# Class 12 Mathematics Chapter 5 Continuity and Differentiability MCQ Question with Answer

Continuity and Differentiability Class 12 MCQ is one of the best strategies to prepare for the CBSE Class 12 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more MCQ on Continuity and Differentiability Class 12, which will help them all through their board test.

## Continuity and Differentiability Class 12 MCQ Questions with Answer

Class 12 Maths MCQ with answers are given here to Chapter 5 Continuity and Differentiability. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 12 Mathematics syllabus. By Solving these Class 12 MCQs, you will be able to analyze all of the concepts quickly in the chapter and get ready for the Class 12 Annual exam.

Learn Continuity and Differentiability Class 12 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 12 Mathematics Continuity and Differentiability MCQ with answers given below.

Question 1. The number of points at which the function f (x) = 1/x-[x] is not continuous is
(a) 1
(b) 2
(c) 3
(d) none of these

D

Question 2. The value of c in Rolle’s theorem for the function f(x) = x3 – 3x in the interval [0, 3] is
(a) 1
(b) –1
(c) 3/2
(d) 1/3

A

Question 3. 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

A

Question 4. The function f (x) = 4-x2 /4x-x3 is
(a) discontinuous at only one point
(b) discontinuous at exactly two points
(c) discontinuous at exactly three points
(d) none of these

C

Question 5. The function f(x) = |x| + |x – 1| is
(a) continuous at x = 0 as well as at x = 1.
(b) continuous at x = 1 but not at x = 0.
(c) discontinuous at x = 0 as well as at x = 1.
(d) continuous at x = 0 but not at x = 1.

A

Question 6. The value of c in Rolle’s Theorem for the function f(x) = ex sin x, in [0, π] is
(a) π/6
(b) π/4
(c) π/2
(d) 3π/4

D

Question 7. Let f (x) = sinx . Then
(a) f is everywhere differentiable
(b) f is everywhere continuos but not differentiable at x = nπ : n ∈ Z
(c) f is everywhere continuous but not differentiable at x (2n + 1)π/2 , n ∈ Z
(d) none of these

B

Question 8. If f (x) x sin 1/x, where x ! 0 , then the value of the function f at x = 0, so that the function is continuous at x = 0, is
(a) 0
(b) –1
(c) 1
(d) None of these

A

Question 9. The function f(x) = [x], where [x] denotes the greatest integer function, is continuous at
(a) 4
(b) –2
(c) 1
(d) 1.5

D

Question 10. The function f : R → R given by f(x) = – |x – 1| is [CBSE 2020 (65/2/1)]
(a) continuous as well as differentiable at x = 1
(b) not continuous but differentiable at x = 1
(c) continuous but not differentiable at x = 1
(d) neither continuous nor differentiable at x = 1

C

Question 11. The value of c in Mean Value Theorem for the function f(x) = x(x – 2), x ∈ [1, 2] is
(a) 3/2
(b) 2/3
(c) 1/2
(d) 7/4

A

Question 12. If u sin-1 (2x/1+x2) and v tan-1 (2x/1-x2) , then du/dv is
(a) 1/2
(b) x
(c) 1-x2/1+x2[4, -4]Φ
(d) 1

D

Question 13. If y = log tanx , then the value of dy/dx at x = π/4 is
(a) 0
(b) 1
(c) 1/2
(d) ∞

B

Question 14. Differential coefficient of sec (tan–1x) w.r.t. x is
(a) x/√(1+x2)
(b) x/(1+x2)
(c) x/(1+x2)
(d) 1/√(1+x2)

A

Question 15. The function (x) =x-1/x(x2-1) is discontinuous at
(a) exactly one point
(b) exactly two points
(c) exactly three points
(d) no point

C

Question 16. If y = A e5x + B e–5x, then d2y/dx2 is equal to
(a) 25 y
(b) 5 y
(c) –25 y
(d) 15 y

A

Question 17. For the curve √x + √y =1 ,dy/dx , at(1/4 ,1/4) is
(a) 1/2
(b) 1
(c) –1
(d) 2

C

Question 18. The set of points where the functions f given by f (x) = |x – 3| cos x is differentiable is
(a) R
(b) R – {3}
(c) (0, ∞)
(d) none of these

B

Question 19. If f ′(1) = 2 and y = f (log ex), then dy/dx at x = e is
(a) 0
(b) 1
(c) e
(d) 2/e

D

Question 20. If f(x) = 2x and g(x) = x2/2 + 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) g(x)/ f(x )

D

Whoever needs to take the CBSE Class 12 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 12 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Continuity and Differentiability Class 12 MCQ are ready by the subject specialists themselves.

## Fill in the blanks

Question 1. d/dx sec(tan-1)= _____________ .

x/√1 + x2

Questions 2. If f (x) = cos x , then f (π/4) = _____________ .

-1/√2

Questions 3. If f(x) = (x + 1), then (d/dx) fof (x) = _____________ .

1

Question 4. The function f (x) = 2 -X2 /9X – Xis discontinuous exactly at _____________ points.

three

Question 5. If cos (xy) = k, where k is a constant and xy ≠ np, n ∈ Z, then dy/dx is equal to _____________ .

-y/x

Question 6. The number of points of discontinuity of f defined by f(x) = |x| – |x + 1| is _____________.

0

Questions 7. The number of points at which the function f(x)=1/log|x| is discontinuous is _________ .

three

Question 8. If y = tan–1 x + cot–1 x, x ∈ R, then dy/dx is equal to _____________ .

0

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