The point representing complex number z for which
 |z – 3| = |z – 5| lies on the locus given by

a) an ellipse

b) a circle

c) a straight line

d) none of these

If f(x) is differentiable and strictly increasing function then the value of  is

a) 1

b) 0

c) – 1

d) 2

If f(x) be the interval of  find

a) ½

b) 1

c) 2

d) 4

Let f : ℝ → ℝ be a differentiable function and f (1) = 4. Then show that the value of   =

 equals

a)

b)

c)

d) 4 f (2)

Find the limiting value of    as x a

The set of all points where the function  is differentiable is

a)

b) [0, ∞)

c)  

d)  (0, ∞)

e)  None of these

The value of  is   

a) 1

b) – 1

c) 0

d) None of these

Let [.] denotes the greatest integer function and

f(x) =  then

a)  does not exist

b) f (x) is continuous at x = 0

c) f (x) is not differentiable at x = 0

d)

The function f(x) =  denotes the greatest integer function is discontinuous at

a) All x

b) All integer points

c) No x

d) x which is not an integer

a) exists and equals

b) exists and equals

c) does not exist because x – 1 → 0

d) does not exist because the left hand limit is not equal to the right hand limit.

 is

a) 2

b) – 2

c)

d)

For x ε R,  is equal to

a) e

b)

c)

d)

 equals

a) – π

b) π

c)

d) 1

The left hand derivative of f (x) = [x] sinπx at k, k an integer is

a) (k – 1)π

b) (k – 1)π

c) kπ

d)  kπ

Evaluate if sin |x| - |x| is differentiable at x = 0.

a) Yes

b) No

Let f : ℝ → ℝ be such that f (1) = 3 and  then

 equals

a) 1

b)

c)

d)

If  where n is a non–zero real number, then a is equal to

a) 0

b)

c) n

d)

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3

Multiple choices

If x + |y| = 2y, then y as a function of x is

a) Defined for all real x

b) Continuous at x = 0

c) Differentiable for all x

d) Such that  for x < 0

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

Let f (x) =   then for all x

a)

b) f is differentiable

c)  is continuous

d) f is continuous

Multiple choices

If f (x) = then

a) f (x) is continuous ∀ x  ℝ

b) f (x) > 0 ∀ x > 1

c) f (x) is continuous but not differentiable ∀ x  ℝ

d) f (x) is not differentiable at two points