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.