MCQ On Class 12 Maths Chapter 5 Continuity and Differentiability

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

View Answer

Answer:1

2 If y = e^3x+n, then the value of dy/dx|_x=0 is

A 1

B 0

C -1

D 3e⁷

View Answer

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

View Answer

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

View Answer

Answer:√2

5 The derivative of e^x³ with respect to log x is

A ee³

B 3x²2ex³

C 3x³ex³

D 3x²ex³+ 3x²

View Answer

Answer:3x³ex³

6 If f(x) = tan^-1

0 ≤ x ≤ π/2, then f'(π/6) is

A –1/4

B –1/2

C 1/4

D 1/2

View Answer

Answer:1/2

7 If y = tan^-1

then y'(1) is equal to

A 0

C -1

D -1/4

View Answer

Answer:-1/4

8 If x^myⁿ = (x + y)^m+n, then dy/dx is equal to

A x+y/xy

B xy

C x/y

D y/x

View Answer

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

View Answer

Answer:y/x

10 Let f(x)=

and g (x) = e^x. Then the value of (g o f)’ (0) is

A 1

B -1

C 0

D None of these

View Answer

Answer:0

11 If f(x) =

+ 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

View Answer

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

View Answer

Answer:4a

13 If f(x) =

then the value of f’ (√π/2) is

A √π/6

B –√π/6

C 1/√6

D π/√6

View Answer

Answer:–√π/6

14 If f(x) =

then

is equal to

A 1/24

B 1/5

C –√24

D 1/√24

View Answer

Answer:1/√24

15 Differential coefficient of

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

View Answer

Answer:14√x = (sec√x)3/2 sin√x

16 If f(x) =

x ≠ 0 be continuous at x = 0, then f(o) =

A 1/2

B 1/4

C 2

D 3/2

View Answer

Answer:1/4

17 If y = tan^-1

then dy/dx is equal to

A 1/2

B π/4

C 0

D 1

View Answer

Answer:1

18 If x = exp

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)

View Answer

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

View Answer

Answer:e

20 If y = 2^x3^2x-1 then dy/dx is equal to dx

A (log 2) (log 3)

B (log lg)

C (log 18²) y²

D y (log 18)

View Answer

Answer:y (log 18)

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