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
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q32
Answer: (c) 2/3

Question 17
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q35
Answer: (a) n2y

Question 18
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q37
Answer: (c) y. (log ab2)2

Question 19

Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q38
Answer: (d) 1/𝑒²

Question 20
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q39
Answer: (a) sec³𝜃/𝑎𝜃

Question 21
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q40
Answer: (d) 0

Question 22
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q11
Answer: (b) 𝜋/6

Question 23
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q12
Answer: (a) √(𝑥+𝑦)−√(𝑦𝑥)  / √(𝑦𝑥)+√(𝑥+𝑦)

Question 24
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q13
Answer: (b) 2𝑎𝑥+𝑏𝑦𝑦² / 2𝑥𝑦𝑏𝑥2𝑦

Question 25
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q14
Answer: (d) 1

Question 26
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q15
Answer:
(c) 1  / 2√(1𝑥2)

Question 27
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q17
Answer:
(c) 2(1𝑥2) / (1+𝑥2)1𝑥2,   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 (2𝑥12)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

Answer:- (c) 6 – √(13/3)

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

Question 36

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

(a) 2
(b) 3
(c) 0
(d) 1

Answer :- (a) 2

Question 37

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°
Answer (c) -1° cosec2 x°

Question 38

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 39

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 40

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)

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