and demand of a goods. Whenever there is a change in the relative prices of goods a rational consumer will be induced to substitute the relatively dearer commodity by buying the cheaper one.
4. Change in consumer number Change in price also effects the number of consumers. When price decrease, number of consumers increases as cheaper goods can be purchased by many consumers, i.e. even those consumers start purchasing goods which were not using it earlier due to high price.

Long Answer Type Questions

Question no. 26 to 33 are Long answer type questions. Answer any 4 of them. Each question carries 5 marks. (4×5 = 20)

Question 26.
What do you mean by credit control ? Explain the methods of credit control by Central Bank.
Answer:
The most important function of the central bank is to control the credit activities of the commercial banks. Credit control refers to the increase or decrease in the value of credit money in accordance with the monetary requirement of the country. More expansion of credit money than necessary leads to the situation of inflation, greater contraction of credit money, on the other hand, might create a situation of deflation. Central bank seeks to contain credit money within reasonable limits. With Central bank keeping credit under proper control, stability in general price level and increase in output and employment can be achieved in the country.

Methods of credit control-In modern times central bank uses two types of controls to regulate the credit created by commercially banks. The following are the method of credit control by a central bank.

A. Quantitative methods-The object of the quantitative controls is to regulate the amount of bank advance. It include the following methods-

I. Bank rate-The bank rate is the rate at which the central bank discounts the first class securities of its member bank. Thus the bank rate is also called discount rate. As the central bank is only the leader of the last resort, the bank rate is normally higher than the rate of interest. The rate of interest means the rate which the commercially banks pay to the depositions a grant their deposits.

The bank rate has close relation with the market rate of interest. The central bank increases the bank rate to increase the supply of money. If there is need for contraction in money supply the bank rate is reduced. Thus the central bank control the quantum of total money supply in the country by making change in the bank rate.

This method of credit control will, however, succeed only if the other rates in the money market follow bank rate.

II. Open market operation-The cnetral bank of the country controls the supply of money through open market operations. According to De-Kock. “In the wider sense, open market operation may be held to cover the purchase or sale by the central bank in the market of any kind of paper in which it deals – whether government securities or other securities. But in the narrow sense, open market operation has come to be applied only to the purchase or sale of government securities both long term & short term.” ‘

In this operation the central bank makes sale and purchase of securities with the commercial banks of the country. If supply of money is needed to be increased the central bank starts purchasing securities from bank and if supply is needed to be reduced it starts selling securities to the banks.

III. Change in reserve ratio-It is one of the methods of credit control by the central bank. The commercial banks deposit certain percentage of their fixed deposit with the central bank & on that basis they create credit in the economy. When theh central bank desires to restrict credit, it may raise the reserve ratio and if it wants to expand the credit, the reserve ratio will be the low.
But this method of credit control has some limitations-

1. The bank may have very large excess of reserves with them
2. A large inflow of gold in payment against export may increase the banks lending power
3. The government policy of keeping interest rate low may discourage the increase in reserve ratio.

IV. Liquidity ratio-The banks are required to maintain certain resources in a liquid form under the provision of the Act. This is known as statutory liquidity ratio. The charge in this ratio will cause a change in the money supply.

B. Qualitative methods-Under this system following method of credit control is adopted-

V. Credit rationing-Under this method the central bank makes rationing of credit by distribution in different sectors, of the economy according to the requirements. This method of controlling credit can be justified only as a measure to meet exceptional emergencies. Central bank makes credit rationing by three following methods-

1. By abolition of rediscounting facilities
2. By restriction of limit of re-discounting
3. By fixing the quota of the loan provided by the bank to different industries.

VI. Moral persuasion-Under this method the central bank may request and persuade member banks not to use their loans for speculation or non-essential activities. This become obligatory to the banks to follow the directions of the central bank. This method of credit control may succeed on the fulfilment of the following condition.

1. The central bank should have full control on commercial banks & money markets.
2. The money market of the country should be developed & organised.
3. There should be good relation between the Central Bank & other bank.

VII. Publicity-The credit creation is based on the state of mind of the people. Sometimes the Central Bank makes publicity and educates the people to control credit expansion. For this purpose central bank issues weekly statistics, periodical review of the money market condition, etc.

VIII. Selective credit control-Sometimes some selective measures such as differential discount rates, regulation of consumers credit, fixing of margin are adopted for the purpose of credit control.

IX. Direct action-The central bank is so powerful that it may take direct action against the commercial banks for their activities which lead to credit expansion for example-Central Bank refuses to rediscount for banks whose credit policy is not in accordance with the wishes of the central bank of whose borrowings from the central bank are excess in relation to their capital & reserve. The commercial banks by the central bank. In this regard various legislative measures are taken to regulate the credit.

From the above methods of credit control, it is clear that every method has its own importance. But in modern economy the importance of quantitative methods is increasing constantly.

Question 27.
What do you mean by Exchange Rare ? Explain the main factors which determine exchange rate.
Answer:
Foreign exchange rate : Meaning-Foreign exchange rate refers to the rate at which one unit of currency of a country can be exchanged for the number of units of currency of another country. In other words, it is the price paid in domestic currency in order to get one unit of foreign currency. In other words, exchange rate expresses the ratio of exchange between the currencies of two countries. Hence, exchange rate is the price of a currency expressed in terms of another currency.
Important definitions:

1. According to Sayers, “The price of currencies in terms of each other are called foreign exchange rate.”
2. According to Crowther, “The rate of exchange measures number of units of one currency which is exchanged in the foreign market for one unit or another.”

Causes of changes in exchange rates-The market or the current rate of exchange is subject to fluctuations due to changes in demand and supply of foreign exchange in the foreign exchange market. Some of the important factors which cause fluctuations in the rate of exchange are given as following-

1. Change in trade-The demand and supply of foreign exchange is influenced by changes in exports and imports. If exports exceed imports, demand for domestic currency increases so that rate of exchange moves in its favour. But, if imports exceed exports, the demand for foreign exchange increases and the rate of exchange will move against the country.
2. Capital movements-Short-term or long-term capital movements also influence the exchange rate. For example, if there is a capital flow from USA for investment in India, the demand for Indian currency will increase in the foreign exchange market. As a result, the rate of exchange of India rupee in terms of US dollar will rise.
3. Sale and purchase of securities-The stock exchange transactions, i.e., the sale and purchase of foreign securities, debentures, shares, etc., influence the demand for foreign exchange, and thereby, the exchange rate.
4. Bank rate-The bank rate also influences the exchange rate. If bank rate is raised, more funds will flow into the country from abroad to earn high interest rate. As a result supply of foreign currency increases and the rate of exchange moves against the foreign exchange. Converse will be the case if the bank rate falls.
5. Speculative activities-Speculation in the foreign exchange market also influences the exchange rate. If the speculators expect a fall in the value of foreign currency, they will sell that currency. As a result, rate of exchange will move against foreign currency and in favour of home currency.
6. Political conditions-If there is political stability, strong and efficient administration foreign investment increases in the country. The demand for domestic currency will increase and the exchange rate will move in favour of the country.

