Class 11th Maths – RD Sharma Chapter 5 : trigonometric Functions Multiple Choice Questions (MCQs Solutions

  Mark the correct alternative in each of the following:

1. If tan x = x − 1/4x , then sec x − tan x is equal to
   (a) −2x , 1/2x
   (b) −1/2x , 2x
   (c) 2x
   (d) 2x , 1/2x  Watch Solution

2. If sec x = x + 1/4x , then sec x + tan x =
   (a) x , 1/x
   (b) 2x , 1/2x
   (c) −2x , 1/2x
   (d) −1/x , x Watch Solution

3. If π/2 < x < 3π/2 , then √((1 − sin x)/(1 + sin x)) is equal to
   (a) sec x − tan x
   (b) sec x + tan x
   (c) tan x − sec x
   (d) none of these Watch Solution

4. If π < x < 2π , then √((1 + cos x)/(1 − cos x)) is equal to
   (a) cosec x + cot x
   (b) cosec x − cot x
   (c) − cosec x + cot x
   (d) − cosec x − cot x Watch Solution

5. If 0 < x < π/2 , and if (y + 1)/(1 − y) = √((1 + sin x)/(1 − sin x)) , then y is equal to
   (a) cot x/2
   (b) tan x/2
   (c) cot x/2 + tan x/2
   (d) cot x/2 − tan x/2 Watch Solution

6. If π/2 < x < π, then √((1 − sin x)/(1 + sin x)) + √((1 + sin x)/(1 − sin x)) is equal to
   (a) 2 sec x
   (b) −2 sec x
   (c) sec x
   (d) − sec x Watch Solution

7. If x = r sin θ cos ϕ, y = r sin θ sin ϕ and z = r cos θ, then x² + y² + z² is independent of
   (a) θ, ϕ
   (b) r, θ
   (c) r, ϕ
   (d) r Watch Solution

8. If tan x + sec x = √3, 0 < x < π, then x is equal to
   (a) 5π/6
   (b) 2π/3
   (c) π/6
   (d) π/3 Watch Solution

9. If tan x = −1/√5 and x lies in the IV quadrant, then the value of cos x is
   (a) √5/√6
   (b) 2/√6
   (c) 1/2
   (d) 1/√6 Watch Solution

10. If 3π/4 < α < π, then √(2 cot α + 1/sin² α) is equal to
    (a) 1 − cot α
    (b) 1 + cot α
    (c) −1 + cot α
    (d) −1 − cot α Watch Solution

11. sin⁶ A + cos⁶ A + 3 sin² A cos² A =
    (a) 0
    (b) 1
    (c) 2
    (d) 3 Watch Solution

12. If cosec x − cot x = 1/2 , 0 < x < π/2 , then cos x is equal to
    (a) 5/3
    (b) 3/5
    (c) −3/5
    (d) −5/3 Watch Solution

13. If cosec x + cot x = 11/2 , then tan x =
    (a) 21/22
    (b) 15/16
    (c) 44/117
    (d) 117/44  Watch Solution

14. sec² x = 4xy/(x + y)² is true if and only if
    (a) x + y ≠ 0
    (b) x = y, x ≠ 0
    (c) x = y
    (d) x ≠ 0, y ≠ 0 Watch Solution

15. If x is an acute angle and tan x = 1/√7 , then the value of (cosec² x − sec² x)/(cosec² x + sec² x) is
    (a) 3/4
    (b) 1/2
    (c) 2
    (d) 5/4 Watch Solution

16. The value of sin² 5° + sin² 10° + sin² 15° + … + sin² 85° + sin² 90° is
    (a) 7
    (b) 8
    (c) 9.5
    (d) 10 Watch Solution

17. sin² π/18 + sin² 2π/9 + sin² 7π/18 + sin² 4π/9 =
    (a) 1
    (b) 4
    (c) 2
    (d) 0 Watch Solution

