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

1. Given functions f(x) = \(\frac{x^{2}-4}{x-2}\) and g(x) = x + 2, x <= R. Then which of the following is correct?
(a) f is continuous at x = 2,
g is continuous at x = 2
(b) f is continuous at x = 2,
g is not continuous at x = 2
(c) f is not continuous at x = 2,
g is continuous at x = 2
(d) f is not continuous at x = 2,
g is not continuous at x = 2

Answer/Explanation

Answer: c
Explaination: (c), as f(2) is not defined so / is not continuous at x = 2 ‘g’ is a polynomial function, so continuous at x = 2.


2.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 2

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 18


3.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 3
for x = 2, then value of k for which f is continuous is
(a) -2
(b) -1
(c) 0
(d) 1

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 19


4. A function /is said to be continuous for x ∈ R, if
(a) it is continuous at x = 0
(b) differentiable at x = 0
(c) continuous at two points
(d) differentiable for x ∈ R

Answer/Explanation

Answer: d
Explaination: (d), as differentiable functions is continuous also.


5. Afunction
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 4
is continuous at x = 0 for
(a) k = 1
(b) k = 2
(c) k = \(\frac{1}{2}\)
(d) k = \(\frac{3}{2}\)

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 21


6. Write the number of points where f(x) = |x + 2| + |x – 3| is not differentiable.
(a) 2
(b) 3
(c) 0
(d) 1

Answer/Explanation

Answer: a
Explaination: (a), as f(x) = |x – a| is continuous at x = a but not differentiable thereat.


7. Derivative of cot x° with respect to x is
(a) cosec x°
(b) cosec x° cot x°
(c) -1° cosec2 x°
(d) -1° cosec x° cot x°

Answer/Explanation

Answer: c
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 30


8.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 13
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 14

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 31


9. If f(x) = \(\log _{x^{2}}(\log x)\), then f(e) is
(a) 0
(b) 1
(c) \(\frac{1}{e}\)
(d) \(\frac{1}{2e}\)

Answer/Explanation

Answer: d
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 40


10. If f(x) = ex and g(x) = loge x, then (gof)’ (x) is
(a) 0
(b) 1
(c) e
(d) 1 + e

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 41


11.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 15
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 16

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 43


12. If y = xx-∞, , then x(l -y log x)\(\frac{d y}{d x}\) is equal to
(a) x²
(b) y²
(c) xy²
(d) x²y

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 50


13. The derivative of sin x with respect to log x is
(a) cos x
(b) x cos x
(c) \(\frac{\cos x}{\log x}\)
(d) \(\frac{1}{x}\) cos x

Answer/Explanation

Answer: b
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 51


14. Ify = Ae5x,+ Be-5x x then \(\frac{d^{2} y}{d x^{2}}\) is equal to
(a) 25y
(b) 5y
(c) -25y
(d) 10y

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 54


15. Given the functionMaths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 1
the function is continuous at x = 0, state true or false.

Answer/Explanation

Answer:
Explaination: False, as ‘f’ is not defined at x = 0. i.e.f (0) does not exist.


46. The function f(x) = \(\frac{x+1}{1+\sqrt{1+x}}\) continuous at x = 0 if/(0) is _________ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 20


17. A function f(x) = \(\frac{x}{x-5}\) x ∈ R, is a continuous function. State true or false.

Answer/Explanation

Answer:
Explaination: False, as for x = 5, f(5) is not defined.


18. A function f(x) = sin x + cos x is continuous function. State true or false.

Answer/Explanation

Answer:
Explaination: True, as sum of two continuous functions is a continuous function.


19. Discuss the continuity of the function fix)= \(\frac{1}{x-5}\) for x ∈ R.

Answer/Explanation

Answer:
Explaination: f(x) = \(\frac{1}{x-5}\), as f(5) is not defined, therefore function is not continuous at x = 5.


20. Discuss the continuity of the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 5

Answer/Explanation

Answer:
Explaination:
f(x)= \(\frac{x^{2}-25}{x-5}\), x ≠ 5. As x ≠ 5, therefore, value of function exists for all x(≠5) ∈ R.
Also \(\lim _{x \rightarrow a}\) f(x) = f(a) = a + 5, (a ≠ 5). Hence, continuous.