Question 28.
Distinguish between Market Economy and Planned Economy.
Answer:
Following are the differences between market economy and planned economy.
Market Economy:

1. Goods and services go where they are most in demand and force market responds quickly to peoples wants and wide variety of goods services
2. No need for and overriding authority to determine allocation of goods and services,
3. Producers
   and Consumers are free to make large profit greater efficiency innovation
4. Producers and consumers are free to make changes to sait their aims,
5. It is not competent to providing certain services
6. It creates inequility of incomes.

Planned Economy :

1. There is more equal distribution of wealth and income
2. Production is for need rather than profit
3. Long term plans can be made taking into account a range of further needs such as population changes and the environment
4. Government is the employer of most workers and tells then how to do their jobs
5. Planners of ten get things wrong shortages of surpluses of some goods
6. People are poorly motivated.

Question 29.
What do you mean by Price Elasticity of Demand ? How is it measured ?
Answer:
Price elasticity of demand may be defined as the percentage change in the quantity demanded of a commodity divided by the percentage change in price of that commodity. According to Marshall. “The elasticity of demand in a market is great or small accerding as the amount demanded increase much or little for a given full in price, or diminishes much or little for a given rise in price.”

However, we can say that price elasticity of demand (PEO or Ed) is a measure used in economics to show the responsiveness, or elasticily, of the quantity demanded of a goods or service to a change in its price. More precisely it gives the percentage change in quantity demanded in response to a one percent change in price

It can be measured as follow :

1. Percentage or Propotionate Method : According to method, for calculating the elasticity of demand, proportionate change in demand is divided by proportionate or percentage hange in price.
   Ed : (-) Proportionate change in Demand / Proportionate change in price.
2. Point Method : This method is also called ‘Geomatric method’, to calculate elasilicity of demand at any point on the Demand curve, tangent to that potet is drawn, on the basis of geomatric method.
   Ed : (=) Lower Segment / upper segment
3. Total Expenditure Method : In this method, amount of changes and direction of changes in total expenditure are determined as a result of change in price of commodity.
   Total expenditure : commodity price x commodity Demand.

Question 30.
Define supply. Mention the causes which determine the supply of a commodity.
Answer:
Meaning of supply : Supply of goods refers to those quantities which a seller is ready to sell at various prices at a certain point of time. Like demand, supply is also related with a certain time and price.

Definitions :

1. According to Thomas, “The supply of goods is the quantity offered for sale in a given market
   at a given time at various prices”
2. According to Mayers, “We may define supply as a schedule of the amount of goods that would be offered for sale at all possible prices at any one instant of time, or during any one period of time (e.g., a day, a week and so on) in which conditions of supply remain the same.”

Following are the causes of supply of commodity :

1. Price of the commodity : There is a direct relationship between price of a commodity and its quantity supplied.
2. Price of Related Goods : The supply of a commodity is also indirectly affected by the price of related goods.
3. Prices of production factors : supply of a commodity is also affected by the price of factors used in the production of the commodity. It the factors price decreases, cost of production also declines, accordingly supply increases.
4. Technological level: Technological level and its change also affects supply of the commodity. Improvement in the techniques of production reduces cost of production.
5. Number of Firms : Market supply of a commodity also depends upon number of firms in the market increase in the number of frims results in the increase in the market supply.
6. Goal of the firm : If the goal of the firm is to maximise profits, more quantity of the commodity will be offered at higher price.
7. Expected Future price: Expected price change in the future also affects the supply. If the producer expects price of the commodity to rise in the near future, current supply of the commodity should reduce. On the other hand, the price is expected to fall in future, current supply increase.
8. Government policy : “Taxation and subsidy” policy of the government also affects market supply of the commodity. Increase in taxation tends to reduce the supply, while subsidies tends to reduce the producer to provide greater supply of the commodity.

Question 31.
How is National Income estimated by Value Added Method ?
Answer:
Measurement of national income by value added method. (1) value Added Method or Product Method
First Step : Identification and Classification of Productive Enterprise : At the very first step, we are to identify and classify various productive enterprises of an economy. Broadly speaking, we can classify the economy into the following three sectors :

1. 1. Primary Sector
   2. Secondary Sector
   3. Tertiary Sector.
2. Primary Sector : It is that sector which produces goods by exploiting natural resources like land, water,
   forests, mines, etc. It includes all agricultural and allied activities, such as fishing, forestry, mining and quarrying.
3. Secondary Sector : This sector is also known
   as manufacturing sector. It transforms one type of commodity into another, using men, machines and materials. For example, manufacturing of cloth from cotton or sugar from sugarcane. ‘
4. Tertiary Sector : This sector is also known as service sector which provides useful services to primary and secondary sectors. It consists of banking, insurance, transport, communication, trade and commerce etc.
   Second Step: Calculation of Net Value of Output: To estimate the net value added in each identified enterprise in first step the following estimates are calculated :
   • Value of Output
   • Value of Intermediate Consumption
   • Consumption of Fixed Capital, i.e., Depreciation.

Value of output is worked out by multiplying the amount of goods and services by each enterprise with their market prices. Value of intermediate consumption calculated by using the prices paid by the enterprises. Consumption of fixed capital is also estimated as per rule and regulations.
To arrive at the net value added by the enterprise, we have to deduct the following items from the value of output:

• Value of Intermediate Consumption
• Consumption of Fixed Capital
• Net Indirect Taxes.

In short, Value Added = Value of Output – Intermediate Consumption – Net Indirect Taxes. By adding the net value added by all the producing enterprises in an industrial sector, we obtain net value added to that industrial sector. The sum total of net values added by all the industrial sectors in the domestic territory of the country, gives us the Net Domestic Product at Factor Cost.

Hence, Net Value Added = Value Added by Primary Sector+Value Added by Secondary Sector+Value Added by Tertiary Sector.

Thrid Step : Calculation of Net Factor Income from Abroad : The third and final step in the estimation of national income is to estimate the net factor income earned from abroad and add it to the net domestic product at factor cost. This gives us the national income.
In shot, NNP_FC = NDP_FC + NFIA

Question 32.
Define central bank and explain its functions.
Answer:
Meaning of Central Bank : Central Bank of a country is the apex monetary institution which works as a pivot for the entire banking system in the economy. Central Bank as an apex monetary institution not only plays the leadership role in banking system but also puts a control on commercial banks. Central Bank frames and executes the monetary policy and is responsible for maintaining stability and economic growth in the economy.

Definitions: According to Samuelson, “Central Bank has one function. It operates to control economy, supply of money and credit.”

According to De Kock, “A Central Bank is a bank which constitutes the apex of the monetary and banking structure of its country.” According to R.P. Kent, “Central Bank is an institution, charged with the responsible of imaging the expansion and contraction of volume of money in the interest of general public welfare.”

In modern times, a proper definition of Central Bank can be given as follows :
“Central Bank is an apex institution in a country’s monetary and banking system which develops, regulates and controls the currency and credit in the country with the objective of economic development and economic stability.”
Functions of Central Bank :

(a) Monopoly in Note Issue: In modern times, central bank alone has the exclusive right to issue notes in every country of the world. The notes issued by the central bank are unlimited legal tender throughout the country.
According to De Kock, “Almost everywhere the privilege of note issue is associated with the origin and development of central banking.”

