JOIN ADRE 2.0 Telegram Group

NCERT Solutions for class 12 Maths | Chapter 5 - Continuity and Differentiability

Questions
1 Let f (x) = ex, g (x) = sin-1 x and h (x) = f |g(x)|, then Class 12 Maths Chapter 5 Continuity and Differentiability is equal to
A esin-1x
B
C sin-1x
D 1/(1−x2)

Answer:
2 The differential coefficient of tan-1 is
A
B
C
D x

Answer:
Advertisement
Article and Schedule Quiz Start Test!

DOWNLOAD CURRENT AFFAIRS PDF FROM APP

3 If xy . yx = 16, then the value of dy/dx at (2, 2) is
A -1
B 0
C 1
D none of these

Answer:-1
4 If y = (tan x)sin x, then dy/dx is equal to
A sec x + cos x
B sec x + log tan x
C (tan x)sin x
D None of these

Answer:None of these
5 If Rolle’s theorem holds for the function f(x) = x3 + bx2 + ax + 5 on [1, 3] with c = Class 12 Maths Chapter 5 Continuity and Differentiability find the value of a and b.
A a = 11, b = -6
B a = 10, b = 6
C a = -11, b = 6
D a = 11, b = 6

Answer:a = 11, b = -6
6 If y = ax2 + b, then dy/dx at x = 2 is equal to
A 4a
B 3a
C 2a
D None of these

Answer:4a
7 If y = (1 + x)(1 + x2)(1 + x4)…..(1 + x2n), then the value of dy/dx at x = 0 is
A 0
B -1
C 1
D None of these

Answer:1
8 The number of discontinuous functions y(x) on [-2, 2] satisfying x2 + y2 = 4 is
A 0
B 1
C 2
D >2

Answer:0
9 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 5/2

Answer:3/2
10 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:6 – √(13/3)
11 A value of c for which the Mean value theorem holds for the function f(x) = logex on the interval [1, 3] is
A 2log3e
B 1/2loge3
C log3e
D loge3

Answer:2log3e
12 The value of c in Rolle’s Theorem for the function f(x) = ex sin x, x ∈ [0, π] is
A π/6
B π/4
C π/2
D 3π/4

Answer:3π/4
13 The value of c in Rolle’s theorem for the function, f(x) = sin 2x in [0, π/2] is
A π/2
B π/4
C π/3
D π/6

Answer:π/4
14 If x2 + y2 = 1, then
A yy” – (2y’)2 + 1 = 0
B yy” + (y’)2 + 1 = 0
C yy” – (y’)2 – 1 = 0
D yy” + (2y’)2 + 1 = 0

Answer:yy” + (y’)2 + 1 = 0
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:1/√2
16 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

Answer:continuous everywhere but not differentiable at x = 0
17 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/2 n ∈ Z
D None of these

Answer:f is everywhere continuous but not differentiable at x = nπ, n ∈ Z
18 For the function f(x) = x + 1/x, x ∈ [1, 3] the value of c for mean value theorem is
A 1
B √3
C 2
D None of these

Answer:√3
19 Let f be defined on [-5, 5] as

f(x) =Class 12 Maths Chapter 5 Continuity and Differentiability Then f(x) is

A continuous at every x except x = 0
B discontinuous at everyx except x = 0
C continuous everywhere
D discontinuous everywhere

Answer:discontinuous at everyx except x = 0
20 Let function f (x) =
A continuous at x = 1
B differentiable at x = 1
C continuous at x = -3
D All of these

Answer:All of these

ADRE 2.0 FULL LENGTH MOCK TEST

Take Mock Tests

Missiles Mock Test Start Test!
SSC MTS Mock Test Start Test
IBPS CLERK MOCK TEST Start Test
SSC MTS 2022 JULY 26 Shift 1 (ENGLISH) Start Test!
SSC GD Previous Year Paper 2021 Nov 17 Shift - I (Hindi) Start Test!
SSC CGL Tier - 1 PYP 2022 April 21 Shift- 1 (ENGLISH) Start Test!
MPSC PAPER I MOCK TEST 1 (ENGLISH) Start Test!
IB Security Assistant Mock test 1 (english) Start Test!
UP POLICE CONSTABLE MOCK TEST 1 Start Test!
DELHI POLICE CONSTABLE MOCK TEST 1 (HINDI) Start Test!

Chapters

Advertisement
Assam Direct Recruitment Test Series