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
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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