MCQ Questions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions with Answers

Question 1.
sin-1 (sin$$\frac{2π}{3}$$) =
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{4π}{3}$$
(d) $$\frac{π}{3}$$

Answer: (d) $$\frac{π}{3}$$

Question 2.
sin-1 (1 – x) – 2 sin-1 x = $$\frac{π}{2}$$ then x = ?
(a) 0, $$\frac{1}{2}$$
(b) 1, $$\frac{1}{2}$$
(c) $$\frac{1}{2}$$
(d) 0

Question 3.
tan-1 √3 – sec-1(-2)
(a) π
(b) –$$\frac{π}{3}$$, 0
(c) $$\frac{π}{3}$$
(d) $$\frac{2π}{3}$$

Answer: (b) –$$\frac{π}{3}$$, 0

Question 4.
sin(sec-1 x + cosec-1x) =
(a) 1
(b) -1
(c) $$\frac{π}{2}$$
(d) $$\frac{π}{3}$$

Question 5.
2 tan-1 $$\frac{1}{3}$$ + tan-1 $$\frac{1}{7}$$ =
(a) tan-1 $$\frac{44}{29}$$
(b) $$\frac{π}{2}$$
(c) 0
(d) $$\frac{π}{4}$$

Answer: (d) $$\frac{π}{4}$$

Question 6.
The principle value of sin-1 $$\frac{√3}{2}$$ is
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{π}{4}$$
(d) $$\frac{π}{3}$$

Answer: (d) $$\frac{π}{3}$$

Question 7.
The value of the expression tan-1($$\frac{1}{2}$$cos-1$$\frac{2}{√5}$$) is
(a) 2 + √5
(b) √5 – 2
(c) $$\frac{√5+2}{4}$$
(d) √5 + 2

Answer: (d) √5 + 2

Question 8.
Simplified form of cos-1 (4x3 – 3x)
(a) 3 sin-1x
(b) 3 cos-1x
(c) π – 3 sin-1x
(d) None of these

Answer: (b) 3 cos-1x

Question 9.
The value of tan(tan-1 $$\frac{4}{5}$$ + tan-1 $$\frac{2}{3}$$) is
(a) $$\frac{6}{17}$$
(b) $$\frac{7}{16}$$
(c) $$\frac{17}{6}$$
(d) None of these

Answer: (d) None of these

Question 10.
tan-1($$\frac{x}{y}$$) – tan-1($$\frac{x-y}{x+y}$$) is equal to
(a) $$\frac{π}{3}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{2}$$
(d) $$\frac{-3π}{4}$$

Answer: (b) $$\frac{π}{4}$$

Question 11.
The value of x for which sin |cot-1(1 – x)| = cos (tan-1 x) is
(a) $$\frac{2}{1}$$
(b) 1
(c) 0
(d) $$\frac{1}{2}$$

Answer: (d) $$\frac{1}{2}$$

Question 12.
Princal value of cos-1($$\frac{-1}{√2}$$)
(a) $$\frac{3π}{4}$$
(b) $$\frac{5π}{4}$$
(c) –$$\frac{π}{4}$$
(d) None of these

Answer: (a) $$\frac{3π}{4}$$

Question 13.
tan-1 √3 – sec-1 (-2) is equal to
(a) π
(b) –$$\frac{π}{3}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{2π}{3}$$

Answer: (b) –$$\frac{π}{3}$$

Question 14.
If y = sec-1 x then
(a) 0 ≤ y ≤ π
(b) 0 ≤ y ≤ $$\frac{π}{2}$$
(c) –$$\frac{π}{2}$$ < y < $$\frac{π}{2}$$
(d) None of these

Answer: (d) None of these

Question 15.
If x + $$\frac{1}{x}$$ = 2 then the principal value of sin-1 x is x
(a) $$\frac{π}{4}$$
(b) $$\frac{π}{2}$$
(c) π
(d) $$\frac{3π}{2}$$

Answer: (d) $$\frac{3π}{2}$$

Question 16.
4 tan-1 $$\frac{1}{5}$$ – tan-1 $$\frac{1}{239}$$
(a) π
(b) $$\frac{π}{2}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{4}$$

Answer: (d) $$\frac{π}{4}$$

Question 17.
The principle value of sin-1(sin$$\frac{2π}{3}$$) is
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{-π}{6}$$
(d) $$\frac{π}{6}$$