18. If tan A + cot A = 4, then tan⁴ A + cot⁴ A is equal to
    (a) 110
    (b) 191
    (c) 80
    (d) 194 Watch Solution

19. If x sin 45° cos² 60° = (tan² 60° cosec 30°)/(sec 45° cot² 30°) , then x =
    (a) 2
    (b) 4
    (c) 8
    (d) 16 Watch Solution

20. If A lies in second quadrant and 3 tan A + 4 = 0, then the value of 2 cot A − 5 cos A + sin A is equal to
    (a) −53/10
    (b) 23/10
    (c) 37/10
    (d) 7/10 Watch Solution

21. If cosec x + cot x = 11/2 , then tan x =
    (a) 21/22
    (b) 15/16
    (c) 44/117
    (d) 117/43 Watch Solution

22. If tan θ + sec θ = eˣ, then cos θ equals
    (a) (eˣ + e⁻ˣ)/2
    (b) 2/(eˣ + e⁻ˣ)
    (c) (eˣ − e⁻ˣ)/2
    (d) (eˣ − e⁻ˣ)/(eˣ + e⁻ˣ) Watch Solution

23. If sec x + tan x = k, cos x =
    (a) (k² + 1)/2k
    (b) 2k/(k² + 1)
    (c) k/(k² + 1)
    (d) k/(k² − 1) Watch Solution

24. If f(x) = cos² x + sec² x, then
    (a) f(x) < 1
    (b) f(x) = 1
    (c) 1 < f(x) < 2
    (d) f(x) ≥ 2 Watch Solution

25. Which of the following is incorrect?
    (a) sin x = −1/5
    (b) cos x = 1
    (c) sec x = 1/2
    (d) tan x = 20 Watch Solution

26. The value of cos 1° cos 2° cos 3° … cos 179° is
    (a) 1/√2
    (b) 0
    (c) 1
    (d) −1 Watch Solution

27. The value of tan 1° tan 2° tan 3° … tan 89° is
    (a) 0
    (b) 1
    (c) 1/2
    (d) not defined Watch Solution

28. Which of the following is correct?
    (a) sin 1° > sin 1
    (b) sin 1° < sin 1
    (c) sin 1° = sin 1
    (d) sin 1° = π/180 sin 1 Watch Solution

29. If tan θ = −4/3, then sin θ is equal to
    (a) −4/5 but not 4/5
    (b) −4/5 or 4/5
    (c) 4/5 but not −4/5
    (d) none of these Watch Solution

30. If sin θ and cos θ are the roots of the equation ax² − bx + c = 0, then a, b and c satisfy the relation
    (a) a² + b² + 2ac = 0
    (b) a² − b² + 2ac = 0
    (c) a² + c² + 2ab = 0
    (d) a² − b² − 2ac = 0 Watch Solution

31. If sin θ + cosec θ = 2, then sin² θ + cosec² θ is equal to
    (a) 1
    (b) 4
    (c) 2
    (d) none of these Watch Solution

32. Which of the following is incorrect?
    (a) sin θ = −1/5
    (b) cos θ = 1
    (c) sec θ = 1/2
    (d) tan θ = 20 Watch Solution

33. If for real values of x, cos θ = x + 1/x , then
    (a) θ is an acute angle
    (b) θ is a right angle
    (c) θ is an obtuse angle
    (d) No value of θ is possible Watch Solution

Chapter 5: Trigonometric Functions – R. D. Sharma Class 11th Maths

1. Trigonometric Functions Exercise 5.1 Video Solution

2. Trigonometric Functions Exercise 5.2 Video Solution

3. Trigonometric Functions Exercise 5.3 Video Solution

4. Trigonometric Functions Multiple Choice Questions (MCQs) Video Solution Video Solution

5. Trigonometric Functions Fill in the Blanks (FBQs) Video Solution

6. Trigonometric Functions Very Short Answer Questions (VSAQs) Video Solution Video Solution