# NCERT Class 12-Mathematics: Chapter – 5 Continuity and Differentiability Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 32**:

Differential coefficient of is

(A)

(B)

(C)

(D)

**Answer**:

(A) Is the correct answer.

**Question 33**:

If is

(A)

(B)

(C)

(D)

**Answer**:

(D) Is the correct answer.

**Question 34**:

The value of *c* in Rolle՚s Theorem for the function is

(A)

(B)

(C)

(D)

**Answer**:

(D) Is the correct answer.

**Question 35**:

The value of in Mean value theorem for the function is

(A)

(B)

(C)

(D)

**Answer**:

(A) Is the correct answer.

**Question 36**:

Match the following

(A) | If a function is continuous at , then is | (a) | |

(B) | Every continuous function is differentiable | (b) | True |

(C) | An example of a function which is continuous everywhere but not differentiable at exactly one point | (c) | |

(D) | The identity function i.e.. is a continuous function | (d) | False |

**Answer**:

## Fill in the Blanks in Each of the Examples 37 to 41

**Question 37**:

The number of points at which the function is discontinuous is ________.

**Answer**:

The given function is discontinuous at and hence the number of points of discontinuity is .

**Question 38**:

If is continuous, then should be equal to ________.

**Answer**:

**Question 39**:

The derivative of is ________.

**Answer**:

.

**Question 40**:

If , then is equal to ________.

**Answer**:

**Question 41**:

The derivative of is ________.

**Answer**: