BITSAT Mathematics Continuity and Differentiability MCQs

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 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)