21. Check whether the function f(x) = 2x² + 1 is continuous at x = 0.

Answer/Explanation

Answer:
Explaination: f(x) = 2x² + 1, as \(\frac{x^{2}-25}{x-5}\) f(x) = f(0) = 1. Hence, continuous


22. Give an example of a function which is continuous but not differentiable at exactly two points.

Answer/Explanation

Answer:
Explaination:
We know function f(x)=|x – a| is continuous at x = a but not differentiable at x = a.
∴ functions |x| and |x – 1| are continuous but not differentiable at x = 0 and 1.
∴ function is h(x) = |x| + |x – 1|.


23. Determine the value of the constant ‘k’
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 6

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 22


24. Determine the value of ‘k’ for which the following function is continuous at x = 3:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 7

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 23


25. For what value of ‘k’ is the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 8
continuous at x = 0?

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 24
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 25


26. Find the value of k, so that the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 9
is continuous at x = 1

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 26


27. Determine the value of the constant ‘k’ so that the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 10
is continuous at x = 0. [Delhi]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 27


28. For what value of ‘k’ is the function
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 11
continuous at x = 0? [Foreign]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 28


29. The derivative of
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 12
State true or false.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 29


30. Find \(\frac{d y}{d x}\), if x² + y² = 5

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 32


31. Differentiate sin-1x², with resepct to x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 33


32. Find \(\frac{d y}{d x}\), if sin y + x = log x

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 34


33. Find \(\frac{d y}{d x}\) at x = 1, y = \(\frac{\pi}{4}\) if sin²y + cos xy = K. [Delhi 2017]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 35
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 36


34. Differentiate tan-1 \(\left(\frac{1+\cos x}{\sin x}\right)\) with respect to x. [CBSE 2018]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 37


35. If y = 2√x, then \(\frac{d y}{d x}\) is _______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 38


36. If y = log (tan x) + log (cot x), then \(\frac{d y}{d x}\) is _______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 42


37. If \(f(x)=9^{x^{2}+2 x}\), then f(-1) is _______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 44


38. Differentiate e-2x with respect to x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 45


39. Differentiate 5sin x, with respect to x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 46


40. Differentiate loge(sin x) with respect to x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 47


41. Differentiate log x² w.r.t x.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 48


42. If y = e-3 log x then find \(\frac{d y}{d x}\).

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 49


43.
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 17

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 52


44. Find \(\frac{d y}{d x}\) at t = \(\frac{2 \pi}{3}\) when x = 10(t – sin t) and y = 12(1 – cos t). [Foreign 2017]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 53


45. Find \(\frac{d^{2} y}{d x^{2}}\), if y = log x

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 55


46. If y = sin 3x, find y2

Answer/Explanation

Answer:
Explaination:
y = sin 3x
y1 = 3 cos 3x
y2 = -9 sin 3x.


47. Find \(\frac{d^{2} y}{d x^{2}}\) if y = e-3x

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 56
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 57


48. Verify the Rolle’s Theorem for the function f(x) = x² in the inverval [-1, 1].

Answer/Explanation

Answer:
Explaination:
Function f(x) = x² is continuous in [-1,1 ], differentiable in ( -1, 1) and f(-1) = f(1). Hence, Rolle’s Theorem verified.
⇒ f'(c) = 0
⇒ 2c = 0
⇒ c = 0 for c ∈ (-1, 1)


49. Verify the Rolle’s Theorem for die functiony(x) = |x| in the inverval [-1, 1]. [HOTS]

Answer/Explanation

Answer:
Explaination: Not verified, as /(x) =|x| is not derivable at x = 0.


50. Verify the Rolle’s Theorem for the function f(x) = sin 2x in [0, π].

Answer/Explanation

Answer:
Explaination:
Function f(x) = sin 2x is continuous in [0, π], differentiable in (0, π) and (0)= f(π)
Hence, Rolle’s theorem verified.
⇒ f'(c) = 2 cos 2c
⇒ 2cos 2c = 0
Maths MCQs for Class 12 with Answers Chapter 5 Continuity and Differentiability 58


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