NCERT Class 12 Chapter 5 Maths Continuity and Differentiability MCQ

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1. The derivative of f(tan x) w.r.t. g(sec x) at x = π4, where f'(1) = 2 and g'(√2) = 4, is

A. 12√

B. √2

C. 1

D. 0

2. The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at:

A. 4

B. -2

C. 1

D. 1.5

3. Which of the following functions are not continuous.

CBSE Class12 Maths Continuity and Differentiability (3Q)

A. (A)

B. (B)

C. (C)

D. (D)

4. If f (x) = 2x and g (x) = x22 + 1, then’which of the following can be a discontinuous function

A. f(x) + g(x)

B. f(x) – g(x)

C. f(x).g(x)

D. g(x)f(x)

CBSE Class12 Maths Continuity and Differentiability (5Q)

A. (a)

B. (b)

C. (c)

D. (d)

6. Let f : (- 1, 1) → R be a differentiable function with f(0) = – 1 and f'(0) = 1. Let g(x) = [f (2f(x) + 2)]². Then g'(0) =

A. 4

B. -4

C. log 2

D. -log 2

7. The Function CBSE Class12 Maths Continuity and Differentiability (7Q)

A. Discontinuous exactly at two points

B. Discontinuous at every points

C. Discontinuous at only one point

D. Discontinuous exactly at three points

8. The function f(x) = 4−x24x−x3 is

A. discontinuous at only one point at x = 0

B. discontinuous at exactly two points

C. discontinuous at exactly three points

D. None of these

CBSE Class12 Maths Continuity and Differentiability (9Q)

A. (a)

B. (b)

C. (c)

D. (d)

10. For x ∈ R, f(x) = |log 2 – sin x| and g(x) =f(f(x)), then

A. g is not differentiable at x = 0

B. g'(0) = cos (log 2)

C. g'(0) = -cos (log 2)

D. g is differentiable at x = 0 and g'(0) = – sin (log 2)

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11. Examine the continuity of the function CBSE Class12 Maths Continuity and Differentiability (11Q)

A. Discontinuous at x=-2

B. Discontinuous at x=2

C. Continuous everywhere

D. Discontinuous at x=4

12. The set of points where the function f given by f (x) =| 2x – 1| sin x is differentiable is

A. R

B. R = {12}

C. (0, ∞)

D. None of these

13. The value of c in mean value theorem for the function f(x) = (x – 3)(x – 6)(x – 9) in [3, 5] is

A. 6 ± √(13/3)

B. 6 + √(13/3)

C. 6 – √(13/3)

D. None of these

14.

BSE Class12 Maths Continuity and Differentiability (14q)

A. a=2,b=0

B. a=1,b=0

C. a=0,b=2

D. a=0,b=0

15. The function f(x) = cot x is discontinuous on the set

A. {x = nπ, n ∈ Z}

B. {x = 2nπ, n ∈ Z}

C. {x = (2n + 1) π2 n ∈ Z}

D. {x – nπ2 n ∈ Z}

16. 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

17. Discuss the continuity of function f(x)=/x-1/+/x+1/, XR

A. discontinuous at x=1

B. discontinuous at x=±1

C. Continuous everywhere

D. discontinuous at x=-1

18. The function f(x) = e^|x| is

A. continuous everywhere but not differentiable at x = 0

B. continuous and differentiable everywhere

C. not continuous at x = 0

D. None of these

19.

CBSE Class12 Maths Continuity and Differentiability (19Q)

A. (a)

B. (b)

C. (c)

D. (d)

20.

CBSE Class12 Maths Continuity and Differentiability (20Q)

A. is continuous at x = 0

B. Continuous everywhere

C. Not continuous at x = 0 but can be made continuous

D. Not continuous at x = 0

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21. Let f(x) = |sin x| Then

A. f is everywhere differentiable

B. f is everywhere continuous but not differentiable at x = nπ, n ∈ Z

C. f is everywhere continuous but no differentiable at x = (2n + 1) π2 n ∈ Z

D. None of these

22. A real function f is said to be continuous if it is continuous at every point in ...... .

A. [-∞,∞]

B. The range of f

C. The domain of f

D. Any interval of real numbers

23. If y = sinx+y−−−−−−−√ then dydx is equal to

A. cosx2y−1

B. cosx1−2y

C. sinx1−xy

D. sinx2y−1

24. The derivative of cos^-1 (2x² – 1) w.r.t cos^-1 x is

A. 2

B. −121−x2√

C. 2x

D. 1 – x²

25.

CBSE Class12 Maths Continuity and Differentiability (25Q)

A. (a)

B. (a)

C. (c)

D. (d)