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

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

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.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q32
Answer:
(c) \(\frac{2}{3}\)

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    Question 3.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q33
    Answer:
    (b) 1

    Question 4.
    img src=”https://live.staticflickr.com/65535/50354653758_a00e3fc2ee_o.png” width=”374″ height=”162″ alt=”Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q34″>
    Answer:
    (c) \(\frac{5}{16 t^{6}}\)

    Question 5.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q35
    Answer:
    (a) n2y

    Question 6.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q36
    Answer:
    (d) \(-\frac{b}{a^{2}} \sec ^{3} \theta\)

    Question 7.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q37
    Answer:
    (c) y. (log ab2)2

    Question 8.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q38
    Answer:
    (d) \(-\frac{1}{e^{2}}\)

    Question 9.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q39
    Answer:
    (a) \(\frac{\sec ^{3} \theta}{a \theta}\)

    Question 10.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q40
    Answer:
    (d) 0

    Question 11.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q11
    Answer:
    (b) \(-\sqrt{\frac{\pi}{6}}\)

    Question 12.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q12
    Answer:
    (a) \(\frac{\sqrt{(x+y)}-\sqrt{y-x}}{\sqrt{y-x}+\sqrt{x+y}}\)

    Question 13.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q13
    Answer:
    (b) \(\frac{2 a x+b y-y^{2}}{2 x y-b x-2 y}\)

    Question 14.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q14
    Answer:
    (d) 1

    Question 15.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q15
    Answer:
    (c) \(\frac{1}{2 \sqrt{1-x^{2}}}\)

    Question 16.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q16
    Answer:
    (d) \(\frac{1}{2}\)

    Question 17.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q17
    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.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q18
    Answer:
    (b) 0

    Question 19.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q19
    Answer:
    (c) sec x tan x

    Question 20.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q20
    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.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q42
    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) = ex 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) = logex on the interval [1, 3] is
    (a) 2log3e
    (b) \(\frac{1}{2} \log _{e} 3\)
    (c) log3e
    (d) loge3
    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.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q1
    Answer:
    (b) ln a + ln b

    Question 29.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q2
    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.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q4
    Answer:
    (c) \(-\frac{1}{2}\)

    Question 32.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q5
    Answer:
    (b) \(\frac{1}{4}\)

    Question 33.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q6
    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.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q8
    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.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q10
    Answer:
    (b) \(\frac{2 y \sqrt{y^{2}-1}\left(x^{2}+x-1\right)}{\left(x^{2}+1\right)^{2}}\)

    Question 38.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q21
    Answer:
    (a) \(\frac{1}{2}\)

    Question 39.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q22
    Answer:
    (c) \(\frac{\log _{10} e}{x}\left(\frac{y}{y-1}\right)\)

    Question 40.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q23
    Answer:
    (d) None of these

    Question 41.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q24
    Answer:
    (d) \(\[\frac{y}{x}\)\]

    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.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q27
    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 xy . yx = 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.
    Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability Q30
    Answer:
    (c) \(\frac{y}{1-y}\)

    We hope the given Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability will help you. If you have any query regarding CBSE Class 12 Maths Continuity and Differentiability MCQs Pdf, drop a comment below and we will get back to you at the earliest.

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