MCQ On Class 12 Maths Chapter 5 Continuity and Differentiability

(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 = e^3x+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 e^x³ with respect to log x is

[A] ee³

[B] 3x²2ex³

[C] 3x³ex³

[D] 3x²ex³+ 3x²

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

Answer: 1/2

(7) If y = tan^-1

then y'(1) is equal to

[A] 0

[B]

[C] -1

[D] -1/4

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

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)= and g (x) = e^x. 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) = + 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) = 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) = then is equal to

[A] 1/24

[B] 1/5

[C] –√24

[D] 1/√24

Answer: 1/√24

(15) Differential coefficient of 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) = 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

then dy/dx is equal to

[A] 1/2

[B] π/4

[C] 0

[D] 1

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)

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 = 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)

Answer: y (log 18)

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