Maths Chapter 6 - Applications of Derivatives MCQs

Maths Chapter 6 – Applications of Derivatives MCQ Question Answers for Various Entrance Exams

1. Question

a.d

b.c

c.b

d.a

2. Question

a.(-∞, 0)

b.(-1, ∞)

c.None of these

d.(-∞, ∞)

3. Question

a.f(x) is an increasing function

b.both f (x) and g (x) are decreasing functions

c.both f (x) and g (x) are increasing functions

d.g (x) is an increasing function

4. Let the f: R → R be defined by f (x) = 2x + cos x, then f

a.has a maximum, at x = 0

b.is a decreasing function

c.is an increasing function

d.has a minimum at x = 3t

5. Question

a.b

b.a

c.d

d.c

6. Question

a.(1, -2)

b.(2, 1)

c.(1, 2)

d. (-1, 2)

7. Question

a.one maxima and one minima

b.no maxima or minima

c.two points of local minimum

d.two points of local maximum

8. Question

a.c

b.d

c.b

d.a

9. The value of b for which the function f (x) = sin x – bx + c is decreasing for x ∈ R is given by

a.b > 1

b.b ≤ 1

c.b < 1

d.b ≥ 1

10. Question

a.d

b.c

c.b

d.a

11. Question

a.160

b.126

c.135

d.0

12. Question

a.a

b.c

c.b

d.d

13. Question

a.4a

b.a

c.3a

d.2a

14. Question

a.minimum

b.zero

c.maximum

d.neither maximum nor minimum

15. Question

a.c

b.a

c.b

d.d

16. Question

a.(1, ∞)

b.(0, ∞)

c.(-1, ∞)

d.(-∞, ∞)

17. Question

a.None of these

b.(0, e)

c.(e, ∞)

d.(0, ∞)

18. Question

a.b

b.a

c.d

d.c

19. Question

a.x + 5y = 2

b.5x + y = 2

c.5x – y = 2

d.x – 5y = 2

20. Question

a. (3, 9)

b.(2, 4)

c.(3, 9), (9, 3)

d.(6, 2)

21. Question

a.c

b.b

c.a

d.d

22. Question

a.a

b.d

c.c

d.b

23. Question

a.Rotation

b.Retardation

c.Acceleration

d.Velocity

24. Question

a.32

b.12

c.16

d.0

25. Question

a.c

b.d

c.a

d.b

26. Question

a.(2, 34), (- 2, 0)

b. (0, 34), (-2, 0)

c.(2, 2), (-2, 34)

d.(2, – 2), (- 2, -34)

27. Question

a.4

b.5

c.0

d.2

28. The function f(x) = x + cos x is

a.always decreasing

b.increasing for certain range of x

c.always increasing

d.None of these

29. Question

a.λ > 1

b.λ < 4

c.λ < 1

d. λ > 4

30. Question

a.d

b.b

c.a

d.c

31. Question

a.an even function

b.None of these

c.an increasing function

d.a decreasing function

32. Question

a.2

b.0

c.1

d.-1

33. Question

a.(1, 3)

b.(3, ∞)

c.None of these

d.(-∞, -1) ∩ (3, ∞)

34. Question

a.x + 3y = 0

b.x + 3y ± 8 = 0

c.3x + y + 8 = 0

d.3x – y = 8

35. Question

a.b

b.a

c.d

d.c

36. A ladder, 5 meter long, standing on a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is

a.110 radian/sec

b.120 radian/sec

c.10 radiah/sec

d.20 radiah/sec

37. Question

a.1 < x < 5

b.all values of x

c.x < 1

d.x > 1

38. Question

a.c

b.a

c.d

d.b

39. Question

a.cos x

b.sin 2x

c.tan x

d. cos 3x

40. Question

a.a horizontal tangent (parallel to x-axis)

b.an oblique tangent

c.no tangent

d.a vertical tangent (parallel to y-axis)

41. Question

a.d

b.a

c.c

d.b

42. Question

a.c

b.a

c.d

d.b

43. Question

a.5.968

b.0.032

c.0.32

d.5.68

44. If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

a.proportional to the radius

b.inversely proportional to the surface area

c.inversely proportional to the radius

d.a constant

45. If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is

a.2%

b.1%

c.4%

d.3%

46. Question

a.b

b.d

c.c

d.a

47. Question

a.-6

b.6

c.1

d.0

48. Question

a.[-2, -1]

b.[-1, ∞]

c.[-1, 1]

d.[-∞, -2]

49. The function f(x) = tan x – x

a.always decreases

b.sometimes increases and sometimes decreases

c.always increases

d.never increases

50. Let the f: R → R be defined by f(x) = 2x + cos x, then f

a.has a minimum at x = 3t

b.has a maximum, at x = 0

c.is a decreasing function

d.is an increasing function

Also See :

Maths Ch 1 – Relations and Functions MCQs
Maths Ch 2 – Inverse Trigonometric Functions MCQs
Maths Ch 3 – Matrices MCQs
Maths Ch 4 – Determinants MCQs
Maths Ch 5 – Continuity and Differentiability MCQs
Maths Ch 7 – Integrals MCQs
Maths Ch 8 – Application of the Integrals MCQs
Maths Ch 9 – Differential Equations MCQs
Maths Ch 10 – Vectors MCQs
Maths Ch 11 – Three Dimensional Geometry MCQs
Maths Ch 12 – Linear Programming MCQs
Maths Ch 13 – Multiplication Theorem Probability MCQs

Maths Chapter 6 – Applications of Derivatives MCQ Question and Answers – MCQs for Practice

Maths Chapter 6 – Applications of Derivatives MCQ Question Answers for Various Entrance Exams

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