Bihar Board 12th Maths VVI Objective Questions Model Set 3 in English

Bihar Board 12th Maths Objective Questions and Answers

Bihar Board 12th Maths VVI Objective Questions Model Set 3 in English

Question 1.

Answer:
(a) \(\frac{\pi}{4}\)

Question 2.
The slope of the tangent to the curve X = t² + 3t – 8, Y = 2t² – 2t – 5 at the point (2, -1) is
(a) \(\frac{12}{7}\)
(b) \(\frac{-6}{7}\)
(c) \(\frac{6}{7}\)
(d) \(\frac{-12}{7}\)
Answer:
(c) \(\frac{6}{7}\)

Question 3.
The modulus of the vector \(19 \overrightarrow{1}+5 \vec{J}-6 \vec{k}\) is
(a) √322
(b) √420
(c) √421
(d) √422
Answer:
(d) √422

Question 4.
\(\int_{0}^{\frac{\pi}{2}} \cos x d x=?\)
(a) -1
(b) 1
(c) \(\frac{\pi}{2}\)
(d) 0
Answer:
(a) -1

Question 5.
The direction cosines of z-axis are
(a) (0, 0, 0)
(b) (1, 0, 0)
(c) (0, 1, 0)
(d) (0, 0, 1)
Answer:
(d) (0, 0, 1)

Question 6.

Answer:
(a) \(\frac{1}{\sqrt{1-x^{2}}}\)

Question 7.
\(\vec{K} \times \vec{K}=?\)
(a) 1
(b) -1
(c) K²
(d) 0
Answer:
(d) 0

Question 8.
Integrating factor of the differential equation \(\frac{d y}{d x}\) + Y sec x = tan x is
(a) sec x + tan x
(b) sec x – tan x
(c) sec x
(d) tan x sec x
Answer:
(c) sec x

Question 9.
Intergrating factor (I.F) of the differential equation \(\frac{d y}{d x}\) + Y cos x = sin x cos x is
(a) e^{-sin x}
(b) e^{sin x}
(c) e^{-cos x}
(d) e^{cos x}
Answer:
(c) e^{cos x}

Question 10.

Answer:
(a) \(\sin ^{-1} \frac{2 x}{1+x^{2}}\)

Question 11.

Answer:
(d) \(\frac{5}{8}\)

Question 12.
If f(x₁) = f(x₂) ⇒ x₁ = x₂ ∀ x₁, x₂ ∈ A, then what type of a function is f : A → B ?
(a) One-one
(b) Constant
(c) Onto
(d) Many one
Answer:
(a) One-one

Question 13.
\((\vec{a} \times \vec{a}) \cdot \vec{b}=?\)
(a) 1
(b) -1
(c) 2
(d) 0
Answer:
(d) 0

Question 14.

Answer:
(a) 0

Question 15.
P(A) + P(A’) = ?
(a) 0
(b) 1
(c) -1
(d) P(E)
Answer:
(b) 1

Question 16.
\(\vec{a} \cdot \vec{b}=?\)
(a) \(-\vec{b} \cdot \vec{a}\)
(b) 1
(c) -1
(d) \(\vec{b} \cdot \vec{a}\)
Answer:
(d) \(\vec{b} \cdot \vec{a}\)

Question 17.
\(\sin ^{-1} \frac{1}{x}=?\)
(a) sex^-1 x
(b) cosec^-1 x
(c) tan^-1 x
(d) sin x
Answer:
(b) cosec^-1 x

Question 18.

Answer:
(b) \(\frac{x^{n+1}}{n+1}+k\)

Question 19.
\(\frac{d}{d x}\) [tan x] = ?
(a) sec²x
(b) sec x
(c) cot x
(d) -sec²x
Answer:
(a) sec²x

Question 20.

Answer:
(a) \(\frac{1}{x}\)

Question 21.

Answer:
(b) \(\frac{\pi}{4}\)

Question 22.

