Bihar Board 12th Maths Objective Answers Chapter 2 Inverse Trigonometric Functions

Bihar Board 12th Maths Objective Questions and Answers

Bihar Board 12th Maths Objective Answers Chapter 2 Inverse Trigonometric Functions

Question 1.

Answer:
(d) \(-\frac{\pi}{6}\)

Question 2.

Answer:
(b) \(\frac{\pi}{3}\)

Question 3.

Answer:
(b) \(\frac{\pi}{3}\)

Question 4.

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

Question 5.

Answer:
(b) \(\frac{3 \pi}{4}\)

Question 6.

Answer:
(d) \(\frac{2 \pi}{3}\)

Question 7.

Answer:
(a) \(\tan ^{2}\left(\frac{\alpha}{2}\right)\)

Question 8.

Answer:
(b) \(\frac{6}{17}\)

Question 9.
If tan^-1 (x – 1) + tan^-1 x + tan^-1 (x + 1) = tan^-1 3x, then the values of x are
(a) \(\pm \frac{1}{2}\)
(b) 0, \(\frac{1}{2}\)
(c) 0, \(-\frac{1}{2}\)
(d) 0, \(\pm \frac{1}{2}\)
Answer:
(d) 0, \(\pm \frac{1}{2}\)

Question 10.
If 6sin^-1 (x² – 6x + 8.5) = π, then x is equal to
(a) 1
(b) 2
(c) 3
(d) 8
Answer:
(b) 2

Question 11.
3 tan^-1 a is equal to

Answer:
(d) \(\tan ^{-1}\left(\frac{3 a-a^{3}}{1-3 a^{2}}\right)\)

Question 12.

Answer:
(d) \(\frac{1}{5}\)

Question 13.
The equation 2cos^-1x + sin^-1x = \(\frac{11 \pi}{6}\) has
(a) no solution
(b) only one solution
(c) two solutions
(d) three solutions
Answer:
(a) no solution

Question 14.

Answer:
(d) x

Question 15.
If tan^-1 2x + tan^-1 3x = \(\frac{\pi}{4}\), then x is
(a) \(\frac{1}{6}\)
(b) 1
(c) (\(\frac{1}{6}\), -1)
(d) none of these
Answer:
(a) \(\frac{1}{6}\)

Question 16.

Answer:
(c) \(\sqrt{\frac{x^{2}+1}{x^{2}+2}}\)

Question 17.

Answer:
(a) \(\sqrt{a b}\)

Question 18.
If tan^-1 x – tan^-1 y = tan^-1 A, then A is equal to
(a) x – y
(b) x + y
(c) \(\frac{x-y}{1+x y}\)
(d) \(\frac{x+y}{1-x y}\)
Answer:
(c) \(\frac{x-y}{1+x y}\)

Question 19.

Answer:
(c) \(\pm \sqrt{\frac{5}{2}}\)

Question 20.
The value of cot^-1 9 + cosec^-1(\(\frac{\sqrt{41}}{4}\)) is given by
(a) 0
(b) \(\frac{\pi}{4}\)
(c) tan^-1 2
(d) \(\frac{\pi}{2}\)
Answer:
(b) \(\frac{\pi}{4}\)

Question 21.

Answer:
(a) \(\frac{6}{17}\)

Question 22.

Answer:
(d) none of these

Question 23.

Answer:
(b) 0

Question 24.

Answer:
(d) \(\frac{1}{\sqrt{2}} \leq x \leq 1\)

Question 25.
cos^-1[cos(2cot^-1(√2 – 1))] = ______
(a) √2 – 1
(b) 1 + √2
(c) \(\frac{\pi}{4}\)
(d) \(\frac{3 \pi}{4}\)
Answer:
(d) \(\frac{3 \pi}{4}\)

Question 26.
The range of sin^-1 x + cos^-1 x + tan^-1 x is
(a) [0, π]
(b) \(\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right]\)
(c) (0, π)
(d) \(\left[0, \frac{\pi}{2}\right]\)
Answer:
(b) \(\left[\frac{\pi}{4}, \frac{3 \pi}{4}\right]\)

Question 27.

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

Question 28.
Find the value of sec² (tan^-1 2) + cosec² (cot^-1 3)
(a) 12
(b) 5
(c) 15
(d) 9
Answer:
(c) 15

Question 29.

