Continuity and Differentiability MCQ Type Questions for ISC Class-12

Continuity and Differentiability MCQ Type Questions for ISC Class-12. These MCQ  / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Physics.

ISC Maths Class-12 Continuity and Differentiability MCQ Type Questions 

Board	ISC
Class	12th (XII)
Subject	Maths
Chapter Name	Continuity and Differentiability
Syllabus	on bifurcated syllabus (after reduction)
bifurcated pattern	Semester-1
Session	2021-22
Topic	MCQ / Objective Type Question

MCQ Type Questions for ISC Class-12 Maths Continuity and Differentiability 

Question 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

Ans:- (d) 1.5

Question 2.
The value of ‘c’ in Rolle’s Theorem for the function f(x) = x³ – 3x in the interval [0, √3] is
(a) 1
(b) -1
(c) 3/2

(c) 1/3

Ans:- (a) 1

Question 3.
The value of ‘c’ in Mean Value Theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is

(a) 3/2
(b) 2/3
(c) 1/2

(c) 3/4

Ans:- (a) 3/2

Question 4
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.

Ans:- (b) -4

Question 5

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)

Ans:- (b) g'(0) = cos (log 2)

Question 6.
If f(x) = x + 7, and g(x) = x – 7, x ∈R, then d/dx fog) (x) = ……………….

(a) 1
(b) 2
(c) 0

(d) 3

Ans:- (a) 1

Question:7

If f(x)= x sin (1/x) ,x is not zero, then the value of the function at x=0,so that the function is continuous at x=0 ,is

a) 0

b) -1

c) 1

d) indeterminate

Ans:- (a) 0

Question: 8

If the function f(x)=(2x- sin^-1x)/(2x+tan^-1x) is continuous at each point of its domain , then the value of f(0) is

a) 1/3

b) -1/3

c) 2/3

d) 2

Ans:- (a)  1/3

Question:9

 Let f(x)=|x| and g(x)=|x³| then

a) f(x) and g(x) both are continuous at x=0

b) f(x) and g(x) both are differentiable at x=0

c) f(x) is differentiable but g(x) is not differentiable at x=0

d) f(x) and g(x) both are not differentiable at x=0

Ans:- (a) f(x) and g(x) both are continuous at x=0

Question:10

 The function f(x)=1+|cosx| is

a) continuous everywhere

b) continuous no where

c) not differentiable at x=0

d) None of these

Answer: a) continuous everywhere

Question:11

 If sin(x+y)=log(x+y) then dy/dx =

a) -1

b) 1

c) -2

d) 2

Answer: a) -1

Question:12

 The derivative of cos^-1(2x²-1) with respect to cos-1x is

a) 2

b) 1/2(1-x2)^1/2

c) 2/x

d) 1-x²

Answer: a) 2

Question 13.
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

Ans:- (a) continuous everywhere but not differentiable at x = 0

Question 14
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) π/2n ∈ Z

Ans:-: (b) f is everywhere continuous but not differentiable at x = nπ, n ∈ Z

Question 15
The derivative of f(tan x) w.r.t. g(sec x) at x = 𝜋/4 where f'(1) = 2 and g'(√2) = 4, is

(a) 1/√2
(b) √2
(c) 1
(d) 0
Answer: (a) 1/√2

Question 16

Answer: (c) 2/3

Question 17

Answer: (a) n²y

Question 18

Answer: (c) y. (log ab²)²

Question 19

Answer: (d) −1/𝑒²

Question 20

Answer: (a) sec³𝜃/𝑎𝜃

Question 21

Answer: (d) 0

Question 22

Answer: (b) −√𝜋/6

Question 23

Answer: (a) √(𝑥+𝑦)−√(𝑦−𝑥)  / √(𝑦−𝑥)+√(𝑥+𝑦)

Question 24

Answer: (b) 2𝑎𝑥+𝑏𝑦−𝑦² / 2𝑥𝑦−𝑏𝑥−2𝑦

Question 25

Answer: (d) 1

Question 26

Answer:
(c) 1  / 2√(1−𝑥2)

Question 27

Answer:
(c) 2(1−𝑥2) / (1+𝑥2)∣1−𝑥2∣,   𝑥≠±1,,0

Question 28

The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at:
(a) 4
(b)-2
(c) 1
(d) 1.5.

Answer: (d) 1.5.

Question 29
The value of ‘c’ in Rolle’s Theorem for the function f(x) = x³ – 3x in the interval [0, √3] is
(a) 1
(b) -1
(c) 3/2
(d) 1/3
Answer: (a) 1

Question 30
The value of ‘c’ in Mean Value Theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is
(a) 3/2
(b) 2/3
(c) 1/2
(d) 3/4

Answer: (a) 3/2

Question 31
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.

Answer: (b) -4

Question 32
If f: R → R is a function defined by
f(x) = [x] cos (2𝑥−12)π, where [x] denotes the greatest integer function, then ‘f’ is
(a) continuous for every real x
(b) discontinuous only at x = 0
(c) discontinuous only at non-zero integral values of x
(d) continuous only at x = 0.

Answer: (a) continuous for every real x

Question 33
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).

Answer: (b) g'(0) = cos (log 2)

Question 34

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

Question 35

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

Answer- (d) differentiable for x ∈ R