Central Bank of the country enjoys monopoly right of note issue which has following merits :

1. It imparts uniformity in monetary system
2. Control on paper currency becomes simple
3. Central bank can change money supply, i.e, maintain the flexibility in system
4. It raises public confidence in the monetary system in the economy
5. Central bank can easily control the credit creation in the economy
6. It becomes successful in maintaining internal or external price stability.

(b) Banker, Agent and Financial Advisor to the Government: Like general public government also needs various services and the central bank performs the same functions as banker to the government as a commercial bank provides to its customers. As a ‘Banker, Agent and Financial Advisor’ to the government central bank performs the following functions :
(1) As a Banker to the Government: As a banker to the government, central bank performs following functions :

• Accounts : It maintains accounts of government transactions and submits the details to the government from time to time.
• Payments : It makes payments of all government expenses from government account.
• Debt and Loans : It arranges loans from national international level and deposit them in government account.
• Payments of Debt and Interest: It arranges and makes payments of interest and the amount of matured debts on behalf of the government.
• Loan to Government: It provides short-term loans to the government whenever it is required.

(2) As an Agent to the Government: It acts as an agent to the government. All dealings of economic transactions are performed by government on behalf of the central bank. Besides, central bank represents the government in various international institutions and conferences.

(3) As a Financial Advisor to the Government: Central bank advises to the government on various economic policies like deficit financing, devaluation, trade policy, foreign exchange, etc.

(c) Bank of Banks : It performs the functions of a banks to all other banks in the country. Central bank has almost the same relation with all. others banks as a commercial bank has with its customers. Central bank keep part of the cash balance of all commercial banks as deposit with a view to meeting liabilities of these banks in times of crises.

(d) Lender of the Last Resort: As banker to the banks the central bank acts as the lender of the last resort.
In other words, in case the commercial banks fail to meet their financial requirements from other sources, they can, as a last resort, approach to the central bank for loans and advances. The central bank assists such banks through discounting of approved securities and bills of exchange.

(e) Custodian of Foreign Exchange Reserves : Central bank also acts as custodian of foreign exchange reserve It is helpful in eliminating difficulties of balance of payments and in maintaining stable exchange rate. For minimising fluctations in foreign exchange rate, central bank buys or sells foreign exchange in the market.

(f) Function of Clearing House : Central bank also performs the function of a clearing house. By cleaming house function of central bank we mean settling the claims of various banks against each other with least use of cash.

(g) Credit Control: The most important function of the central bank is to control the credit activities of the commercial banks. Credit control refers to the increase or decrease in the volume of credit money in accordance with the monetary requirement of the country. More expansion of credit money-than necessary leads to the situation of inflation.

(h) Development Related Functions : For promoting economic development central bank performs following functions :

1. It extends organised banking system and established new financial institutions
2. It ensures sufficient money supply for development activities
3. Adopts cheap money policy for inducing investment.

(I) Other Functions :

1. collection of statistics
2. Relations with International Financial Institution
3. Survey of Banks
4. Arranging seminars.

Question 33.
What is law of diminishing marginal utility ? Explain its importance and limitations.
Answer:
Law of diminishing marginal utility also called law of supply, is an important law of consumption which is universally accepted.
According to this law, as we go on utilising standard additional units of a commodity continuously, marginal utility obtained from use of every additional unit decreases. It occures or happens in all goods and services. Therefore, this law is called fundamental and universal law of satisfaction. According to marshall, The additional benefit which a person derives from a given stock of a thing diminishes with evey increase in the stock that he already has”
Conditions or Assumptions of the Law :

1. Consumption of goods should be continuous. In case of time gap, this law is not applicable.
2. Size of consumptions units should be proper. Small size of unit increases marginal utility
3. Price of available substitutes of goods should be stable
4. Income and consumptions propensity of consumer should remain constant
5. All units of consumptions should be homogeneous. In case of heterogeneity of units, law becomes in applicables.
6. No change should take place in fashion, nature and interests of consumer.

Bihar Board 12th Physics Model Papers

Bihar Board 12th Physics Model Question Paper 3 in English Medium

Instructions for the candidates :

1. Candidates are required to give answers in their own words as far as practicable.
2. Figures in the Right-hand margin indicates full marks.
3. While answering the questions, candidates should adhere to the words limit as far as practicable.
4. 15 Minutes of extra time has been allotted to read the questions carefully.
5. This question paper is divided into two sections : Section -A and Section-B
6. In Section A there are 35 Objective type questions which are compulsory, each carrying 1 mark. Darken the circle with Blue/Black ball pen against the correct option on OMR Sheet provided to you. Do not use Whitener/Liquid/ Blade/Nail on OMR Sheet, otherwise, your result will be treated as invalid.
7. In section-B, there are 18 Short answer type questions (each carrying 2 marks), out of which only 10 (ten) questions are to be answered Apart from this there are 06 Long Answer type questions each carrying 5 marks, out of which 3 questions are to be answered.
8. Use of any electronic device is prohibited.

Time : 3 Hours 15 Minute
Total Marks : 70

Objective Type Questions

There are 1 to 35 objective type questions with 4 options. Choose the correct option which is to be answered on OMR Sheet. (35 x 1 = 35)

Question 1.
Torque acting on dipole in electric field E is
\((a) \overrightarrow{\mathrm{p}} \times \overrightarrow{\mathrm{E}}
(b) \overrightarrow{\mathrm{P}} \cdot \overrightarrow{\mathrm{E}}
(c) \overrightarrow{\mathrm{E}} \times \overrightarrow{\mathrm{P}}
(d) P/E\)
Answer:
\((a) \overrightarrow{\mathrm{p}} \times \overrightarrow{\mathrm{E}}\)

Question 2.
The algebraic sum of currents meeting at a point in the electric circuit becomes
(a) Infinity
(b) Positive
(c) Zero
(d) Negative
Answer:
(c) Zero

Question 3.
The density of metal is d and sp. resistance is r. It is in the form of wire whose length is 1 and resistance is R. The resistance mass of metal should be

Answer:
(a)

Question 4.
The emf of cell is measured by
(a) Voltmeter
(b) Ammeter
(c) Galvanometer
(d) Potentiometer
Answer:
(d) Potentiometer

Question 5.
The balancing point is obtained in potentiometer by increasing the length of wire
(a) On minimum length
(b) On maximum length
(c) On the same length
(d) Indefinite
Answer:
(b) On maximum length

Question 6.
If two cells of E₁ and E₂ are balanced at length l₁ and l₂ in potentiometer wire then

Answer:
(b)

Question 7.
The phase difference between current and emf in the condition of resonance is
(a) π/2
(b) π/4
(c) π
(d) zero
Answer:
(d) zero

Question 8.
A copper ring lies in horizontal place. A bar magnet lies along its axis above the ring. The bar magnet is now released then
(a) Acceleration of the bar will be ‘g’
(b) Copper ring will go an cooling
(c) The acceleration of bar will be less than g
(d) The velocity of the bar will become upward
Answer:
(a) Acceleration of the bar will be ‘g’

Question 9.
The induced emf of rod is
(a) BLV
(b) B²L²V
(c) Zero
(d) None of these
Answer:
(c) Zero