Answer:
(c) \(\left[\begin{array}{ll}
1 & 4 \\
2 & 5 \\
3 & 6
\end{array}\right]\)

Question 23.
P(A∪B) = ?
(a) P(A) + P(B) + P(A∩B)
(b) P(A) – P(B) – P(A∩B)
(c) P(A) + P(B) – P(A∩B)
(d) P(A) – P(B) + P(A∩B)
Answer:
(c) P(A) + P(B) – P(A∩B)

Question 24.
The value of x when \(\left[\begin{array}{cc}
x & 15 \\
4 & 4
\end{array}\right]=0\) is
(a) 15
(b) -15
(c) 4
(d) 4x
Answer:
(a) 15

Question 25.
∫cosec²x dx = ?
(a) tan x + c
(b) -cot x + c
(c) 2cosec x + c
(d) -cosec x + 2
Answer:
(b) -cot x + c

Question 26.
\(\frac{d}{d x}\) [sin²x] = ?
(a) 2 sin x cos x
(b) 2 sin x
(c) cos²x
(d) sin x cos x
Answer:
(a) 2 sin x cos x

Question 27.
The distance of the point (3, 4, 5) from x-axis is
(a) 3
(b) 5
(c) √41
(d) None of these
Answer:
(c) √41

Question 28.
In the set of all straight lines in a plane, the relation R to be Perpendicular is
(a) Reflexive and transitive
(b) Symmetric and transitive
(c) Symmetric
(d) None of these
Answer:
(c) Symmetric

Question 29.
Which of the following is a homogenous differential equation?
(a) x²y dx – (x³ + y³) dy = 0
(b) (xy) dx – (x⁴ + y⁴) dy = 0
(c) (2x + y – 3) dy – (x + 2y – 3) dx = 0
(d) (x – y) dy = (x² + y + 1) dx
Answer:
(c) (2x + y – 3) dy – (x + 2y – 3) dx = 0

Question 30.
Evaluate \(\left[\begin{array}{cc}
1 & -1 \\
y & x
\end{array}\right]\)
(a) x + y
(b) x – y
(c) -y – x
(d) 1 – x
Answer:
(d) 1 – x

Question 31.
The value of the determinant \(\left[\begin{array}{lll}
1 & 2 & 4 \\
1 & 3 & 6 \\
1 & 4 & 9
\end{array}\right]\) is
(a) 1
(b) -1
(c) 0
(d) 2
Answer:
(a) 1

Question 32.
The operation * is defined as a * b = 2a + b, then (2 * 3) * 4 is
(a) 18
(b) 17
(c) 19
(d) 21
Answer:
(d) 21

Question 33.
Which of the following is the unit matrix of order 3 × 3?

Answer:
(b) \(\left[\begin{array}{lll}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}\right]\)

Question 34.
\(\int \frac{d x}{1+x^{2}}=?\)
(a) tan x + c
(b) tan² x + c
(c) cot x + c
(d) -cot^-1 x + c
Answer:
(c) cot x + c

Question 35.
\(\int \frac{d x}{1+x^{2}}=?\)
(a) tan x + c
(b) tan² x + c
(c) cot x + c
(d) -cot^-1 x + c
Answer:
(a) tan x + c

Question 36.
P(E) = ?
(a) n(E) + n(s)
(b) \(\frac{n(s)}{n(E)}\)
(c) n(E) – n(s)
(d) \(\frac{n(E)}{n(s)}\)
Answer:
(a) n(E) + n(s)

Question 37.

Answer:
(a) 1

Question 38.

Answer:
(b) 0

Question 40.
The order of the differential equation \(\frac{d^{2} y}{d x^{2}}+x^{3}\left(\frac{d y}{d x}\right)^{3}=x^{4}\) is
(a) 1
(b) 2
(c) 4
(d) 3
Answer:
(b) 2

Question 41.

Answer:
(c) \(\log \frac{1}{2}\)

Question 42.
f: A → B will be an onto function of
(a) f(A) ⊂ B
(b) f(A) = B
(c) f(A) ⊃ B
(d) f(A) ≠ B
Answer:
(b) f(A) = B

Question 43.

Answer:
(a) \(\frac{b^{3}-a^{3}}{3}\)

Question 44.

Answer:
(b) \(\frac{1}{4} \tan -^{-1} \frac{x}{4}+k\)

Question 45.

Answer:
(d) -15

Question 46.

Answer:
(b) \(\left[\begin{array}{ll}
27 & 36 \\
25 & 10
\end{array}\right]\)

Question 47.
tan^-1 x + cot^-1 x = ?
(A) 0
(B) 1
(c) \(\frac{\pi}{2}\)
(d) \(-\frac{\pi}{2}\)
Answer:
(c) \(\frac{\pi}{2}\)

Question 48.

Answer:
(b) \(\frac{1}{4}\)

Question 49.
The position vector of the point (x, y, z) is

Answer:
(d) \(x \vec{i}+y \vec{j}+z \vec{k}\)

Question 50.

(a) (x = -2, y = 8)
(b) (x = 2, y = n – 8)
(c) (x = 3, y = -6)
(d) (x = -3, y = 6)
Answer:
(b) (x = 2, y = n – 8)