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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 x = et sin t, y = etcos t, t is a parameter, then dy/dx at (1, 1) is equal to
[A] –1/2
[B] –1/4
[C] 0
[D] 1/2
Answer: 0
(2) If y = e3x+n, then the value of dy/dx|x=0 is
[A] 1
[B] 0
[C] -1
[D] 3e7
Answer: 0

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(3) If x = is equal to dx
[A] –y/x
[B] y/x
[C] –x/y
[D] x/y
Answer: –x/y
(4) The derivative of y = (1 – x) (2 – x)…. (n – x) at x = 1 is equal to
[A] 0
[B] (-1) (n – 1)!
[C] n ! – 1
[D] (-1)n-1 (n – 1)!
Answer: (-1) (n – 1)!
(5) 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
(6) If y = then dy/dx is equal to
[A] 1/2 sec² x
[B] sec² x
[C] sec x tan x
[D] e1/2 log(1+tan²x)
Answer: sec x tan x
(7) If x sin (a + y) = sin y, then dy/dx is equal to
[A] sin2(a+y)/sina
[B] sina/sin2(a+y)
[C] sin(a+y)/sina
[D] sina/sin(a+y)
Answer: sin2(a+y)/sina
(8) The derivative of cos-1 (2x² – 1) w.r.t cos-1 x is
[A] 2
[B]
[C] 2x
[D] 1 – x²
Answer: 2
(9) If f(x) = x² sin1/x, where x ≠ 0, then the value of the function f(x) at x = 0, so that the function is continuous at x = 0 is
[A] 0
[B] -1
[C] 1
[D] None of these
Answer: 0
(10) The function f(x) = is
[A] discontinuous at only one point at x = 0
[B] discontinuous at exactly two points
[C] discontinuous at exactly three points
[D] None of these
Answer: discontinuous at only one point at x = 0
(11) The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval [o, √3] is
[A] 1
[B] -1
[C] 3/2
[D] 1/3
Answer: 1
(12) If ax² + 2hxy + by² = 1, then dy/dx equals
[A] hx+by/ax+by
[B] ax+by/hx+by
[C] ax+hy/hx+hy
[D] −(ax+hy)/hx+by
Answer: −(ax+hy)/hx+by
(13) If y = sin-1 then dy/dx is equal to
[A] 1
[B] 0
[C] π/2
[D] None of these
Answer: 0
(14) If y = aex+ be-x + c Where a, b, c are parameters, they y’ is equal to
[A] aex – be-x
[B] aex + be-x
[C] -(aex + be-x)
[D] aex – bex
Answer: aex – be-x
(15) If x = a cos4 θ, y = a sin4 θ. then dy/dx at θ = 3π/4 is
[A] -1
[B] 1
[C] -a²
[D] a²
Answer: -1
(16) Let y = t10 + 1 and x = t8 + 1, then  d2y/dx2 , is equal to
[A] d2y/dx2
[B] 20t8
[C] 5/16t6
[D] None of these
Answer: None of these
(17) If x = sin-1 (3t – 4t³) and y = cos-1 then dy/dx is equal to
[A] 1/2
[B] 2/5
[C] 3/2
[D] 1/3
Answer: 1/3
(18) If y = log then dy/dx is equal to
[A] 7
[B] 3/x−2
[C] 3/(x−1)
[D] None of these
Answer: None of these
(19) The derivative of sin-1 with respect to cos-1 is
[A] -1
[B] 1
[C] 2
[D] 4
Answer: 1
(20) If xy = ex-y then dy/dx is
[A] 1+x/1+logx
[B] 1−logx/1+logy
[C] not defined
[D] −y/(1+logx)2
Answer: −y/(1+logx)2

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