Answer: (b) $$\frac{π}{3}$$

Question 18.
The value of cos-1($$\frac{1}{2}$$) + 2sin-1($$\frac{1}{2}$$) is equal to
(a) $$\frac{π}{4}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{2π}{3}$$
(d) $$\frac{5π}{6}$$

Answer: (b) $$\frac{π}{6}$$

Question 19.
Algebraic expression for sin (cot-1 x) is
(a) $$\frac{1}{1+x^2}$$
(b) $$\frac{1}{\sqrt{1+x^2}}$$
(c) $$\frac{x}{\sqrt{1+x^2}}$$
(d) None of these

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

Question 20.
If sin-1($$\frac{2x}{1+x^2}$$) + sin-1$$\frac{2y}{1+y^2}$$ = 2 tan-1 a then a is equal to
(a) $$\frac{x-y}{1+xy}$$
(b) $$\frac{y}{1+xy}$$
(c) $$\frac{y}{1-xy}$$
(d) $$\frac{x+y}{1-xy}$$

Answer: (d) $$\frac{x+y}{1-xy}$$

Question 21.
Princal value of tan-1 (-1) is
(a) $$\frac{π}{4}$$
(b) $$\frac{-π}{2}$$
(c) $$\frac{5π}{4}$$
(d) $$\frac{-π}{4}$$

Answer: (d) $$\frac{-π}{4}$$

Question 22.
tan-1($$\frac{1}{4}$$) + tan-1($$\frac{2}{9}$$) equal to

Answer: (d) tan-1($$\frac{1}{2}$$)

Question 23.
Principal value of sin-1($$\frac{1}{√2}$$)
(a) $$\frac{π}{4}$$
(b) $$\frac{3π}{4}$$
(c) $$\frac{5π}{4}$$
(d) None of these

Answer: (a) $$\frac{π}{4}$$

Question 24.
sin-1 x = y Then
(a) 0 ≤ y ≤ π
(b) –$$\frac{π}{2}$$ ≤ y ≤ $$\frac{π}{2}$$
(c) 0 < y < π
(d) –$$\frac{π}{2}$$ < y < –$$\frac{π}{2}$$

Answer: (b) –$$\frac{π}{2}$$ ≤ y ≤ $$\frac{π}{2}$$

Question 25.
cos-1(cos$$\frac{7π}{6}$$) is equal to
(a) $$\frac{7π}{6}$$
(b) $$\frac{5π}{6}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{6}$$

Answer: (b) $$\frac{5π}{6}$$

Question 26.
sin[$$\frac{π}{3}$$ – sin-1(-$$\frac{1}{2}$$)] is equal to
(a) $$\frac{1}{2}$$
(b) $$\frac{1}{3}$$
(c) $$\frac{1}{4}$$
(d) 1

Question 27.
tan-1$$\frac{1}{2}$$ + tan-1$$\frac{2}{11}$$ = tan-1 a then a = ?
(a) $$\frac{1}{4}$$
(b) $$\frac{1}{2}$$
(c) $$\frac{3}{4}$$
(d) 1

Answer: (c) $$\frac{3}{4}$$

Question 28.
tan-1$$\frac{1}{2}$$ + tan-1$$\frac{1}{3}$$ =
(a) $$\frac{π}{4}$$
(b) $$\frac{π}{2}$$
(c) $$\frac{π}{3}$$
(d) π

Answer: (a) $$\frac{π}{4}$$

Question 29.
If sin-1 x + sin-1 y = $$\frac{2π}{3}$$ then cos-1 x + cos-1 y =
(a) $$\frac{2π}{3}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{2}$$

Answer: (c) $$\frac{π}{3}$$

Question 30.
The principal value of cosec-1 (-2) is
(a) –$$\frac{2π}{3}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{2π}{3}$$
(d) –$$\frac{π}{6}$$

Answer: (d) –$$\frac{π}{6}$$

Question 31.
The domain of the following f(x) = $$\sqrt{sin^{-1}x}$$ is
(a) [0, 1]
(b) [-1, 1]
(c) [-, 0]
(d) [0, 1]

Answer: (a) [0, 1]

Question 32.
Which of the following is the principal value branch of cos-1 x?
(a) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$]
(b) (0, π)
(c) (0, π)
(d) (0, π) – {$$\frac{π}{2}$$}

Answer: (c) (0, π)