Question 10.
The energy due to flow of current I in inductance L is
\((a) Zero
(b) \frac{1}{2} \mathrm{LI}^{2}
(c) \frac{1}{2} \mathrm{LI}
(d) \frac{1}{2} \mathrm{L}^{2} \mathrm{I}^{2}\)
(a) Zero
Answer:
\((b) \frac{1}{2} \mathrm{LI}^{2}\)

Question 11.
The power loss in A.C. circuit is
(a) only resistance
(b) only capacity
(c) only inductance
(d) All of these
Answer:
(a) only resistance

Question 12.
The unit of mutualinductance is
(a) Weber
(b) Ohm
(c) Henry
(d) Gauss
Answer:
(c) Henry

Question 13.
If the real and apparent power of A.C. circuit is PT and PA respectively then power factor is
\((a) \frac{P_{T}}{P_{A}}
(b) \mathrm{P}_{\mathrm{T}} \times \mathrm{P}_{\mathrm{A}}
(c) \frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{T}}}
(d) \mathrm{P}_{\mathrm{A}}+\mathrm{P}_{\mathrm{T}}$\)
Answer:
\((a) \frac{P_{T}}{P_{A}}\)

Question 14.
Which have minimum wave length in the following?
(a) x-ray
(b) y-ray
(c) Micro wave
(d) Radio-wave
Answer:
(b) y-ray

Question 15.
A Thin prism \(\left(\mu=\frac{3}{2}\right)\) in air is immersed in water \(\left(\mu=\frac{6}{4}\right)\). The ratio of angle of deviation in both condition will be
\((a) \frac{15}{8}
(b) \frac{8}{15}
(c) \frac{5}{2}
(d) \frac{2}{5}\)
Answer:
\((c) \frac{5}{2}\)

Question 16.
The refractive index of material of prism is ^3 • The minimum deviation for this prism is :
(a) 30°
(b) 37°
(c) 45°
(d) 60°
Answer:
(d) 60°

Question 17.
The cause of coloured thin film is
(a) Scattering
(b) Interference
(c) Dispersion
(d) Diffraction
Answer:
(b) Interference

Question 18.
The radius of curvature of double convex lens is 20cm and μ = 1.5 then its power is
(a) 5D
(b) 10D
(c) 25D
(d) 20D
Answer:
(a) 5D

Question 19.
The vertical section of cornea is not symmetrical about their axis. The defects of vision in eye is called
(a) Short sightedness
(b) Hypermetropia
(c) Presbyopia
(d) Astigmatism
Answer:
(c) Presbyopia

Question 20.
The radius of curvature of plane mirror is
(a) Infinity
(b) Zero
(c) +5 cm
(d) -5 cm
Answer:
(a) Infinity

Question 21.
The ratio of intensity of two waves is 9:1 produces interference. The ratio of maximum and minimum intensity will be
(a) 10 : 8
(b) 9 : 1
(c) 4 : 1
(d) 2 : 1
Answer:
(c) 4 : 1

Question 22.
If the frequency of photon incident on the metallic surface becomes double then maximum kinetic energy of emitted electrons will be
(a) double
(b) more than double
(c) not change
(d) none of these
Answer:
(b) more than double

Question 23.
The photo electric effect supports
(a) Wave nature of light
(b) Particle nature of light
(c) Dual nature of light
(d) None of these
Answer:
(a) Wave nature of light

Question 24.
The electron in hydrogen atom comes from third orbit to second orbit, then released energy is
(a) 1.5 leV
(b) 3.4 eV
(c) 1.89 eV
(d) 0.54 eV
Answer:
(c) 1.89 eV

Question 25.
The angular momentum of electron in hydrogen atom in lowest energy level is
\((a) \frac{h}{\pi}
(b) \frac{h}{2 \pi}
(c) \frac{2 \pi}{h}
(d) \frac{\pi}{h}\)
Answer:
\((b) \frac{h}{2 \pi}\)

Question 26.
In nuclear reactor the controlling rods are made up
(a) of Cadmium
(b) of Uranium
(c) of Graphite
(d) of Plutonium
Answer:
(a) of Cadmium

Question 27.
Which is unstable?
(a) neutron
(b) proton
(c) electron
(d) α-particle
Answer:
(a) neutron

Question 28.
The Boolean expression of NOR gate is
(a) A + B = y
(b) \(\overline{\mathrm{A.B}}=y\)
(c) A.B = y
(d) \(\overline{\mathrm{A+B}}=y\)
Answer:
\((d) [latex]\overline{\mathrm{A+B}}=y\)

Question 29.
In figure logic gate is

(a) OR
(b) NOR
(c) NAND
(d) AND
Answer:
(d) AND

Question 30.
The majority current carrier in p-type semiconductor is
(a) electron
(b) hole
(c) photon
(d) proton
Answer:
(b) hole

Question 31.
The semi conductor behaves at absolute temperature
(a) fully conductor
(b) fully insulator
(c) super conductor
(d) semi conductor
Answer:
(b) fully insulator

Question 32.
The conduction band are empty in
(a) Insulator
(b) Semi conductor
(c) In metal
(d) None of these
Answer:
(b) Semi conductor

Question 33.
Which is not the example of digital communications?
(a) E-mail
(b) Cellular phone
(c) Television
(d) Communication satellite
Answer:
(c) Television

Question 34.
The value of amplitude modulation index is
(a) Always zero
(b) between 1 and
(c) Between 0 and 1
(d) Always infinity
Answer:
(c) Between 0 and 1

Question 35.
The relation between a and P in transistor is

Answer:
(b)

Non-Objective Type Questions
Short Answer Type Questions-

Q.No. 1 to 18 are short answers type question. Each question carries 2 marks. Answer any ten (10) question.

Question 1.
What is Electrostatic shielding?
Answer:
The electrostatic shielding is the best way to protect some area in vaccum from the influence of external electric field. ,
The technique of electrostatic shielding is applied basically in designing the cable for television.

Question 2.
What is polar and non polar dielectrics?
Answer:
Non-Polar dielectric :
A dielectric, in the atom or molecule of which, the centre of gravity of positive and negative charge coincide is called non-polar dielectric. Due to zero separation between +ve and -ve charges the electric dipole moment of such atom or molecules is zero.

Polar dielectric :
A dielectric, in the atom or molecules of which the centre of gravity of +ve and -ve charge do not coincide, is called polar dielectric

eg-NH₃, HC1, H₂O, CO₂ etc.

Due to finite separation +ve and -ve charges, such atoms or molecules possess a finite electric dipole moment.

Question 3.
What is current density? Write its S.I. unit and dimension.
Answer:
Current per unit area is called current density. It is denoted by ‘J’
\(\mathrm{J}=\frac{1}{\mathrm{A}}\)

It is a vector quantity
S.I. unit : Ampere/m²
Dimension : [M°L^-2 T°]

Question 4.
Write two factors on which resistivity of conductor depends.
Answer:
The resistivity of conductor depends upon following factors :

• It depends upon temperature,
• It depends upon nature of substance of conductor.

Question 5.
Calculate the value of I in given circuit.

