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

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Questions
1 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
2 If y = e3x+n, then the value of dy/dx|x=0 is
A 1
B 0
C -1
D 3e7

Answer:(A + B)-1 = B-1 + A-1
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3 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
4 If f(x) = cos x, cos 2 x, cos 4 x, cos 8 x, cos 16 x, then the value of'(π/4) is
A 1
B √2
C 1/√2
D 0

Answer:√2
5 The derivative of ex3 with respect to log x is
A ee3
B 3x22ex3
C 3x3ex3
D 3x2ex3+ 3x2

Answer:3x3ex3
6 If f(x) = tan-1 Class 12 Maths Chapter 5 Continuity and Differentiability 0 ≤ x ≤ π/2, then f'(π/6) is
A –1/4
B –1/2
C 1/4
D 1/2

Answer:1/2
7 If y = tan-1 Class 12 Maths Chapter 5 Continuity and Differentiability then y'(1) is equal to
A 0
B Class 12 Maths Chapter 5 Continuity and Differentiability
C -1
D -1/4

Answer:-1/4
8 If xmyn = (x + y)m+n, then dy/dx is equal to
A x+y/xy
B xy
C x/y
D y/x

Answer:y/x
9 If sec (x−y/x+y) = a then dy/dx is
A –y/x
B x/y
C –x/y
D y/x

Answer:y/x
10 Let f(x)= Class 12 Maths Chapter 5 Continuity and Differentiability and g (x) = ex. Then the value of (g o f)’ (0) is
A 1
B -1
C 0
D None of these

Answer:0
11 If f(x) = Class 12 Maths Chapter 5 Continuity and Differentiability + cos² (2x + 1), then f'(0) =
A 5 + 2 sin 2
B 5 + 2 cos 2
C 5 – 2 sin 2
D 5 – 2 cos 2

Answer:5 – 2 sin 2
12 If y = ax² + b, then dy/dx at x = 2 is equal to ax
A 4a
B 3a
C 2a
D None of these

Answer:4a
13 If f(x) = Class 12 Maths Chapter 5 Continuity and Differentiability then the value of f’ (√π/2) is
A √π/6
B –√π/6
C 1/√6
D π/√6

Answer:–√π/6
14 If f(x) = Class 12 Maths Chapter 5 Continuity and Differentiability then is equal to
A 1/24
B 1/5
C –√24
D 1/√24

Answer:1/√24
15 Differential coefficient of Class 12 Maths Chapter 5 Continuity and Differentiability is
A 1/4√x = sec √x sin √x
B 1/4√x = (sec√x)3/2 sin√x
C 1/2√x sec√x sin √x.
D 1/2√x (sec√x)3/2 sin√x

Answer:14√x = (sec√x)3/2 sin√x
16 If f(x) = Class 12 Maths Chapter 5 Continuity and Differentiability x ≠ 0 be continuous at x = 0, then f(o) =
A 1/2
B 1/4
C 2
D 3/2

Answer:1/4
17 If y = tan-1 Class 12 Maths Chapter 5 Continuity and Differentiability then dy/dx is equal to
A 1/2
B π/4
C 0
D 1

Answer:1
18 If x = exp Class 12 Maths Chapter 5 Continuity and Differentiability then dy/dx equals
A 2x [1 + tan (log x)] + x sec² (log x)
B x [1 + tan (log x)] + sec² (log x)
C 2x [1 + tan (logx)] + x² sec² (log x)
D 2x [1 + tan (log x)] + sec² (log x)

Answer:2x [1 + tan (log x)] + x sec² (log x)
19 If sin y + e-xcos y = e, then dy/dx at (1, π) is equal to
A sin y
B -x cos y
C e
D sin y – x cos y

Answer:e
20 If y = 2x32x-1 then dy/dx is equal to dx
A (log 2) (log 3)
B (log lg)
C (log 18²) y²
D y (log 18)

Answer:y (log 18)

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