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NCERT Class 12 Chapter 5 Maths Continuity and Differentiability MCQ | Questions & Answers: Hello! Here we have come up with another NCERT Class 12 Chapter 5 Maths Continuity and Differentiability MCQ Quiz. Give your best for it and get to know the knowledge you have in the particular area of interest. Good luck!

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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

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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

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3. Which of the following functions are not continuous.

A. (A)

B. (B)

C. (C)

D. (D)

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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)

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5.

A. (a)

B. (b)

C. (c)

D. (d)

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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

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7. The Function

A. Discontinuous exactly at two points

B. Discontinuous at every points

C. Discontinuous at only one point

D. Discontinuous exactly at three points

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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

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9.

A. (a)

B. (b)

C. (c)

D. (d)

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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

A. Discontinuous at x=-2

B. Discontinuous at x=2

C. Continuous everywhere

D. Discontinuous at x=4

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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

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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

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14.

A. a=2,b=0

B. a=1,b=0

C. a=0,b=2

D. a=0,b=0

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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}

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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

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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

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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

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19.

A. (a)

B. (b)

C. (c)

D. (d)

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20.

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

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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

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

A. cosx2y−1

B. cosx1−2y

C. sinx1−xy

D. sinx2y−1

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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

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25.

A. (a)

B. (a)

C. (c)

D. (d)

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