Answer:
According to figure
R₁ and R₂ are in series
R_s = R₁ + R₂
R_s = 30 + 30 = 60Ω
Now, R₃ and R_s are in parallel

Question 6.
Write Lenz’s law for electromagnetic induction.
Answer:
Lenz’s law: This law states that whenever electric current is produced in circuit or in coil due to electromagnetic induction then it opposes that causes due to which it is produced.
\(\mathrm{e}=-\mathrm{n} \frac{\mathrm{d} \phi}{\mathrm{dt}}\)
e = induced emf

This law obeys the principle of Conservation of Energy.

Question 7.
Write two applications of ultraviolet waves.
Answer:

• They are used to preserve food stuff and make drinking water free from bacteria, as these rays can kill bacteria, germs etc.
• They are used for sterlizing surgical instruments.

Question 8.
The power of two lens are 12 D and -2D are kept in contact. What is the focal length of combination.?
Answer:
Power of combination P = P₁ + P₂
P = 12 – 2 = 10
Focal length of combination
\(f=\frac{1}{p}=\frac{1}{10} \times 100=10 \mathrm{cm} ; f=10 \mathrm{cm}\)

Question 9.
Write Brewter’s law.
Answer:
This law states that when the unpolarised light is incident on the surface on polarising angle then refractive index of medium is equal to tangent of polarising angle.
\(\mu=\tan i_{p}\)

Question 10.
State properties of photon.
Answer:
Properties of photon are as follows :

• A photon travels with a speed of light in vacuum.
• A photon has zero rest mass.

Question 11.
State two uses of photo diode.
Answer:

• They are used as photo detectors to detect intensity of radiation.
• They are used as light operated switches.

Question 12.
What is Binding Energy per nucleon?
Answer:

• The binding energy per nucleon of a nucleus is the binding energy divided by the total number of nucleons.

B.E./Nucleon =
\(\frac{\Delta m \times 931 \mathrm{ev}}{\Delta}\)

Question 13.
What are limitations of amplitude modulation?
Answer:

• The quality of audio signal is not good,
• The atmospheric and industrial noise affect the audio signal,
• The efficiency of amplitude modulation is low.

Question 14.
Write the differences between N-type and P- type semi-conductor.
Answer:
N-type :

• when pentavalent impurity atom like As, Sb etc. are added in the intrinsic semi-conductor we get N- type of semi-conductor.
• The majority carriers in the N-type semi-conductor are electrons and minority carriers are hole.
• n_e >> n₀

P-type:

• When invalent impurity atoms like Gallium, Indium etc. are added in the intrinsic semi-condcutor we get p-type of semi conductors.
• The majority carriers in P-type semiconductor are holes and minority carriers are electrons.
• n_h >>n_e

Question 15.
What are base band and band width?
Answer:
Base Band:
In telecommunication and signal processing it describes channel and system what range of frequency is measured from zero Hz to cut off frequency.

Band Width :
It refers to the frequency range our which as equipotent rates on the portion of spectrum occupied by the signal.

Question 16.
Define Electric Intensity. Write its S.I. unit and dimension.
Answer:
Electric Intensity :
The electric intensity at a point in the electric field is defined as the force which is experienced by unit positive charge placed at the point. It is denoted by \(\vec{E}\)
\(\vec{E}=\frac{\vec{F}}{q_{0}}\)

S.I. unit : Newton/Coulomb
or
Volt/metre
Dimension : [MLT³I^-1]

Question 17.
Write properties of electric lines of force.
Answer:

• The electric lines of force originated from positive charge and terminate on negative charge.
• The electric lines of force never intersect to each other.

Question 18.
Why internal resistance of secondary cell is low?
Answer:
As in secondry cell, distance between two plates is greater and their size are big. There is no polarisation in secondary cell. Due to this, internal resistance of secondary¬cell is 10w.

Long Answer Type Questions

Q.No. 19 to 24 are long answers type question. Each question of this category carries 5 marks. Answer any three (3) question. (3 x 5 = 15)

Question 19.
State and Prove Gauss’s Theorem in electrostatics.
Answer:
Statement of Gauss’s Theorem : The net- outward normal electric flux through any closed surface of any shape is equal to l/ε₀ times the total charge contained within that surface i.e.

where indicates the surface integral over the whole

of the closed surface. Σ_q is the algebraic sum of all the charges (i.e. net charge in Coulombs) enclosed by surface S.

Proof of Gauss’s Theorem :
Let a point charge + q coulomb be placed at O within the closed surface. Let E be the electric field strength at P. Let OP=r and the permitivity of free space or vacuum be e0.

Consider a small area’ \(\overrightarrow{d S}\) of the surface surrounding the point P. Then the electric flux through \(\overrightarrow{d S}\) is given by

subtended by area dS at point O. Here 0 is the angle between \(\overrightarrow{d S}\) and \(\overrightarrow{E}\)

Hence electric flux through whole of the closed surface.
\(\phi=\oint_{S} \overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{dS}}=\frac{q}{4 \pi \varepsilon_{0}} \times \oint d \Omega\)

But \(\oint d \Omega\) is the solid angle due to the entire closed surface S at an internal point O = 4π
∴ \( \quad \phi=\frac{q}{4 \pi \varepsilon_{0}} \cdot 4 \pi=\frac{1}{\varepsilon_{0}} q\)

It there are several charges, + q₁, + q₂, + q₃ + q₁ – q₂ – q₃ ………… inside the closed surface, each will contribute to the total electric flux. For positive charges the flux will be outward and hence positive; for negative charges the flux will be inward and negative. Therefore, the total electric flux in such a case

where Zq is the algebraic sum of the charges within the closed surface.

Hence total electric flux through any closed surface is equal to l/e0 times the total charge (in Coulomb) enclosed within the surface which is Gauss’s law.

Question 20.
Find an expression for the capacitance of a parallel plate capacitor when a dielectric slab of dielectric constant K and thickness \(t=\frac{d}{2}\) but of same area on the plates is inserted between the capacitor plate. (d = separation between the plates).
Answer:
Consider a paralled plate capacitor, area of each plate being A, the separation between the plates being d. Let a dielectric slab of dielectric constant K and thickness t < d be placed between the plates. The thickness of air between the plates is (d – t). If charges on plates are + Q and -Q, then surface charge density

The electric field between the plates in air,
\(\mathrm{E}_{1}=\frac{\sigma}{\varepsilon_{0}}=\frac{Q}{\varepsilon_{0} \mathrm{A}}\)

The electric field between the plates in slab,
\(\mathrm{E}_{2}=\frac{\sigma}{\mathrm{K} \varepsilon_{0}}=\frac{Q}{\mathrm{K} \varepsilon_{0} \mathrm{A}}\)

∴ The potential difference between the plates VAB = work done in carrying unit positive charge from one plate to another
= Σex (as field between the plates is not constant).

∴ Capacitance of capacitor.

