Choose the correct or the most suitable answer from the given four alternatives.
1. The value of sin−1 (cos x), 0 ≤ x ≤ π is
(1) π - x
(2) x - π/2
(3) π/2 - x
(4) x - π
2. If sin−1 x + sin−1 y (2π/3) ; then cos−1 x + cos−1 y is equal to
(1) 2π /3
(2) π /3
(3) π /6
(4) π
3. is equal to
(1) 2π
(2) π
(3) 0
(4) tan-1 (12/65)
4. If sin−1 x = 2 sin−1 α has a solution, then
(1) |α| ≤ (1/√2)
(2) |α| ≥ (1/√2)
(3) |α| < (1/√2)
(4) |α| > (1/√2)
5. is valid for
(1) − π ≤ x ≤ 0
(2) 0 ≤ x ≤ π
(3) -π/2 ≤ x ≤ π/2
(4) -π/4 ≤ x ≤ 3π/4
6. If sin-1 x + sin-1 y + sin-1z = 3π / 2 , the value of x2017 + y2018 + z2019 – [ 9/ (x101 + y101 + z101)] is
(1) 0
(2) 1
(3) 2
(4) 3
7. If cot−1 x =2π/3 for some x ∈ R , the value of tan−1 x is
(1) – π/10
(2) π/5
(3) π/10
(4) - π/5
8. The domain of the function defined by f (x) = sin-1√(x-1) is
(1) [1,2]
(2) [-1,1]
(3) [0,1]
(4) [-1,0]
9. If x =1/5 , the value of cos (cos−1 x + 2 sin−1 x) is
(1) – √(24/25)
(2) √(24/25)
(3) 1/5
(4) -1/5
10. is equal to
Ans: (4)
11. If the function f (x) = sin−1 (x2 − 3) , then x belongs to
(1) [-1,1]
(2) [√2,2]
(3) [-2-√2]U[√2,2]
(4) [-2,- √2]
12. If cot−1 2 and cot−1 3 are two angles of a triangle, then the third angle is
(1) π/4
(2) 3π/4
(3) π/6
(4) π/3
13. . Then x is a root of the equation
(1) x2 − x − 6 = 0
(2) x2 − x −12 = 0
(3) x2 + x −12 = 0
(4) x2 + x − 6 = 0
14. sin−1 (2 cos2 x −1) + cos−1 (1− 2 sin2 x) =
(1) π/2
(2) π/3
(3) π/4
(4) π/6
15. If then cos 2u is equal to
(1) tan2 α
(2) 0
(3) -1
(4) tan 2α
16. If |x| ≤ 1 , then 2tan-1 x - sin-1 2x/ (1+ x2) is equal to
(1) tan-1 x
(2) sin-1 x
(3) 0
(4) π
17. The equation tan-1x - cot-1 x = tan-1 ( 1/√3) has
(1) no solution
(2) unique solution
(3) two solutions
(4) infinite number of solutions
18.If , then x is equal to
(1) 1/2
(2) 1/√5
(3) 2/√5
(4) √3/2
19. If then the value of x is
(1) 4
(2) 5
(3) 2
(4) 3
20. sin(tan−1 x), | x |<1 is equal to
Ans: (4)
Choose the correct or the most suitable answer from the given four alternatives.
1. The value of sin−1 (cos x), 0 ≤ x ≤ π is
(1) π - x
(2) x - π/2
(3) π/2 - x
(4) x - π
2. If sin−1 x + sin−1 y (2π/3) ; then cos−1 x + cos−1 y is equal to
(1) 2π /3
(2) π /3
(3) π /6
(4) π
3. is equal to
(1) 2π
(2) π
(3) 0
(4) tan-1 (12/65)
4. If sin−1 x = 2 sin−1 α has a solution, then
(1) |α| ≤ (1/√2)
(2) |α| ≥ (1/√2)
(3) |α| < (1/√2)
(4) |α| > (1/√2)
5. is valid for
(1) − π ≤ x ≤ 0
(2) 0 ≤ x ≤ π
(3) -π/2 ≤ x ≤ π/2
(4) -π/4 ≤ x ≤ 3π/4
6. If sin-1 x + sin-1 y + sin-1z = 3π / 2 , the value of x2017 + y2018 + z2019 – [ 9/ (x101 + y101 + z101)] is
(1) 0
(2) 1
(3) 2
(4) 3
7. If cot−1 x =2π/3 for some x ∈ R , the value of tan−1 x is
(1) – π/10
(2) π/5
(3) π/10
(4) - π/5
8. The domain of the function defined by f (x) = sin-1√(x-1) is
(1) [1,2]
(2) [-1,1]
(3) [0,1]
(4) [-1,0]
9. If x =1/5 , the value of cos (cos−1 x + 2 sin−1 x) is
(1) – √(24/25)
(2) √(24/25)
(3) 1/5
(4) -1/5
10. is equal to
Ans: (4)
11. If the function f (x) = sin−1 (x2 − 3) , then x belongs to
(1) [-1,1]
(2) [√2,2]
(3) [-2-√2]U[√2,2]
(4) [-2,- √2]
12. If cot−1 2 and cot−1 3 are two angles of a triangle, then the third angle is
(1) π/4
(2) 3π/4
(3) π/6
(4) π/3
13. . Then x is a root of the equation
(1) x2 − x − 6 = 0
(2) x2 − x −12 = 0
(3) x2 + x −12 = 0
(4) x2 + x − 6 = 0
14. sin−1 (2 cos2 x −1) + cos−1 (1− 2 sin2 x) =
(1) π/2
(2) π/3
(3) π/4
(4) π/6
15. If then cos 2u is equal to
(1) tan2 α
(2) 0
(3) -1
(4) tan 2α
16. If |x| ≤ 1 , then 2tan-1 x - sin-1 2x/ (1+ x2) is equal to
(1) tan-1 x
(2) sin-1 x
(3) 0
(4) π
17. The equation tan-1x - cot-1 x = tan-1 ( 1/√3) has
(1) no solution
(2) unique solution
(3) two solutions
(4) infinite number of solutions
18.If , then x is equal to
(1) 1/2
(2) 1/√5
(3) 2/√5
(4) √3/2
19. If then the value of x is
(1) 4
(2) 5
(3) 2
(4) 3
20. sin(tan−1 x), | x |<1 is equal to
Ans: (4)
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