Objective Type Question and Answers On Class 12 Maths Chapter 5 Continuity and Differentiability

(1) If x = e^t sin t, y = e^tcos 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 = e^3x+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) x^y. y^x = 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] e^1/2 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 = ae^x+ be^-x + c Where a, b, c are parameters, they y’ is equal to

[A] ae^x – be^-x

[B] ae^x + be^-x

[C] -(ae^x + be^-x)

[D] ae^x – be^x

Answer: ae^x – 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 x^y = e^x-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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