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Continuity and Differentiability MCQ Questions And Answers - Mathematics Class 12

Continuity and Differentiability MCQs : This section focuses on the "Continuity and Differentiability" in Mathematics Class 12. These Multiple Choice Questions (MCQs) should be practiced to improve the Mathematics Class 12 skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.

Question 1

A function is said to be continuous in a given interval if there is no break in the graph of the function in the entire interval range.

A. TRUE

B. FALSE

C. Can be true or false

D. Can not say

Question 2

A function is said to be ___________ if it can be drawn without picking up the pencil.

A. discontinuous

B. continuous

C. Both A and B

D. None of the above

Question 3

How many different types of discontinuities there?

A. 1

B. 2

C. 3

D. 4

Question 4

In ______________, a function which has well- defined two-sided limits at x = a, but either f(a) is not defined or f(a) is not equal to its limits.

A. jump discontinuity

B. infinite discontinuity

C. Both A and B

D. removable discontinuity

Question 5

The set of points where the function f given by f (x) =| 2x – 1| sin x is differentiable is

A. R

B. R = {1/2}

C. 0

D. None of the above

Question 6

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 the above

Question 7

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. Both A and B

D. None of the above

Question 8

The derivative of y = (1 – x) (2 – x)…. (n – x) at x = 1 is equal to

A. 0

B. n ! – 1

C. (-1) (n – 1)!

D. None of the above

Question 9

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

Question 10

Jump Discontinuity is a type of discontinuity, in which the left-hand limit and right-hand limit for a function x = a exists, but they are not equal to each other.

A. Yes

B. No

C. Can be yes or no

D. Can not say