BITSAT Mathematics Continuity and Differentiability MCQs with answers available in Pdf for free download. The MCQ Questions for BITSAT Mathematics with answers have been prepared as per the latest BITSAT Mathematics syllabus, books and examination pattern. Multiple Choice Questions form important part of competitive exams and BITSAT exam and if practiced properly can help you to get higher rank. Refer to more topic wise BITSAT Mathematics Questions and also download more latest study material for all subjects and do free BITSAT Mathematics Mock Test
MCQ for BITSAT Mathematics Continuity and Differentiability
BITSAT Mathematics students should refer to the following multiple-choice questions with answers for Continuity and Differentiability in BITSAT. These MCQ questions with answers for BITSAT Mathematics will come in exams and help you to score good marks
Continuity and Differentiability MCQ Questions with Answers
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)