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## Continuity and Differentiability Class 12 Maths MCQs Pdf

**Continuity And Differentiability Class 12 MCQ Question 1.**

The derivative of f(tan x) w.r.t. g(sec x) at x = \(\frac{\pi}{4}\), where f'(1) = 2 and g'(âˆš2) = 4, is

(a) \(\frac{1}{\sqrt{2}}\)

(b) âˆš2

(c) 1

(d) 0

Answer:

(a) \(\frac{1}{\sqrt{2}}\)

**Continuity And Differentiability MCQ Class 12 Question 2.**

Answer:

(c) \(\frac{2}{3}\)

**Differentiation MCQ Class 12 Question 3.**

Answer:

(b) 1

**MCQ On Continuity And Differentiability Class 12 Question 4.**

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Answer:

(c) \(\frac{5}{16 t^{6}}\)

**Class 12 Maths Chapter 5 MCQ Question 5.**

Answer:

(a) n^{2}y

**MCQ Questions On Differentiation Class 12 Question 6.**

Answer:

(d) \(-\frac{b}{a^{2}} \sec ^{3} \theta\)

**MCQ On Differentiation Class 12 Question 7.**

Answer:

(c) y. (log ab^{2})^{2}

**MCQ Of Continuity And Differentiability Class 12 Question 8.**

Answer:

(d) \(-\frac{1}{e^{2}}\)

**MCQ Of Differentiation Class 12 Question 9.**

Answer:

(a) \(\frac{\sec ^{3} \theta}{a \theta}\)

**Continuity And Differentiability Class 12 MCQ With Answers Question 10.**

Answer:

(d) 0

**MCQ Of Chapter 5 Maths Class 12 Question 11.**

Answer:

(b) \(-\sqrt{\frac{\pi}{6}}\)

Question 12.

Answer:

(a) \(\frac{\sqrt{(x+y)}-\sqrt{y-x}}{\sqrt{y-x}+\sqrt{x+y}}\)

Question 13.

Answer:

(b) \(\frac{2 a x+b y-y^{2}}{2 x y-b x-2 y}\)

Question 14.

Answer:

(d) 1

Question 15.

Answer:

(c) \(\frac{1}{2 \sqrt{1-x^{2}}}\)

Question 16.

Answer:

(d) \(\frac{1}{2}\)

Question 17.

Answer:

(c) \(\frac{2\left(1-x^{2}\right)}{\left(1+x^{2}\right)\left|1-x^{2}\right|}, x \neq\pm 1,0\)

Question 18.

Answer:

(b) 0

Question 19.

Answer:

(c) sec x tan x

Question 20.

Answer:

(d) 3e^{7}

Question 21.

If x^{2} + y^{2} = 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:

(b) yy” + (y’)^{2} + 1 = 0

Question 22.

Answer:

(c) -9y

Question 23.

The value of c in Rolle’s theorem for the function, f(x) = sin 2x in [0, \(\frac{\pi}{2}\)] is

(a) \(\frac{\pi}{2}\)

(b) \(\frac{\pi}{4}\)

(c) \(\frac{\pi}{3}\)

(d) \(\frac{\pi}{6}\)

Answer:

(b) \(\frac{\pi}{4}\)

Question 24.

The value of c in Rolle’s Theorem for the function f(x) = e^{x} sin x, x âˆˆ [0, Ï€] is

(a) \(\frac{\pi}{6}\)

(b) \(\frac{\pi}{4}\)

(c) \(\frac{\pi}{2}\)

(d) \(\frac{3 \pi}{4}\)

Answer:

(d) \(\frac{3 \pi}{4}\)

Question 25.

A value of c for which the Mean value theorem holds for the function f(x) = log_{e}x on the interval [1, 3] is

(a) 2log_{3}e

(b) \(\frac{1}{2} \log _{e} 3\)

(c) log_{3}e

(d) log_{e}3

Answer:

(a) 2log_{3}e

Question 26.

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 Â± âˆš(13/3)

(b) 6 + âˆš(13/3)

(c) 6 – âˆš(13/3)

(d) None of these

Answer:

(c) 6 – âˆš(13/3)

Question 27.

The value of c in Mean value theorem for the function f(x) = x(x – 2), x âˆˆ [1, 2] is

(a) \(\frac{3}{2}\)

(b) \(\frac{2}{3}\)

(c) \(\frac{1}{2}\)

(d) \(\frac{5}{2}\)

Answer:

(a) \(\frac{3}{2}\)

Question 28.

Answer:

(b) ln a + ln b

Question 29.

Answer:

(c) 8

Question 30.

The number of discontinuous functions y(x) on [-2, 2] satisfying x^{2} + y^{2} = 4 is

(a) 0

(b) 1

(c) 2

(d) >2

Answer:

(a) 0

Question 31.

Answer:

(c) \(-\frac{1}{2}\)

Question 32.

Answer:

(b) \(\frac{1}{4}\)

Question 33.

Answer:

(c) \(\frac{-1}{(1+x)^{2}}\)

Question 34.

If y = (1 + x)(1 + x^{2})(1 + x^{4})…..(1 + x^{2n}), then the value of \(\frac{d y}{d x}\) at x = 0 is

(a) 0

(b) -1

(c) 1

(d) None of these

Answer:

(c) 1

Question 35.

Answer:

(d) \(\frac{1}{\sqrt{24}}\)

Question 36.

If y = ax^{2} + b, then \(\frac{d y}{d x}\) at x = 2 is equal to

(a) 4a

(b) 3a

(c) 2a

(d) None of these

Answer:

(a) 4a

Question 37.

Answer:

(b) \(\frac{2 y \sqrt{y^{2}-1}\left(x^{2}+x-1\right)}{\left(x^{2}+1\right)^{2}}\)

Question 38.

Answer:

(a) \(\frac{1}{2}\)

Question 39.

Answer:

(c) \(\frac{\log _{10} e}{x}\left(\frac{y}{y-1}\right)\)

Question 40.

Answer:

(d) None of these

Question 41.

Answer:

(d) \([latex]\frac{y}{x}\)[/latex]

Question 42.

If Rolle’s theorem holds for the function f(x) = x^{3} + bx^{2} + ax + 5 on [1, 3] with c = (2 + \(\frac{1}{\sqrt{3}}\)), 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) a = 11, b = -6

Question 43.

If y = (tan x)^{sin x}, then \(\frac{d y}{d x}\) is equal to

(a) sec x + cos x

(b) sec x + log tan x

(c) (tan x)^{sin x}

(d) None of these

Answer:

(d) None of these

Question 44.

Answer:

(d) \(\frac{\log x}{(1+\log x)^{2}}\)

Question 45.

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:

(b) (-1)(n – 1)!

Question 46.

If x^{y} . y^{x} = 16, then the value of \(\frac{d y}{d x}\) at (2, 2) is

(a) -1

(b) 0

(c) 1

(d) none of these

Answer:

(a) -1

Question 47.

Answer:

(c) \(\frac{y}{1-y}\)

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