Question 21.
State Biot-Savart law, giving the mathematical expression for it.
Use this law to derive the expression for the magnetic field due to a circular coil carrying current at a point along it axis.
How does a circular loop carrying current behave as a magnet?
Answer:
(i) Magnetic field at the axis of a circular loop : Consider a circular loop of radius R carrying current I, with its plane perpendicular to the plane of paper. Let P be a point of observation on the axis of this circular loop at a distance x from its centre O. Consider a small element of length dl of the coil at point A. The magnitude of the magnetic induction \(\overrightarrow{\mathrm{dB}}\) at point P due to this element is given by

The direction of \(\overrightarrow{\mathrm{dB}}\) is perpendicular to the plane containing \(\overrightarrow{\mathrm{dl}}\) and \(\overrightarrow{\mathrm{r}}\) is given by right hand screw rule. As the angle between \(\overrightarrow{\mathrm{dl}}\) and \(\overrightarrow{\mathrm{r}}\) is 90°, the magnitude of the magnetic induction \(\overrightarrow{\mathrm{dB}}\) is given by,
\(\overrightarrow{\theta B}=\frac{\mu_{0} t}{4 \pi} \frac{d \sin 9 \sigma^{0}}{r^{2}}=\frac{\mu_{0} d t^{2}}{4 \pi^{2}}\) …….(ii)

If we consider the magnetic induction produced by the whole of the circular coil, then by symmetry the components of magnetic induction perpendicular, to the axis will be cancelled out, while those parallel to the axis will be added up. Thus the resultant magnetic induction \(\overrightarrow{\mathrm{B}}\) at axial point P is along the axis and may be evaluated as follows :

The component of \(\overrightarrow{\mathrm{dB}}\) along the axis,

Therefore the magnitude of resultant magnetic induction at axial point P due to the whole circular coil is given by

Question 22.
Derive an expression for the force per unit length between two long straight parallel current carrying conductors. Hence define S.I. unit of current (ampere).
Answer:
Suppose two long thin straight conductors (or wires) PQ and RS are placed parallel to each other in vacuum (or air) carrying currents I₁ and I₂ respectively. It has been observed experimentally that when the current in the wire are in the same direction, they experience an attractive force (fig. a) and when they carry currents in opposite directions, they experience a repulsive force (fig. b). Let the conductors PQ and RS carry currents I₁ and I₂ in same direction and placed at separation r. (fig). Consider a current-element ‘ab’ of length AL of wire RS. The magnetic field produced by current-carrying conductor PQ at the location of other wire RS.

\(\mathrm{B}_{1}=\frac{\mu_{0} \mathrm{l}_{1}}{2 \pi r}\) ……………………… (i)

According to Maxwell’s right hand rule or right hand palm rule no. I, the direction of B l will be perpendicular to the plane of paper and directed downward. Due to this magnetic field, each element of other wire experiences a force. The direction of current element is perpendicular to the magnetic field; therefore the magnetic force on element ab of length ΔL.
\(\Delta F=\mathrm{B}_{x} \mathrm{I}_{2} \Delta \mathrm{L} \sin 90^{\circ}=\frac{\mu_{0} \mathrm{I}_{1}}{2 \pi r} \mathrm{I}_{2} \Delta \mathrm{L}\)

∴ The total force on conductor of length L will be
\(\mathrm{F}=\frac{\mu_{0} \mathrm{I}_{1} \mathrm{I}_{2}}{2 \pi r} \Sigma \Delta \mathrm{L}=\frac{\mu_{0} \mathrm{I}_{1} \mathrm{I}_{2}}{2 \pi r} \mathrm{L}\)

∴ Force acting on per unit length of conductor
\(f=\frac{F}{L}=\frac{\mu_{0} I_{1} I_{2}}{2 \pi r} N / m\)

According to Flemming’s left hand rule, the direction of magnetic force will be towards PQ i.e., the force will be attractive.

On the other hand if the currents I₁ and I₂ in wires are in opposite directions, the force will be repulsive. The magnitude of force in each case remains the same.

Definition of S.I. unit of Current (ampere):
In S.I. system of fundamental unit of current ‘ampere’ has been define assuming the force between the two currents carrying wires as standard.

The force between two parallel currents carrying conductors of separation r is

Thus I ampere is the current which when flowing in each of parallel conductors placed at separation I m in vacuum exert a force of 2 x 10^-7 on 1 m length of either wire.

Question 23.
With the help of a ray diagram, show the formation of image of a point object by refraction of light at a spherical surface separating two media of refractive indices n₁ and n₂ (n₂ > n₁), respectively. Using this diagram, derive the relation \(\frac{n_{2}}{v}-\frac{n_{1}}{u}=\frac{n_{1}-n_{1}}{R}\)

Write the sign conventions used. What happens to the focal length of convex lens when it is immersed in water?
Answer:
Formula for Refraction at Spherical Surface Concave Spherical Surface :
Let SPS’ be a spherical refracting surface, which separates media ‘1’ and ‘2’. Medium ‘ 1’ is rarer and medium ‘2’ is denser. The refractive indices of media ‘1’ and ‘2’ are n₁ and n₂ respectively (n₁ < n₂). Let P be the pole and C the centre of curvature and PC the principal axis of spherical refracting surface.

O is a point-object on the principal axis. An incident ray OA, after refraction at A on the spherical surface bends towards the normal OAN and moves along AB. Another incident ray OP falls on the surface normally and hence passes undeviated after refraction. These two rays, when produced backward meet at point I on principal axis. Thus I is the virtual image of O.

Let angle of incidence of ray OA be / and angle of refraction be r i.e.

If point A is very near to P, then angles i, r, a, P, Y will be very small, therefore sin i = i and sin r = r
From equation (iii)
\(\frac{i}{r}=\frac{n_{2}}{n_{1}}\)
Substituting values of i and r from (i) and (ii) we get
\(\frac{\gamma-\alpha}{\gamma-\beta}=\frac{n_{2}}{n_{1}} \text { or } n_{1}(\gamma-\alpha)=n_{2}(\gamma-\beta) \quad \ldots \text { (iv) }\)

The length of perpendicular AM dropped from A on the principal axis is h, i.e. AM = h. As angles a, P and y are very small, therefore
tana = α, tan β = β, tan γ = γ
Substituting these values in equation (iv)
n1 (tanY-tanoO = /j2(tanY-tanP) ……………. (v)
As point A is very close to P, point M is coincident with F

Let u, v and R be the distance of object O, image I and centre of curvature C from pole P. By sign convention PO, PI and PC are negative i.e. u = – PO, v = – PI and R = – PC

Substituting these values in (vii) we get

Question 24.
Derive Einstein’s photoelectric equation ^
\(\frac{1}{2}\)
\(m v^{2}=h v-h v_{0}\)
Answer:
Einstein’s Explanation of Photoelectric Effect: Einstein’s Photoelectric Equation :

Einstein explained photoelectric effect on the basis of quantum theory.

The main points are :

1. Light is propagated in the form of bundles of energy. Each bundle of erergy is called a quantum or photon and has energy hv, where h = Plank’s constant and v = frequency of light.

2. The photoelectric effect is due to collision of a photon of incident metal light and a bound electron of the metallic cathode.

3. When a photon of incident light falls on the metallic surface, it is completely absorbed. Before being absorbed it penetrates through a distance of nearly 10-8 m (or 100 A). The absorbed photon transfers its whole energy to a single electron. The energy of photon goes in two parts : a part of energy is used in releasing the electron from the metal surface (i.e., in overcoming work function) and the remaining part appears in the form of kinetic energy of the same electron.

