Check the below NCERT MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Continuity and Differentiability Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Q.1 The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at:

(a) 4

(b)-2

(c) 1

(d) 1.5

## Q.2 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

## Q.3 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)

## Q.4 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

## Q.5 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

## Q.6 Write the number of points where f(x) = |x + 2| + |x – 3| is not differentiable.

(a) 2

(b) 3

(c) 0

(d) 1

## Q.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°