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

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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:
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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

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