Let f : ℝ → ℝ and g : ℝ → ℝ be continuous functions. Then the value of integral  is

a) π

b) 1

c) – 1

d) 0

The value of  is

a) 0

b) 1

c)

d)

If  and , then constants A and B are

a)

b)

c)

d)

The value of  where [.] represents the greatest integer function is

a)

b)

c)

d)

a)

b)

c)

d)

If  then g(x + π) equals

a) g(x) + g(π)

b) g(x) − g(π)

c) g(x) g(π)

d)

Let f be a positive function. Let
 
 where
2k – 1 > 0 then  is

a) 2

b) k

c)

d) 1

If  then the value of f(1) is

a)

b) 0

c) 1

d)

If  f(x) = x – [x] for every real number x, where [x] is the integral part of x, then  is

a) 1

b) 2

c) 0

d)

 is equal to

a) 2

b) –2

c)

d)

If for real number y, [y] is the greatest integer less than or equal to y then the value of the integral   is

a)

b)

c)

d)

Let , where f is such that  and  then g(2) satisfies the inequality

a)

b)

c)

d)

If

Then  =

a) 0

b) 1

c) 2

d) 3

The value of the integral  

a)

b)

c) 3

d) 5

The value of  is

a) π

b) aπ

c)

d) 2π

The integral  equals

a)

b)

c) 1

d)

If  then the expression for  in terms of  is

a)

b)

c)

d)

If f (x) is differentiable and  , then  equals

a)

b)

c)

d)

The value of the integral  is

a)

b)

c)

d)

is equal to

a) 0

b) 4

c) 6

d) −4

If  then f

a)

b)

c) 3

d) None

Show that

Evaluate   where n is a positive integer and t is a parameter independent of x.

a)

b)

c)

d)