# NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 7

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## 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.