Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 5 Continuity and Differentiability. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Continuity and Differentiability MCQs Pdf with Answers to know their preparation level.

Continuity and Differentiability Class 12 Maths MCQs Pdf

1. Given functions f(x) = Image may be NSFW.
Clik here to view. and g(x) = x + 2, x <= R. Then which of the following is correct?
(a) f is continuous at x = 2,
g is continuous at x = 2
(b) f is continuous at x = 2,
g is not continuous at x = 2
(c) f is not continuous at x = 2,
g is continuous at x = 2
(d) f is not continuous at x = 2,
g is not continuous at x = 2

2.
Image may be NSFW.
Clik here to view.

3.
Image may be NSFW.
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for x = 2, then value of k for which f is continuous is
(a) -2
(b) -1
(c) 0
(d) 1

4. A function /is said to be continuous for x ∈ R, if
(a) it is continuous at x = 0
(b) differentiable at x = 0
(c) continuous at two points
(d) differentiable for x ∈ R

5. Afunction
Image may be NSFW.
Clik here to view.
is continuous at x = 0 for
(a) k = 1
(b) k = 2
(c) k = Image may be NSFW.
Clik here to view.
(d) k = Image may be NSFW.
Clik here to view.

6. Write the number of points where f(x) = |x + 2| + |x – 3| is not differentiable.
(a) 2
(b) 3
(c) 0
(d) 1

7. Derivative of cot x° with respect to x is
(a) cosec x°
(b) cosec x° cot x°
(c) -1° cosec2 x°
(d) -1° cosec x° cot x°

8.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.

9. If f(x) = Image may be NSFW.
Clik here to view., then f(e) is
(a) 0
(b) 1
(c) Image may be NSFW.
Clik here to view.
(d) Image may be NSFW.
Clik here to view.

10. If f(x) = e^x and g(x) = log_e x, then (gof)’ (x) is
(a) 0
(b) 1
(c) e
(d) 1 + e

11.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.

12. If y = x^x-∞, , then x(l -y log x)Image may be NSFW.
Clik here to view. is equal to
(a) x²
(b) y²
(c) xy²
(d) x²y

13. The derivative of sin x with respect to log x is
(a) cos x
(b) x cos x
(c) Image may be NSFW.
Clik here to view.
(d) Image may be NSFW.
Clik here to view. cos x

14. Ify = Ae^5x,+ Be^-5x x then Image may be NSFW.
Clik here to view. is equal to
(a) 25y
(b) 5y
(c) -25y
(d) 10y

15. Given the functionImage may be NSFW.
Clik here to view.
the function is continuous at x = 0, state true or false.

46. The function f(x) = Image may be NSFW.
Clik here to view. continuous at x = 0 if/(0) is _________ .

17. A function f(x) = Image may be NSFW.
Clik here to view. x ∈ R, is a continuous function. State true or false.

18. A function f(x) = sin x + cos x is continuous function. State true or false.

19. Discuss the continuity of the function fix)= Image may be NSFW.
Clik here to view. for x ∈ R.

20. Discuss the continuity of the function
Image may be NSFW.
Clik here to view.

21. Check whether the function f(x) = 2x² + 1 is continuous at x = 0.

22. Give an example of a function which is continuous but not differentiable at exactly two points.

23. Determine the value of the constant ‘k’
Image may be NSFW.
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24. Determine the value of ‘k’ for which the following function is continuous at x = 3:
Image may be NSFW.
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25. For what value of ‘k’ is the function
Image may be NSFW.
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continuous at x = 0?

26. Find the value of k, so that the function
Image may be NSFW.
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is continuous at x = 1

27. Determine the value of the constant ‘k’ so that the function
Image may be NSFW.
Clik here to view.
is continuous at x = 0. [Delhi]

28. For what value of ‘k’ is the function
Image may be NSFW.
Clik here to view.
continuous at x = 0? [Foreign]

29. The derivative of
Image may be NSFW.
Clik here to view.
State true or false.

30. Find Image may be NSFW.
Clik here to view., if x² + y² = 5

31. Differentiate sin^-1x², with resepct to x.

32. Find Image may be NSFW.
Clik here to view., if sin y + x = log x

33. Find Image may be NSFW.
Clik here to view. at x = 1, y = Image may be NSFW.
Clik here to view. if sin²y + cos xy = K. [Delhi 2017]

34. Differentiate tan^-1 Image may be NSFW.
Clik here to view. with respect to x. [CBSE 2018]

35. If y = 2^√x, then Image may be NSFW.
Clik here to view. is _______ .

36. If y = log (tan x) + log (cot x), then Image may be NSFW.
Clik here to view. is _______ .

37. If Image may be NSFW.
Clik here to view., then f(-1) is _______ .

38. Differentiate e^-2x with respect to x.

39. Differentiate 5^{sin x}, with respect to x.

40. Differentiate log_e(sin x) with respect to x.

41. Differentiate log x² w.r.t x.

42. If y = e^{-3 log x} then find Image may be NSFW.
Clik here to view..

43.
Image may be NSFW.
Clik here to view.

44. Find Image may be NSFW.
Clik here to view. at t = Image may be NSFW.
Clik here to view. when x = 10(t – sin t) and y = 12(1 – cos t). [Foreign 2017]

45. Find Image may be NSFW.
Clik here to view., if y = log x

46. If y = sin 3x, find y₂

47. Find Image may be NSFW.
Clik here to view. if y = e^-3x

48. Verify the Rolle’s Theorem for the function f(x) = x² in the inverval [-1, 1].

49. Verify the Rolle’s Theorem for die functiony(x) = |x| in the inverval [-1, 1]. [HOTS]

50. Verify the Rolle’s Theorem for the function f(x) = sin 2x in [0, π].

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