JEE Mathematics Continuity and Differentiability MCQs

Question:

• a) x=2m+1/1-2m
• b) x = 0
• c) x=2m-1/2m+1
• d) None of these

Answer: x=2m+1/1-2m

Question: If the function 

is continuous,then the value of k is equal to :

• a) 3
• b) – 3
• c) 2
• d) 4

Answer: 3

Question:

is continuous at x = 0, then the value of k is :

• a) 2
• b) 1
• c) – 2
• d) 1/2

Answer: 2

Question:

Let

Then, f (x) is continuous at x = 4, when

• a) a = 1, b = – 1
• b) a = 1, b = 1
• c) a = 0, b = 0
• d) a = – 1, b = 1

Answer: a = 1, b = – 1

Question: f(x) = a sin| x | +be^|x| is differentiable at x = 0, when :

• a) a + b = 0
• b) a – b = 0
• c) a = 0
• d) b = 0

Answer: a + b = 0

Question:

• a)

  

• b) –1
• c) 1
• d) None of these

Answer:

Question:

where [ . ] represents greatest integer function and { . } represents fractional part of x, then which of the following is true –
(1) f (x) is injective discontinuous function
(2) f (x) is surjective non-differentiable function
(3) max {values of x at which the function is discontinuous} = f (1)

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: Which of the following function(s) has/have removable discontinuity at x = 1?

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question: The function

(1) continuous at x = 1 (2) differentiable at x = 1
(3) continuous at x =3 (4) differentiable at x = 3

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question:

Statement 1 : f (x) = sin x + [x] is discontinuous at x = 0.
Statement 2 : If g (x) is continuous and h (x) is discontinuous at x = a, then g (x) + h (x) will necessarily be discontinuous at x = a.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

More Questions..............................

Question:

Statement 1 : | x³ | is differentiable at x = 0.
Statement 2 : If f (x) is differentiable at x = a then | f (x) | is also differentiable at x = a.

• a) Statement -1 is True, Statement-2 is False.
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• d) None of these

Answer: Statement -1 is True, Statement-2 is False.

Question:

Statement 1 : Sum of left hand derivative and right hand derivative of f (x) = | x² – 5x + 6 | at x = 2 is equal to zero.

Statement 2 : Sum of left hand derivative and right hand derivative of f (x) = | (x – a) (x – b) | at x = a (a < b) is equal to zero,

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question: If f (x) = x^1/x – 1 for all positive x ≠1 and f is continuous at 1, then f(1) equals:

• a) 0
• b) e
• c) e²
• d) 1/e

Answer: 0

Question:

• a) f (x) is continuous but not differentiable at x = 0
• b) f (x) is differentiable at x = 0
• c) f (x) is differentiable but not continuous at x = 0
• d) f (x) is not differentiable at x = 0

Answer: f (x) is continuous but not differentiable at x = 0

Question: If a function

• a) f(x) is discontinuous at x = 0
• b) none of these.
• c) f(x) is continuous as well as differentiable at x = 0
• d) f(x) is continuous at x = 0 but not differentiable at x = 0

Answer: f(x) is discontinuous at x = 0

Question: Let [x] denotes the greatest integer function and f(x) = [tan² x], then :

• a) f(x) is continuous at x = 0
• b) f(x) is discontinuous at x = 0
• c) f(0) = 1
• d) None of these

Answer: f(x) is continuous at x = 0

Question:

• a) continuous for all x.
• b) discontinuous for all x
• c) discontinuous at x = – 1
• d) contiuous at x = – 1

Answer: continuous for all x.

Question:

If f (x) is continuous at x = 2, then the value of k:

• a) 3/4
• b) 3
• c) 2
• d) 2/3

Answer: 3/4

Question:

• a) for all real value of x
• b) for all integral value of x only
• c) for all real value of x except x = 2
• d) for x = 2 only

Answer: for all real value of x

Question: The function f (x)= log(1 ax) log(1 bx)/x is not defined at x = 0, the value of which should be assigned to f at x = 0, so that it is continuous at x = 0, is :

• a) a + b
• b) log a – log b
• c) a – b
• d) log a + log b

Answer: a + b

Question:

• a) at all integral points
• b) at all negative non-integral points
• c) at all positive non-integral points
• d) at all non-integral points

Answer: at all integral points

Question:

Then the value of a in order that f (x) may be continuous at x = 0 is :

• a) – 8
• b) – 4
• c) 8
• d) 4

Answer: – 8

Question:

is continuous at x = 0, then the value of k is :

is continuous at x = 0, then the value of k is :

• a) 0
• b) 1/2
• c) None of these
• d) 1/4

Answer: 0

Question:

• a)

  

• b)

  

• c)

  

• d) m = 1, n = 0

Answer:

Question:

• a) None
• b) – 1
• c) 1
• d) 0

Answer: None

Question: The function

• a) discontinuous everywhere
• b) discontinuous at x = 0
• c) discontinuous at 1
• d) continuous at x = 1

Answer: discontinuous everywhere

Question:

• a) f (x) is discontinuous at x = 0
• b) f (x) is continuous at x = 0
• c) none of these
• d) Both

Answer: f (x) is discontinuous at x = 0