The largest interval lying in  for which the function  is defined, is

• [0, π]

• 

• [-π/4, π/2)

• [-π/4, π/2)

Let f : R → R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true ?

• f(x) ≥ 1 for all x ∈ R

• f(x) is not differentiable at x = 1

• f(x) is differentiable everywhere

• f(x) is differentiable everywhere

The function f: R ~ {0} → R given by

can be made continuous at x = 0 by defining f(0) as

• 2

• -1

• 1

• 1

The number of values of x in the interval [0, 3π] satisfying the equation 2sin² x + 5sinx − 3 = 0 is

• 4

• 6

• 1

• 1

The set of points where x f(x) = x /1+|x| is differentiable is

• (−∞, 0) ∪ (0, ∞)

• (−∞, −1) ∪ (−1, ∞)

• (−∞, ∞)

• (−∞, ∞)

Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} be a relation on the set A = {3, 6, 9, 12}. The relation is

• reflexive and transitive only

• reflexive only

• an equivalence relation

• an equivalence relation

Let f : (-1, 1) → B, be a function defined by  then f is both one-one and onto when B is the interval

• 

• [0, π/2)

• 
• 

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

• Interval	Function
  (-∞, ∞)	x3 – 3x2 + 3x + 3

• Interval	Function
  [2, ∞)	2x3 – 3x2 – 12x + 6

• Interval	Function
  (-∞, 1/3]	3x2 – 2x + 1

• Interval	Function
  (-∞, 1/3]	3x2 – 2x + 1

Suppose f(x) is differentiable x = 1 and 

• 3

• 4

• 5

• 5

A real valued function f(x) satisfies the functional equation f(x – y) = f(x) f(y) – f(a – x) f(a + y) where a is a given constant and f(0) = 1, f(2a – x) is equal to

• –f(x)

• f(x)

• f(a) + f(a – x)

• f(a) + f(a – x)