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

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

Question 1.

Answer:
(d) −π6

Question 2.

Answer:
(b) π3

Question 3.

Answer:
(b) π3

Question 4.

Answer:
(a) π4

Question 5.

Answer:
(b) 3π4

Question 6.

Answer:
(d) 2π3

Question 7.

Answer:
(a) tan2(α2)

Question 8.

Answer:
(b) 617

Question 9.
If tan-1 (x – 1) + tan-1 x + tan-1 (x + 1) = tan-1 3x, then the values of x are
(a) ±12
(b) 0, 12
(c) 0, −12
(d) 0, ±12
Answer:
(d) 0, ±12

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(3a−a31−3a2)

Question 12.

Answer:
(d) 15

Question 13.
The equation 2cos-1 x + sin-1 x = 11π6 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 = π4, then x is
(a) 16
(b) 1
(c) (16, -1)
(d) none of these
Answer:
(a) 16

Question 16.

Answer:
(c) x2+1x2+2−−−−√

Question 17.

Answer:
(a) ab−−√

Question 18.
If tan-1 x – tan-1 y = tan-1 A, then A is equal to
(a) x – y
(b) x + y
(c) x−y1+xy
(d) x+y1−xy
Answer:
(c) x−y1+xy

Question 19.

Answer:
(c) ±52−−√

Question 20.
The value of cot-1 9 + cosec-1(41√4) is given by
(a) 0
(b) π4
(c) tan-1 2
(d) π2
Answer:
(b) π4

Question 21.

Answer:
(d) none of these

Question 23.

Answer:
(d) 12√≤x≤1

Question 25.
cos-1[cos(2cot-1(√2 – 1))] = ______
(a) √2 – 1
(b) 1 + √2
(c) π4
(d) 3π4
Answer:
(d) 3π4

Question 26.
The range of sin-1 x + cos-1 x + tan-1 x is
(a) [0, π]
(b) [π4,3π4]
(c) (0, π)
(d) [0,π2]
Answer:
(b) [π4,3π4]

Question 27.

Answer:
(c) π4

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) 2x

Question 30.
The equation sin-1 x – cos-1 x = cos-1(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 = 5150
(a) 12√
(b) 152√
(c) 2√2
(d) 5√2
Answer:
(b) 152√

Question 32.

Answer:
(b) 376−−√

Question 34.

Answer:
(d) π4

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) 32
(b) 12√
(c) 3√2
(d) 23√
Answer:
(c) 3√2

Question 37.
If sin-1 x – cos-1 x = π6, then x =
(a) 12
(b) 3√2
(c) −12
(d) −3√2
Answer:
(b) 3√2

Question 38.
If tan-1 (cot θ) = 2θ, then θ is equal to
(a) π3
(b) π4
(c) π6
(d) None of these
Answer:
(c) π6

Question 39.
cot(π4 – 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) 15
(c) 514
(d) 145
Answer:
(b) 15

Question 41.

Answer:
(d) −2425

Question 42.
sin-1 (1 – x) – 2sin-1 x = π2
(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) x2+1x2+2−−−−√

Question 45.

Answer:
(a) 3π5

Question 46.
The domain of the function defind by f(x) = sin−1x−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(12)
(a) π6
(b) 5π6
(c) 7π6
(d) 1
Answer:
(b) 5π6

Question 49.

Answer:
(c) 2425

Question 50.
The value of the expression tan(12cos−123√)
(a) 2 + √5
(b) √5 – 2
(c) 5√+22
(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