MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability with Answers Set-A

Continuity and Differentiability Class 12 Maths MCQs Questions with Answers

Check the below NCERT MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have Provided Continuity and Differentiability Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

Class 12 Maths Chapter 5 Quiz

Class 12 Maths Chapter 5 MCQ Online Test

You can refer to NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Continuity and Differentiability Class 12 Maths MCQ online test

Q1.	If f (x) = 2x and g (x) = \(\frac{x^2}{2}\) + 1, then’which of the following can be a discontinuous function
	A. f(x) + g(x)
	B. f(x) – g(x)
	C. f(x).g(x)
	D. \(\frac{g(x)}{f(x)}\)

Ans: \(\frac{g(x)}{f(x)}\)

Q2.	The function f(x) = \(\frac{4-x^2}{4x-x^3}\) 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

Ans: discontinuous at only one point at x = 0

Q3.	The set of points where the function f given by f (x) =\| 2x – 1\| sin x is differentiable is
	A. R
	B. R = {\(\frac{1}{2}\)}
	C. (0, ∞)
	D. None of these

Ans: R = {\(\frac{1}{2}\)}

Q4.	The function f(x) = cot x is discontinuous on the set
	A. {x = nπ, n ∈ Z}
	B. {x = 2nπ, n ∈ Z}
	C. {x = (2n + 1) \(\frac{π}{2}\) n ∈ Z}
	D. {x – \(\frac{nπ}{2}\) n ∈ Z}

Ans: {x = nπ, n ∈ Z}

Q5.	The function f(x) = e^\|x\| is
	A. continuous everywhere but not differentiable at x = 0
	B. continuous and differentiable everywhere
	C. not continuous at x = 0
	D. None of these

Ans: continuous everywhere but not differentiable at x = 0

Q6.	If f(x) = x² sin\(\frac{1}{x}\), 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

Ans: 0

Q7.	If f(x) =is continuous at x = \(\frac{π}{2}\), then
	A. m = 1, n = 0
	B. m = \(\frac{nπ}{2}\) + 1
	C. n = \(\frac{mπ}{2}\)
	D. m = n = \(\frac{π}{2}\)

Ans: n = \(\frac{mπ}{2}\)

Q8.	If y = log(\(\frac{1-x^2}{1+x^2}\)), then \(\frac{dy}{dx}\) is equal to
	A. \(\frac{4x^3}{1-x^4}\)
	B. \(\frac{-4x}{1-x^4}\)
	C. \(\frac{1}{4-x^4}\)
	D. \(\frac{-4x^3}{1-x^4}\)

Ans: \(\frac{-4x}{1-x^4}\)

Q9.	Let f(x) = \|sin x\| Then
	A. f is everywhere differentiable
	B. f is everywhere continuous but not differentiable at x = nπ, n ∈ Z
	C. f is everywhere continuous but no differentiable at x = (2n + 1) \(\frac{π}{2}\) n ∈ Z
	D. None of these

Ans: f is everywhere continuous but not differentiable at x = nπ, n ∈ Z

Q10.	If y = \(\sqrt{sin x+y}\) then \(\frac{dy}{dx}\) is equal to
	A. \(\frac{cosx}{2y-1}\)
	B. \(\frac{cosx}{1-2y}\)
	C. \(\frac{sinx}{1-xy}\)
	D. \(\frac{sinx}{2y-1}\)

Ans: \(\frac{cosx}{2y-1}\)

Q11.	The derivative of cos^-1 (2x² – 1) w.r.t cos^-1 x is
	A. 2
	B. \(\frac{-1}{2\sqrt{1-x^2}}\)
	C. \(\frac{2}{x}\)
	D. 1 – x²

Ans: 2

Q12.	If x = t², y = t³, then \(\frac{d^2y}{dx^2}\)
	A. \(\frac{3}{2}\)
	B. \(\frac{3}{4t}\)
	C. \(\frac{3}{2t}\)
	D. \(\frac{3}{4t}\)

Ans: \(\frac{3}{4t}\)

Q13.	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. \(\frac{3}{2}\)
	D. \(\frac{1}{3}\)

Ans: 1

Q14.	For the function f(x) = x + \(\frac{1}{x}\), x ∈ [1, 3] the value of c for mean value theorem is
	A. 1
	B. √3
	C. 2
	D. None of these

Ans: √3

Q15.	Let f be defined on [-5, 5] as f(x) = {\(_{-x, if x is irrational}^{x, if x is rational}\) Then f(x) is
	A. continuous at every x except x = 0
	B. discontinuous at everyx except x = 0
	C. continuous everywhere
	D. discontinuous everywhere

Ans: discontinuous at everyx except x = 0

Q16.	Let function f (x) =
	A. continuous at x = 1
	B. differentiable at x = 1
	C. continuous at x = -3
	D. All of these

Ans: All of these

Q17.	If f(x) = \(\frac{\sqrt{4+x}-2}{x}\) x ≠ 0 be continuous at x = 0, then f(o) =
	A. \(\frac{1}{2}\)
	B. \(\frac{1}{4}\)
	C. 2
	D. \(\frac{3}{2}\)

Ans: \(\frac{1}{4}\)

Q18.	let f(2) = 4 then f”(2) = 4 then \(_{x→2}^{lim}\) \(\frac{xf(2)-2f(x)}{x-2}\) is given by
	A. 2
	B. -2
	C. -4
	D. 3

Ans: -4

Q19.	It is given that f'(a) exists, then \(_{x→2}^{lim}\) [/latex] \(\frac{xf(a)-af(x)}{(x-a)}\) is equal to
	A. f(a) – af'(a)
	B. f'(a)
	C. -f’(a)
	D. f (a) + af'(a)

Ans: f(a) – af'(a)

Q20.	If f(x) = \(\sqrt{25-x^2}\), then \(_{x→2}^{lim}\)\(\frac{f(x)-f(1)}{x-1}\) is equal to
	A. \(\frac{1}{24}\)
	B. \(\frac{1}{5}\)
	C. –\(\sqrt{24}\)
	D. \(\frac{1}{\sqrt{24}}\)

Ans: \(\frac{1}{\sqrt{24}}\)

MCQ Questions for Class 12 Maths

NCERT Solution of Maths Class 12

Class 12 Maths

NCERT SOLUTIONS FOR CLASS 12

MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability with Answers

MCQ Questions for Class 12 Maths Chapter 5 Continuity and Differentiability with Answers Set-A

Continuity and Differentiability Class 12 Maths MCQs Questions with Answers

Class 12 Maths Chapter 5 Quiz

Class 12 Maths Chapter 5 MCQ Online Test

Continuity and Differentiability Class 12 Maths MCQ online test

MCQ Questions for Class 12 Maths

NCERT Solution of Maths Class 12

Class 12 Maths

NCERT Solution of Maths Class 12 Chapter 1

NCERT Solution of Maths Class 12 Chapter 2

NCERT Solution of Maths Class 12 Chapter 3

NCERT Solution of Maths Class 12 Chapter 4

NCERT Solution of Maths Class 12 Chapter 5

NCERT Solution of Maths Class 12 Chapter 6

NCERT Solution of Maths Class 12 Chapter 7

NCERT Solution of Maths Class 12 Chapter 8

NCERT Solution of Maths Class 12 Chapter 9

NCERT Solution of Maths Class 12 Chapter 10

NCERT Solution of Maths Class 12 Chapter 11

NCERT Solution of Maths Class 12 Chapter 12

NCERT Solution of Maths Class 12 Chapter 13

MCQ QUESTIONS WITH ANSWER

NCERT SOLUTIONS FOR CLASS 12

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