If v be the frequency of incident light, the energy of photon = hv. If W be the work function of metal and Ek the maximum kinetic energy of photoelectron, then according to Einstein’s explanation.

hv = W + EK
or, EK = hv – W …………………….(i)

This is called Einstein’s photoelectric equation.

If v₀ be the threshold frequency, then if frequency of incident light is less then v0, no electron will be emitted and if the frequency of incident light be v0, then E_k = 0; so from equation (i)
0 = hv₀ – W or W = hv₀

If λ₀ be the threshold wavelength, then \(v_{0}=\frac{c}{\lambda_{0}}\), where c is the speed of light in vacuum.

∴ Work function
\(\mathrm{W}=h v_{0}=\frac{h c}{\lambda_{0}}\) ………………… (ii) Substituting this value in equation (i), we get
E_k = hv – hv₀ ……………….(iii)
This is another form of Einstein’s photoelectric equation.

Bihar Board 12th Biology Objective Questions and Answers

Bihar Board 12th Biology Objective Answers Chapter 2 Sexual Reproduction in Flowering Plants

Question 1.
Science of cultivation, breeding, marketing and arrangement of flowers is called
(a) arboriculture
(b) floriculture
(c) horticulture
(d) anthology
Answer:
(b) floriculture

Question 2.
Nonessential floral organs in a flower are
(a) sepals and petals
(b) anther and ovary
(c) stigma and filament
(d) petals only.
Answer:
(a) sepals and petals

Question 3.
The stamens represent
(a) microsporangia
(b) male gametophyte
(c) male gametes
(d) microsporophylls.
Answer:
(d) microsporophylls

Question 4.
Anther is generally
(a) monosporangiate
(b) bisporangiate
(c) letrasporangiate
(d) trisporangiate.
Answer:
(c) letrasporangiate

Question 5.
The anther wall consists of four wall layers where
(a) tapetum lies just inner to endothecium
(b) middle layers lie between endothecium and tapetum
(c) endothecium lies inner to middle layers
(d) tapetum lies next to epidermis.
Answer:
(b) middle layers lie between endothecium and tapetum

Question 6.
The innermost layer of anther is tapetum whose function is
(a) dehiscence
(b) mechanical
(c) nutrition
(d) protection.
Answer:
(c) nutrition

Question 7.
Callase enzyme which dissolves callose of pollen tetrads to separate four pollens is provided by
(a) pollens
(b) tapetum
(c) middle layers
(d) endothecium.
Answer:
(b) tapetum

Question 8.
In angiosperms various stages of reductional division can best be studied in
(a) young anthers
(b) mature anthers
(c) young ovules
(d) endosperm cells.
Answer:
(a) young anthers

Question 9.
Study of pollen grains is called
(a) micrology
(b) anthology
(c) palynology
(d) pomology
Answer:
(c) palynology

Question 10.
Several pollen grains form a unit designated as pollinium in Family
(a) Asteraceae
(c) Asclepiadaceae Pollen
(b) Cucurbitaceae
(d) Brassicaceae
Answer:
(c) Asclepiadaceae Pollen

Question 11.
Pollen grain is a
(a) megaspore
(b) microspore
(b) microspore
(d) microsporangium.
Answer:
(b) microspore

Question 12.
How many pollen mother cells should undergo meiotic division to produce 64 pollen grains ?
(a) 64
(b) 32
(c) 16
(d) 8
Answer:
(c) 16

Question 13.
How many meiotic divisions are required for the formation of 100 pollen grains ?
(a) 100
(b) 50
(c) 25
(d) 26
Answer:
(c) 25

Question 14.
One of the most resistant biological material present in the exine of pollen grain is
(a) pectocellulose
(b) sporopollenin
(c) suberin
(d) cellulose.
Answer:
(b) sporopollenin

Question 15.
What is the function of germ pore ?
(a) Emergence of radicle
(b) Absorption of water for seed germination
(c) Initiation of pollen tube
(d) All of these .
Answer:
(c) Initiation of pollen tube

Question 16.
_______of the pollen grain divides to form two male gametes.
(a) Vegetative cell
(b) Generative cell
(c) Microspore mother cell
(d) None of these
Answer:
(b) Generative cell

Question 17.
The three cells found in a pollen grain when it is shed at 3-celled stage are
(a) 1 vegetative cell, 1 generative cell, 1 male gamete
(b) 1 vegetative cell, 2 male gametes
(c) 1 generative cell, 2 male gametes
(d) either (a) or (b).
Answer:
(b) 1 vegetative cell, 2 male gametes

Question 18.
Megasporangium along with its protective integuments is called
(a) ovary
(b) ovule
(c) funicle
(d) chalaza
Answer:
(b) ovule

Question 19.
Mature ovules are classified on the basis of funiculus. If micropyle comes to lie close to the funiculus the ovule is termed as
(a) orthotropous
(b) anatropous
(c) hemitropous
(d) campylotropous
Answer:
(b) anatropous

Question 20.
When micropyle, chalaza and hilum lie in a straight line, the ovule is said to be
(a) anatropous
(b) orthotropous
(c) amphitropous
(d) campylotropous.
Answer:
(b) orthotropous

Question 21.
What is the function of filiform apparatus in an angiospermic embryo sac?
(a) Brings about opening of the pollen tube
(b) Guides the pollen tube into a synergid
(c) Prevents entry of more than one pollen tube into a synergid
(d) None of these
Answer:
(b) Guides the pollen tube into a synergid

Question 22.
The female gametophyte of a typical dicot at the time of fertilisation is
(a) 8 – celled
(b) 7 – celled
(c) 6 – celled
(d) 5 – celled
Answer:
(b) 7 – celled

Question 23.
Polygonum type of embryo sac is
(a) 8 – nucleate, 7 – celled
(b) 8 – nucleate, 8 – celled
(c) 7 – nucleate, 7 – celled
(d) 4 – nucleate, 3 – celled
Answer:
(a) 8 – nucleate, 7 – celled

Question 24.
Both chasmogamous and cleistogamous flowers are present in
(a) Helianthus
(b) Commelina
(c) Rosa
(d) Gossypium
Answer:
(b) Commelina

Question 25.
Even in absence of pollinating agents seed-setting is assured in
(a) Commelina
(b) Zostera
(c) Salvia
(d) Fig
Answer:
(a) Commelina

Question 26.
Male and female flowers are present on different plants (dioecious) to ensure xenogamy, in
(a) papaya
(b) bottle gourd
(c) maize
(d) all of these.
Answer:
(a) papaya

Question 27.
Feathery stigma occurs in
(a) pea
(b) wheat
(c) Datura
(d) Caesalpinia
Answer:
(b) wheat

Question 28.
Plants with ovaries having only one or a few ovules are generally pollinated by
(a) bees
(b) butterflies
(c) birds
(d) wind
Answer:
(d) wind

Question 29.
Which of the following is not a water pollinated plant ?
(a) Zostera
(b) Vallisneria
(c) Hydrilla
(d) Cannabis
Answer:
(d) Cannabis

