**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 **

**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^{-1}x)/(2x+tan^{-1}x) 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)=|x^{3}| 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}(2x^{2}-1) with respect to cos-1x is

a) 2

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

c) 2/x

d) 1-x^{2}

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) n^{2}y

**Question 18**

Answer: (c) y. (log ab^{2})^{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

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**

(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)

-: End of **Continuity and Differentiability MCQ** Type Questions for ISC Class-12 Maths:-

-: also visit :-

- ISC Class-12 Text book Solutions, Notes , Syllabus, Paper
- MCQ Type Questions ISC Class-12 Semester-1 Session 2021-22

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