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 e^{x–1} + x – 2 = 0 is

- a) 1
- b) 2
- c) 3
- d) 4

**Answer: 1**

#### Question: If y =then is

- a) n
^{2}y - b) – n
^{2}y - c) –y
- d) 2x
^{2}y

**Answer: ****n ^{2}y**

#### 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 +thenis 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) = x^{α} 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 = x^{x2} , 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 y_{4} + 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 x^{2})^{2} then is equal to :

- a) – 4x sin 2x
^{2} - b) – x sin x
^{2} - c) – 2x sin 2x
^{2} - d) – x cos 2x
^{2}

**Answer: ****– 2x sin 2x ^{2}**

#### 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, x^{2}}, 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 = v^{2}, then is equal to

- a) 0
- b) 1/4
- c) 1/2
- d) 1/v

**Answer: 1/v**

#### Question: If y^{2} = 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)**