Question 33.
Which of the following is the principal value branch of cosec-1 x?
(a) ($$\frac{-π}{2}$$, $$\frac{π}{2}$$)
(b) (0, π) – {$$\frac{π}{2}$$}
(c) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$]
(d) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$] – [0]

Answer: (d) [$$\frac{-π}{2}$$, $$\frac{π}{2}$$] – [0]

Question 34.
If 3 tan-1 x + cot-1 x = π, then x equals
(a) 0
(b) 1
(c) -1
(d) $$\frac{1}{2}$$

Question 35.
The value of cos-1[cos($$\frac{33π}{5}$$)] is
(a) $$\frac{3π}{5}$$
(b) $$\frac{-3π}{5}$$
(c) $$\frac{π}{10}$$
(d) –$$\frac{-π}{10}$$

Answer: (a) $$\frac{3π}{5}$$

Question 36.
The domain of the function cos-1 (2x – 1) is
(a) [0, 1]
(b) [-1, 1]
(c) [-1, -1]
(d) [0, π]

Answer: (a) [0, 1]

Question 37.
The domain of the function defined 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 38.
If cos(sin-1$$\frac{2}{5}$$ + cos-1 x) = 0 then x is equal to
(a) $$\frac{1}{5}$$
(b) $$\frac{2}{5}$$
(c) 0
(d) 1

Answer: (b) $$\frac{2}{5}$$

Question 39.
The value of sin (2 tan-1 (.75)) is equal to
(a) .75
(b) 1.5
(c) .96
(d) sin 1.5

Question 40.
The value of cos-1 (cos$$\frac{3π}{2}$$) is equal to
(a) $$\frac{π}{2}$$
(b) $$\frac{3π}{2}$$
(c) $$\frac{5π}{2}$$
(d) –$$\frac{7π}{2}$$

Answer: (a) $$\frac{π}{2}$$

Question 41.
The value of expression 2 sec-1 2 + sin-1 ($$\frac{1}{2}$$) is
(a) $$\frac{π}{6}$$
(b) $$\frac{5π}{6}$$
(c) $$\frac{7π}{6}$$
(d) 1

Answer: (b) $$\frac{5π}{6}$$

Question 42.
If tan-1 x + tan-1 y = $$\frac{4π}{5}$$ then cot-1 x + cot-1 y equals
(a) $$\frac{π}{5}$$
(b) $$\frac{2π}{5}$$
(c) $$\frac{3π}{5}$$
(d) π

Answer: (a) $$\frac{π}{5}$$

Question 43.
If sin-1($$\frac{2a}{1+a^2}$$) + cos-1($$\frac{1-a^2}{1+a^2}$$) = tan-1($$\frac{2x}{1-x^2}$$) where a, x ∈ |0, 1| then the value of x is
(a) 0
(b) $$\frac{a}{2}$$
(c) a
(d) $$\frac{2a}{1-a^2}$$

Answer: (d) $$\frac{2a}{1-a^2}$$

Question 44.
The value of sin [cos-1($$\frac{7}{25}$$)] is
(a) $$\frac{25}{24}$$
(b) $$\frac{25}{7}$$
(c) $$\frac{24}{25}$$
(d) $$\frac{7}{24}$$

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

Question 45.
If |x| ≤ 1, then 2 tan-1 x + sin-1($$\frac{2x}{1+x^2}$$) is equal to
(a) 4 tan-1 x
(b) $$\frac{π}{2}$$
(c) 0
(d) π

Answer: (a) 4 tan-1 x

Question 46.
If cos-1 α + cos-1 β + cos-1 γ = 3π, then α(β + γ) + β (γ + α) + γ(α + β) equals
(a) 0
(b) 1
(c) 6
(d) 12

Question 47.
The number of real solution of the equation is
$$\sqrt{1+cos 2x}$$ = √2 cos-1(cos x) in [$$\frac{π}{2}$$, π] is
(a) 0
(b) 1
(c) 2
(d) None of these

Question 48.
If cos-1 x > sin-1 x, then
(a) $$\frac{1}{√2}$$ < x ≤ 1
(b) 0 ≤ x < $$\frac{1}{√2}$$
(c) -1 ≤ x < $$\frac{1}{√2}$$ (d) x > 0

