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

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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 .

(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 .

(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.