# NCERT Class 12-Mathematics: Chapter – 5 Continuity and Differentiability Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

Get unlimited access to the best preparation resource for CBSE/Class-12 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-12.

## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Examples 24 to 35

**Question 24**:

The function is continuous at , then the value of is

(A)

(B)

(C)

(D)

**Answer**:

(B) Is the Correct answer.

**Question 25**:

The function , where denotes the greatest integer function, is continuous at

(A)

(B)

(C)

(D)

**Answer**:

(D) Is the correct answer.

The greatest integer function is discontinuous at all integral values of . Thus D is the correct answer.

**Question 26**:

The number of points at which the function is not continuous is

(A)

(B)

(C)

(D) None of these

**Answer**:

(D) Is the correct answer.

As , when x is an integer so is discontinuous for all .

**Question 27**:

The function given by is discontinuous on the set

(A)

(B)

(C)

(D)

**Answer**:

C is the correct answer.

**Question 28**:

Let . Then,

(A) is everywhere differentiable.

(B) is everywhere continuous but not differentiable at .

(C) is everywhere continuous but not differentiable at .

(D) None of these.

**Answer**:

C is the correct answer.

**Question 29**:

The function is

(A) Continuous at as well as at .

(B) Continuous at but not at .

(C) Discontinuous at as well as at .

(D) Continuous at but not at .

**Answer**:

Correct answer is A.

**Question 30**:

The value of which makes the function defined by continuous at is

(A)

(B)

(C)

(D) None of these

**Answer**:

(D) Is the correct answer.

Indeed does not exist.

**Question 31**:

The set of points where the functions given by is differentiable is

(A)

(B)

(C)

(D) None of these

**Answer**:

B is the correct answer.