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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) Let f (x) = ex, g (x) = sin-1 x and h (x) = f |g(x)|, then 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 = 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) = 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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