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

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Free download in PDF Class 12 Maths Chapter 5 Continuity and Differentiability Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>

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(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 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 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)= 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) = + 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 = 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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