Answer: (b) 0 ≤ x < $$\frac{1}{√2}$$

Question 49.
sin-1($$\frac{-1}{2}$$)
(a) $$\frac{π}{3}$$
(b) –$$\frac{π}{3}$$
(c) $$\frac{π}{6}$$
(d) –$$\frac{π}{6}$$

Answer: (d) –$$\frac{π}{6}$$

Question 50.
sec-1($$\frac{-2}{√3}$$)
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{5π}{6}$$
(d) –$$\frac{2π}{3}$$

Answer: (c) $$\frac{5π}{6}$$

Question 51.
cos-1($$\frac{1}{2}$$)
(a) –$$\frac{π}{3}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{π}{2}$$
(d) $$\frac{2π}{3}$$

Answer: (b) $$\frac{π}{3}$$

Question 52.
cosec-1($$\frac{-2}{√3}$$)
(a) –$$\frac{π}{3}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{π}{2}$$
(d) –$$\frac{π}{2}$$

Answer: (a) –$$\frac{π}{3}$$

Question 53.
cot-1(1)
(a) $$\frac{π}{3}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{2}$$
(d) 0

Answer: (b) $$\frac{π}{4}$$

Question 54.
cos-1($$\frac{√3}{2}$$)
(a) $$\frac{5π}{6}$$
(b) $$\frac{π}{6}$$
(c) $$\frac{4π}{9}$$
(d) $$\frac{2π}{3}$$

Answer: (a) $$\frac{5π}{6}$$

Question 55.
cosec-1(2)
(a) $$\frac{π}{6}$$
(b) $$\frac{2π}{3}$$
(c) $$\frac{5π}{6}$$
(d) 0

Answer: (a) $$\frac{π}{6}$$

Question 56.
sec-1(2)
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{2π}{3}$$
(d) $$\frac{5π}{6}$$

Answer: (b) $$\frac{π}{3}$$

Question 57.
tan-1(√3)
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{2π}{3}$$
(d) $$\frac{5π}{6}$$

Answer: (b) $$\frac{π}{3}$$

Question 58.
cot-1(-√3)
(a) $$\frac{5π}{6}$$
(b) $$\frac{π}{3}$$
(c) $$\frac{π}{2}$$
(d) $$\frac{π}{4}$$

Answer: (a) $$\frac{5π}{6}$$

Question 59.
tan-1 + cos-1 ($$\frac{-1}{2}$$) + sin-1 ($$\frac{-1}{2}$$)
(a) $$\frac{2π}{3}$$
(b) $$\frac{3π}{4}$$
(c) $$\frac{π}{2}$$
(d) 6π

Answer: (b) $$\frac{3π}{4}$$

Question 60.
tan-1 (√3) + sec-1 (-2) – cosec-1 ($$\frac{2}{√3}$$)
(a) $$\frac{5π}{6}$$
(b) $$\frac{2π}{3}$$
(c) $$\frac{π}{3}$$
(d) 0

Question 61.
cos-1 ($$\frac{-1}{2}$$) + 2sin-1 ($$\frac{-1}{2}$$)
(a) $$\frac{π}{3}$$
(b) $$\frac{2π}{3}$$
(c) $$\frac{3π}{4}$$
(d) $$\frac{5π}{8}$$

Answer: (a) $$\frac{π}{3}$$

Question 62.
If cot-1 ($$\sqrt{cosα}$$) – tan-1 ($$\sqrt{cosα}$$) = x then sin x is equal to
(a) tan² ($$\frac{α}{2}$$)
(b) cot² ($$\frac{α}{2}$$)
(c) tan α
(d) cot ($$\frac{α}{2}$$)

Answer: (a) tan² ($$\frac{α}{2}$$)

Question 63.
4 tan-1 $$\frac{1}{5}$$ – tan-1 $$\frac{1}{70}$$ + tan-1 $$\frac{1}{99}$$ is equal to
(a) $$\frac{π}{6}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{3}$$
(d) $$\frac{π}{2}$$

Answer: (b) $$\frac{π}{4}$$

Question 64.
If 6 sin-1 (x² – 6x + 8.5) = π, then x is equal to
(a) 1
(b) 2
(c) 3
(d) 8

Question 65.
Number of solutions of the equation
tan-1 ($$\frac{1}{2x+1}$$) + tan-1 ($$\frac{1}{4x+1}$$) = tan-1 ($$\frac{2}{x^2}$$)
(a) 1
(b) 2
(c) 3
(d) 4