Question 30.
Spiny or sticky pollen grains and large, attractively coloured flowers are associated with
(a) hydrophily
(b) entomophily
(c) ornithophily
(d) anemophily
Answer:
(b) entomophily

Question 31.
Fragrant flowers with well developed nectaries are an adaptation for
(a) hydrophily
(b) anemophily
(c) entomophily
(d) none of these
Answer:
(c) entomophily

Question 32.
Pollen kitt is generally found in
(a) anemophilous flowers
(b) entomophilous flowers
(c) ornithophilous flowers
(d) malacophilous flowers
Answer:
(b) entomophilous flowers

Question 33.
Which of these is a condition that makes flowers invariably autogamous ?
(a) Dioecy
(b) Self incompatibility
(c) Cleistogamy
(d) Xenogamy
Answer:
(c) Cleistogamy

Question 34.
Heterostyly as a contrivance for cross-pollination is found in
(a) Pennisetum
(b) Impatiens
(c) Primula vulgaris
(d) Oenothera
Answer:
(c) Primula vulgaris

Question 35.
The part of gynoecium that determines the compatible nature of pollen is
(a) stigma
(b) style
(c) ovary
(d) synergids
Answer:
(a) stigma

Question 36.
Part of the gynoecium which receives the pollen is called
(a) style
(b) stigma
(c) ovule
(d) ovary
Answer:
(b) stigma

Question 37.
Growth of pollen tube towards embryo sac is
(a) chemotropic
(b) thigmotaxis
(c) geotropic
(d) none of these
Answer:
(a) chemotropic

Question 38.
During the process of fertilisation the pollen tube of the pollen grain usually enters the embryo sac through
(a) integument
(b) nucellus
(c) chalaza
(d) micropyle
Answer:
(d) micropyle

Question 39.
Fusion of one of the male gametes with egg nucleus is referred to as
(a) generative fertilisation
(b) syngamy
(c) vegetative fertilisation
(d) both (a) and (b)
Answer:
(d) both (a) and (b)

Question 40.
The total number of nuclei involved in double fertilisation in angiospersm are
(a) two
(b) three
(c) four
(d) five
Answer:
(d) five

Question 41.
Triple fusion in Capsella bursa pastoris is fusion of male gamete with
(a) egg
(b) synergid
(c) secondary nucleus
(d) antipodal.
Answer:
(c) secondary nucleus

Question 42.
Double fertilisation was first discovered in 1898 by _______ in Fritillaria and Lilium.
(a) Nawaschin
(b) Strasburger
(c) Amici
(d) Focke
Answer:
(a) Nawaschin

Question 43.
If an endosperm cell of an angiosperm contains 24 chromosomes, the number of chromosomes in each cell of the root will be
(a) 8
(b) 4
(c) 16
(d) 24
Answer:
(c) 16

Question 44.
The cells of endosperm have 24 chromosomes. What will be the number of chromosomes in the gametes ?
(a) 8
(b) 16
(c) 23
(d) 32
Answer:
(a) 8

Question 45.
The true embryo develops as a result to fusion of
(a) two polar nuclei of embryo sac
(b) egg cell and male gamete
(c) synergid and male gamete
(d) male gamete and antipodals.
Answer:
(b) egg cell and male gamete

Question 46.
Father of Indian embryology is
(a) P. Maheshwari
(b) Swaminathan
(c) R. Misra
(d) Butler
Answer:
(a) P. Maheshwari

Question 47.
The portion of embryonal axis between plumule (future shoot) and cotyledons is called
(a) hypocotyl
(b) epicotyl
(c) coleorhiza
(d) coleoptile.
Answer:
(b) epicotyl

Question 48.
Coleoptile and coleorhiza are the protective sheaths _______ covering _______ and _______ respectively.
(a) plumule, epicotyl
(b) radicle, plumule
(c) plumule, radicle
(d) radicle, hypocotyl
Answer:
(c) plumule, radicle

Question 49.
_______ is not an endospermic seed.
(a) Pea
(b) Castor
(c) Maize
(d) Wheat
Answer:
(a) Pea

Question 50.
Endosperm is completely consumed by the developing embryo in
(a) pea and groundnut
(b) maize and castor
(c) castor and groundnut
(d) maize and pea.
Answer:
(a) pea and groundnut

Question 51.
Endospermic seeds are found in
(a) castor
(b) barley
(c) coconut
(d) all of these
Answer:
(d) all of these

Question 52.
In albuminous seeds, food is stored in _______ and in non albuminous seeds, it is stored in _______.
(a) endosperm, cotyledons
(b) cotyledons, endosperm
(c) nucellus, cotyledons
(d) endosperm, radicle
Answer:
(a) endosperm, cotyledons

Question 53.
Persistent nucellus is called as _______ and is found in _______.
(a) perisperm, black pepper
(b) perisperm, groundnut ‘
(c) endosperm, black pepper
(d) endosperm groundnut
Answer:
(a) perisperm, black pepper

Question 54.
Indentify the wrong statement regarding post-fertilisation development.
(a) The ovary wall develops into pericarp.
(b) The outer integument of ovule develops into tegmen.
(c) The fusion nucleus (triple nucleus) develops into endosperm.
(d) The ovule develops into seed.
Answer:
(b) The outer integument of ovule develops into tegmen.

Question 55.
Polyembryony commonly occurs in
(a) banana
(b) tomato
(c) potato
(d) citrus.
Answer:
(d) citrus.

Question 56.
An embryo may sometimes develop from any cell of embryo sac other than egg. It is termed as
(a) apospory
(b) apogamy
(c) parthenogenesis
(d) parthenocarpy
Answer:
(b) apogamy

Question 57.
Embryo sac is to ovule as _______ is to an anther.
(a) Stamen
(b) filament
(c) pollen grain
(d) androecium
Answer:
(c) pollen grain

Question 58.
The outermost and innermost wall layers of microsporangium in an anther are respectively
(a) endothecium and tapetum
(b) epidermis and endodermis
(c) epidermis and middle layer
(d) epidermis and tapetum.
Answer:
(d) epidermis and tapetum.

Question 59.
During microsporogenesis, meiosis occurs in
(a) endothecium
(b) microspore mother cells
(c) microspore tetrads
(d) pollen grains
Answer:
(b) microspore mother cells

Question 60.
From among the sets of terms given below, identify those that are associated with the gynoecium.
(a) Stigma, ovule, embryo sac, placenta
(b) Thalamus, pistil, style, ovule
(c) Ovule, ovary, embryo sac, tapetum
(d) Ovule, stamen, ovary, embryo sac
Answer:
(a) Stigma, ovule, embryo sac, placenta

Question 61.
Starting from the innermost part, the correct sequence of parts in an ovule are
(a) egg, nucellus, embryo sac, integument
(b) egg, embryo sac, nucellus, integument
(c) embryo sac, nucellus, integument, egg
(d) egg. integument, embryo sac, nucellus.
Answer:
(b) egg, embryo sac, nucellus, integument

Question 62.
The phenomenon wherein, the ovary develops into a fruit without fertilisation is called
(a) parthenocarpy
(b) apomixis
(c) asexual reproduction
(d) sexual reproduction
Answer:
(a) parthenocarpy