Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 5 Continuity and Differentiability. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Continuity and Differentiability MCQs Pdf with Answers to know their preparation level.

Continuity and Differentiability Class 12 Maths MCQs Pdf

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'(√2) = 4, is
(a) \(\frac{1}{\sqrt{2}}\)
(b) √2
(c) 1
(d) 0
Answer:
(a) \(\frac{1}{\sqrt{2}}\)

Question 2.

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

Question 3.

Answer:
(b) 1

Question 4.
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Answer:
(c) \(\frac{5}{16 t^{6}}\)

Question 5.

Answer:
(a) n²y

Question 6.

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

Question 7.

Answer:
(c) y. (log ab²)²

Question 8.

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

Question 9.

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

Question 10.

Answer:
(d) 0

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) 3e⁷

Question 21.
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:
(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 ∈ [0, π] 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_ex on the interval [1, 3] is
(a) 2log₃e
(b) \(\frac{1}{2} \log _{e} 3\)
(c) log₃e
(d) log_e3
Answer:
(a) 2log₃e

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 ± √(13/3)
(b) 6 + √(13/3)
(c) 6 – √(13/3)
(d) None of these
Answer:
(c) 6 – √(13/3)

Question 27.
The value of c in Mean value theorem for the function f(x) = x(x – 2), x ∈ [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 x² + y² = 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 + x²)(1 + x⁴)…..(1 + x²ⁿ), 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 = ax² + 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) = x³ + bx² + 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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