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-1 x + sin-1 x = \(\frac{11 \pi}{6}\) 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