Mathematics Objective Questions and Answers: Continuity and Differentiability
Access targeted multiple-choice questions for Continuity and Differentiability designed to align with the latest BITSAT academic syllabus for BITSAT Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.
Download Continuity and Differentiability MCQs with Answers
View or download the dedicated Continuity and Differentiability MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.
Question: The function 
is continuous on the interval
- a) [–1, 1]
- b) (–1, 1)
- c) {–1, 1] – { 0 }
- d) (–1, 1) – {0}
Answer: [–1, 1]
Question: If
then f(x) is
- a) Continuous as well as differentiable at x = 0
- b) Continuous but not differentiable at x = 0
- c) Differentiable but not continuous at x = 0
- d) Neither continuous nor differentiable at x = 0
Answer: Continuous as well as differentiable at x = 0
Question: If f (x) =
then the value of f ' (e) is equal to
- a) 1
- b)
- c)
- d)
Answer:
Question: The number of points at which the function 
is discontinuous is :
- a) 1
- b) 2
- c) 3
- d) 4
Answer: 3
Question: Let f (x) = 
be real valued function. Then f ¢(x) for 1 < x < 26 is
- a) 0
- b)
- c) 2 √x -1-5
- d) None of these
Answer: 0
Question: For any differentiable function y of x, 
- a) 0
- b) y
- c) – y
- d) x
Answer: 0
Question: If a function f(x) is given by
then at x = 0, f(x)
- a) Has no limit
- b) Is not continuous
- c) Is continuous but not differentiable
- d) Is differentiable
Answer: Is not continuous
Question: If g is the inverse of function f and f ¢(x) = sin x, then g¢(x) is equal to
- a) cosec {g(x)}
- b) sin {g(x)}
- c)
- d) None of these
Answer:
Question: The number of real roots of the equation ex–1 + x – 2 = 0 is
- a) 1
- b) 2
- c) 3
- d) 4
Answer: 1
Question: If y =
then 
is
- a) n2y
- b) – n2y
- c) –y
- d) 2x2y
Answer: n2y
Question:
(cos–1 x + sin–1 x) is
- a) π/2
- b) 0
- c)
- d) None of these
Answer: 0
Question:
Let ( ) =
Then which one of the following is true?
- a) f is differentiable at x = 0 and x =1
- b) f is differentiable at x = 0 but not at x = 1
- c) f is differentiable at x = 1 but not at x = 0
- d) f is neither differentiable at x = 0 nor at x =1
Answer: f is differentiable at x = 0 but not at x = 1
Question: If y =1 + x +
then
is equal to
- a) x
- b) 1
- c) y
- d) None of these
Answer: y
Question: If
is continuous at x = –5, then the value of ‘a’ will be
- a) 3/2
- b) 7/8
- c) 8/7
- d) 2/3
Answer: 7/8
Question: If x = a sin θ and y = b cos θ, then 
is
- a)
- b)
- c)
- d)
Answer:
Question: If f(x) = xα log x and f(0) = 0, then the value of α for which Rolle’s theorem can be applied in [0, 1] is
- a) –2
- b) –1
- c) 0
- d) 1/2
Answer: 1/2
Question: If the function f(x) =
is continuous at x = 2 and 4, then the values of a and b are
- a) 3, 5
- b) 3, – 5
- c) 0, 3
- d) 0, 5
Answer: 3, – 5
Question: If y = xx2 , then 
is equal to
- a) (2 ln x)
- b) (2 ln x +1)
- c) (ln ln x +1)x x2
- d) None of these
Answer: None of these
Question: The function f (x) = (x -1) √| ln x | is at x = 1
- a) Discontinuous
- b) Continuous but not differentiable
- c) Differentiable with f ' (1) = 0
- d) Differentiable with f ¢ (1) ≠ 0
Answer: Differentiable with f ' (1) = 0
Question: Let 
Then f (x) is derivable at x = 1, if
- a) a = 2
- b) a = 1
- c) a = 0
- d) a = 1/2
Answer: a = 1/2
Question: If y = e–x cos x and y4 + ky = 0, where 
then k =
- a) 4
- b) – 4
- c) 2
- d) – 2
Answer: 4
Question: The set of points of discontinuity of the function 1/log | x | is –
- a) {–1, 0, 1}
- b) {0}
- c) {0, 1}
- d) None of these
Answer: {–1, 0, 1}
Question: If y = (cos x2)2 then 
is equal to :
- a) – 4x sin 2x2
- b) – x sin x2
- c) – 2x sin 2x2
- d) – x cos 2x2
Answer: – 2x sin 2x2
Question: If
then the points of discontinuity of the function f [ f {f(x)}] are
- a) {0, –1}
- b) {0,1}
- c) {1, –1}
- d) None of these
Answer: {0,1}
Question: If
f
is continuous at x = 0, then the value of k will be
- a) 1
- b) -1
- c) 0
- d) None of these
Answer: 0
Question: Let
Then f (x) is derivable at x = 1, if
- a) a = 2
- b) a = 1
- c) a = 0
- d) a = 1/2
Answer: a = 1/2
Question: Let h(x) = min {x, x2}, for every real number of x, Then
- a) h is continuous for all x
- b) h is differentiable for all x
- c) h’(x) = 2, for all x > 1
- d) h is not differentiable at three values of x.
Answer: h is continuous for all x
Question: If f(x) = (x + 1)cot x is continuous at x = 0, then f(0) is equal to
- a) 0
- b) 1
- c) 1/e
- d) e
Answer: e
Question: If 2t = v2, then 
is equal to
- a) 0
- b) 1/4
- c) 1/2
- d) 1/v
Answer: 1/v
Question: If y2 = P (x), is a polynomial of degree, then
equals
- a) P'''(x) + P' (x)
- b) P''(x). P'''(x
- c) P (x). P''' (x)
- d) a constant
Answer: P (x). P''' (x)
Free study material for Mathematics
Multiple Choice Questions (MCQs) for BITSAT Mathematics Continuity and Differentiability
Download Multiple Choice Questions: Continuity and Differentiability (BITSAT Mathematics)
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FAQs
You can get most exhaustive BITSAT Mathematics Continuity and Differentiability MCQs for free on StudiesToday.com. These MCQs for BITSAT Mathematics are updated for the 2026-27 academic session as per BITSAT examination standards.
Yes, our BITSAT Mathematics Continuity and Differentiability MCQs include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the BITSAT paper is now competency-based.
By solving our BITSAT Mathematics Continuity and Differentiability MCQs, BITSAT students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.
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