1. The value of cos-1(cos 10) is
A: 4π - 10
A: 
A: 
A: 15
5. The value of sin(2sin-1 0.8) is equal to
A: 0.96
A: 
A: 
A: 
A: 
A: 
11. If y = cos-1(cos 4), then y =
A: 2p - 4
A: 
A: 0
A: 
A: 
A: xy + yz + zx = 1
A: 1
A: 12
A: tan-1 2
A: 
Ans: 
Ans: 1
Ans: 30º
Ans: 
25. If cos−1 x > sin−1 x, then
Ans: x < 0
Ans: 
27. The set of values of λ for which x2 − λx + sin−1 (sin 4) > 0 for all x ϵ R, is
Ans: ∅
Ans: 0
Ans: 
Ans: 3
Ans: sin2q
Ans: 0
Ans: 
35. The value of "a" for which ax2 + sin−1 (x2 − 2x + 2) + cos−1 (x2 − 2x + 2) = 0 has a real solution, is
Ans: 
Ans: 
37. For the equation 2x = tan(2 tan−1 a) + 2 tan(tan−1 a + tan−1 a3), which of the following is valid?
Ans: a2x + 2a =x
38. If x1, x2, x3 are the roots of x3 − 6x2 + 11x − 6 = 0, then cot−1 (x1) + cot−1 (x2) + cot−1 (x3) is equal to
Ans: 
Ans: 
Ans: 
Ans: two
Ans: 
43. If the mapping f(x) = ax + b, a > 0 maps [−1, 1] onto [0, 2], then cot[cot−1 7 + cot−1 8 + cot−1 18] is equal to
Ans: f(2)
Ans: 
Ans: 5
46. The solution of the inequality (cot-1 x)2 − 5 cot-1 x + 6 > 0 is
Ans: 
Ans: 
Ans: 
49. The area bounded by the identity curve in the first quadrant by y = 0 and x = sin-1 (a4 + 1) + cos-1 (a4 + 1) - tan-1 (a4 + 1) is
Ans: 
50. The complete solution set of [tan-1 x]2 - 8 [tan-1 x] + 16 ≤ 0, where [ ] denotes the greatest integer function, is
Ans: [tan 4, tan 5]
More than one correct answer type
A) α > β B) 4α - 3β = 0 C) 
D) α = β
Ans: B, C
52. The values of x satisfying sin-1 x + sin-1 (1 - x) = cos-1 x are
A) 0 B) 
C) 1 D) 2
Ans: A, B
A) α > β B) β > γ C) γ > α D) None of these
Ans: B, C
54. Which one is true?
A) 
B) 
C) 
D) 
Ans: A, B
A) a > x > b B) a < x < b C) a = x = b D) a > b and x takes any value
Ans: A, B
56. If the equation sin-1(x2 + x + 1) + cos-1 (λx + 1) = 
has exactly two solutions, then λ cannot have the integral value
A) -1 B) 0 C) 1 D) 2
Ans: A, C, D
A) 
B) 
C) 
D) 
Ans: B, C
A) 
B) 
C) 
D) 
Ans: A, D
A) α > β B) β > γ C) γ > α D) α < β
Ans: B, C
60. The value(s) of x satisfying the equation 
is/are given by (n is any integer)
A) nπ - 1 B) nπ C) nπ + 1 D) 2nπ + 1
Ans: A, B, C
61. Let y = (sin-1 x)3 + (cos- x)3 , then
A) 
B) 
C) 
D) 
Ans: B, C
A) two B) four C) zero D) one
Ans: D
63. If the equation sin-1 (x2 + x + 1) + cos-1 (λx + 1) = 
has exactly two solutions, then λ cannot have the integral value
A) -1 B) 0 C) 1 D) 2
Ans: A, C, D
64. If A = sin-1(sin 10), B = cos-1(cos 10), then
A) A = 3π - 10 B) A = 3π + 10 C) A > B D) A < B
Ans: A, D
65. Exhaustive set of parameter "a" so that sin-1 x - tan-1 x = a has a solution is
A) 
B) 
C) 
D) 
Ans: B, C
Comprehension Passage
Passage 1:
We know that corresponding to every bijection (one-one function) f : A → B, there exists a bijection g : B → A defined by g(y) = x if and only if f(x) = y. The function g : B → A is called the inverse of function f : A→ B and is denoted by f-1. Thus, we have f(x) = y ⇒ f-1(y) = x. We have also learnt that for all x ϵ A and (fof-1) = f[(f-1)(y)] = f(x) = y, for all y ϵ B. We know that trigonometric functions are periodic functions and hence, in general all trigonometric functions are not bijectives. Consequently, their inverse do not exists. However, if we restrict their domains and codomains, they can be made bijections and we can obtain their inverse.
66. cos-1(cos θ) = θ, for all θ belonging to
Ans: [0, π]
67. sec−1(sec θ) = θ, for all θ belonging to
Ans: 
68. tan−1(tan θ) = θ − 2π, for all θ belonging to
Ans: 
69. The value of sin−1(sin 12) + cos−1(cos 12), is
Ans: 0
Ans: 
Passage - 2:
Ans: 
Ans:
Ans: cot−1 2
Matrix Match Type:
74. Match the items of Column - I with the items Column - II.
Ans: A-S; B-R; C-P; D-Q.
75. Match the following numerical quantities with their principal values.
Ans: A-P; B-S; C-Q; D-R.
Integer Type
76. If the sum of the series cot−1 2 + cot−1 8 + cot−1 18 + ....... upto ∞ is 
, then find k.
Ans: 1
Ans: 2
Ans: 1
Ans: 1
Ans: 1
Ans: 1
Ans: 2
Ans: 2
Ans: 3
85. 2 tan−1 (2x − 1) = cos−1 x, then x = ............
Ans: 0
