BITSAT Mathematics Continuity and Differentiability MCQs

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 BITSAT Mathematics Determinants 36is continuous on the interval

  • a) [–1, 1]
  • b) (–1, 1)
  • c) {–1, 1] – { 0 }
  • d) (–1, 1) – {0}

Answer: [–1, 1]

 

Question: If

 BITSAT Mathematics Continuity 1

 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) =BITSAT Mathematics Continuity 2then the value of f ' (e) is equal to

  • a) 1
  • b)

    BITSAT Mathematics Continuity 3

  • c)

    BITSAT Mathematics Continuity 4

  • d)

    BITSAT Mathematics Continuity 5

Answer:

 BITSAT Mathematics Continuity 3

Question: The number of points at which the function BITSAT Mathematics Continuity 6is discontinuous is :

  • a) 1
  • b) 2
  • c) 3
  • d) 4

Answer: 3

 

Question: Let f (x) = BITSAT Mathematics Continuity 7 be real valued function. Then f ¢(x) for 1 < x < 26 is

  • a) 0
  • b) 

    BITSAT Mathematics Continuity 8

  • c) 2 √x -1-5
  • d) None of these

Answer: 0 

Question: For any differentiable function y of x, BITSAT Mathematics Continuity 9

  • a) 0
  • b) y
  • c) – y
  • d) x

Answer: 0

 

Question: If a function f(x) is given by

 BITSAT Mathematics Continuity 10

BITSAT Mathematics Continuity 11

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)

    BITSAT Mathematics Continuity 12

  • d) None of these

Answer:

 BITSAT Mathematics Continuity 12

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 =BITSAT Mathematics Continuity 13then BITSAT Mathematics Continuity 14 is

  • a) n2y
  • b) – n2y
  • c) –y
  • d) 2x2y

Answer: n2y

 

Question:  

BITSAT Mathematics Continuity 15(cos–1 x + sin–1 x) is

  • a) π/2
  • b) 0
  • c) 

    BITSAT Mathematics Continuity 16

  • d) None of these

Answer: 0

 

Question:

Let ( ) =BITSAT Mathematics Continuity 17

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 +BITSAT Mathematics Continuity 18thenBITSAT Mathematics Continuity 19is equal to

  • a) x
  • b) 1
  • c) y
  • d) None of these

Answer: y

 

Question: If

BITSAT Mathematics Continuity 20

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 BITSAT Mathematics Continuity 21is

  • a)

    BITSAT Mathematics Continuity 22

  • b)

    BITSAT Mathematics Continuity 23

  • c)

    BITSAT Mathematics Continuity 24

  • d)

    BITSAT Mathematics Continuity 25

Answer:

BITSAT Mathematics Continuity 23

  

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) =BITSAT Mathematics Continuity 26is 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 BITSAT Mathematics Continuity 27is 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 BITSAT Mathematics Continuity 28 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 BITSAT Mathematics Continuity 29 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 BITSAT Mathematics Continuity 30is equal to :

  • a) – 4x sin 2x2 
  • b) – x sin x2
  • c) – 2x sin 2x2
  • d) – x cos 2x2

Answer: – 2x sin 2x2

 

Question: If

 BITSAT Mathematics Continuity 31

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

fBITSAT Mathematics Continuity 32

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

 BITSAT Mathematics Continuity 28

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 BITSAT Mathematics Continuity 33is 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

 BITSAT Mathematics Continuity 34

 equals

  • a) P'''(x) + P' (x)
  • b) P''(x). P'''(x
  • c) P (x). P''' (x)
  • d) a constant

Answer: P (x). P''' (x)

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