Answer:
(d) \(\frac{2}{x}\)

Question 30.
The equation sin^-1 x – cos^-1 x = cos^-1(\(\frac{\sqrt{3}}{2}\)) has
(a) unique solution
(b) no solution
(c) infinitely many solution
(d) none of these
Answer:
(a) unique solution

Question 31.
Solve for x : {xcos(cot^-1 x) + sin(cot^-1 x)}² = \(\frac{51}{50}\)
(a) \(\frac{1}{\sqrt{2}}\)
(b) \(\frac{1}{5 \sqrt{2}}\)
(c) 2√2
(d) 5√2
Answer:
(b) \(\frac{1}{5 \sqrt{2}}\)

Question 32.

Answer:
(c) tan^-1(15)

Question 33.

Answer:
(b) \(\sqrt{\frac{3}{76}}\)

Question 34.

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

Question 35.
If sin^-1(x² – 7x + 12) = nπ, ∀ n ∈ I, then x =
(a) -2
(b) 4
(c) -3
(d) 5
Answer:
(b) 4

Question 36.
If cos^-1 x + sin^-1 x = π, then the value of x is
(a) \(\frac{3}{2}\)
(b) \(\frac{1}{\sqrt{2}}\)
(c) \(\frac{\sqrt{3}}{2}\)
(d) \(\frac{2}{\sqrt{3}}\)
Answer:
(c) \(\frac{\sqrt{3}}{2}\)

Question 37.
If sin^-1 x – cos^-1 x = \(\frac{\pi}{6}\), then x =
(a) \(\frac{1}{2}\)
(b) \(\frac{\sqrt{3}}{2}\)
(c) \(-\frac{1}{2}\)
(d) \(-\frac{\sqrt{3}}{2}\)
Answer:
(b) \(\frac{\sqrt{3}}{2}\)

Question 38.
If tan^-1 (cot θ) = 2θ, then θ is equal to
(a) \(\frac{\pi}{3}\)
(b) \(\frac{\pi}{4}\)
(c) \(\frac{\pi}{6}\)
(d) None of these
Answer:
(c) \(\frac{\pi}{6}\)

Question 39.
cot(\(\frac{\pi}{4}\) – 2cot^-1 3) =
(a) 7
(b) 6
(c) 5
(d) None of these
Answer:
(a) 7

Question 40.
If tan^-1 3 + tan^-1 x = tan^-1 8, then x =
(a) 5
(b) \(\frac{1}{5}\)
(c) \(\frac{5}{14}\)
(d) \(\frac{14}{5}\)
Answer:
(b) \(\frac{1}{5}\)

Question 41.

Answer:
(d) \(-\frac{24}{25}\)

Question 42.
sin^-1(1 – x) – 2sin^-1 x = \(\frac{\pi}{2}\)
(a) 0
(b) 1/2
(c) 0, 1/2
(d) -1/2
Answer:
(a) 0

Question 43.
2tan^-1(cos x) = tan^-1(2cosec x)
(a) 0
(b) π/3
(c) π/4
(d) π/2
Answer:
(c) π/4

Question 44.

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

Question 45.

Answer:
(a) \(\frac{3 \pi}{5}\)

Question 46.
The domain of the function defind by f(x) = \(\sin ^{-1} \sqrt{x-1}\) is
(a) [1, 2]
(b) [-1, 1]
(c) [0, 1]
(d) none of these
Answer:
(a) [1, 2]

Question 47.
The value of sin (2tan^-1 (0.75)) is equal to
(a) 0.75
(b) 1.5
(c) 0.96
(d) sin 1.5
Answer:
(c) 0.96

Question 48.
The value of expression 2 sec^-1 2 + sin^-1(\(\frac{1}{2}\))
(a) \(\frac{\pi}{6}\)
(b) \(\frac{5 \pi}{6}\)
(c) \(\frac{7 \pi}{6}\)
(d) 1
Answer:
(b) \(\frac{5 \pi}{6}\)

Question 49.

Answer:
(c) \(\frac{24}{25}\)

Question 50.
The value of the expression \(\tan \left(\frac{1}{2} \cos ^{-1} \frac{2}{\sqrt{3}}\right)\)
(a) 2 + √5
(b) √5 – 2
(c) \(\frac{\sqrt{5}+2}{2}\)
(d) 5 + √2
Answer:
(b) √5 – 2

Question 51.

Answer:
(a) 4tan^-1 x

Question 52.
The number of real solutions of the equation is

(a) 0
(b) 1
(c) 2
(d) none of these
Answer:
(c) 2