Evaluate
 

Evaluate
 

Evaluate

Let  for  and , where in the composition, f occurs n times. Then  is equal to

a)

b)

c)

d)

Evaluate

Evaluate

If  then

a)

b)

c) 3

d)

a)

b)

c)

d) 1

If the area bounded by  and  is 1 then the value of a is

a) 1

b)

c)

d)

Let p(x) be a function defined on R such that  for all . Then

a)

b) 21

c) 41

d) 42

The area bounded by the curves  between the ordinates and is

a)

b)

c)

d)

 denotes the greatest integer function, is equal to

a)

b) 1

c) – 1

d)

The value of  is

a)

b)

c)

d)

Evaluate

a)  ln tan (

b)  ln tan (

c) ln tan (

d) ln tan (

The area enclosed between the curve  and  is

a)

b) 1

c)

d)

The value of the integral  dx

Evaluate

a)  

b)  

c)  

d)  

a)

b)

c)

d)

The value of  where [x] denotes the greatest

integer not exceeding x is

a)

b)

c)

d)

a)

b) tan1

c)

d)

Let f(x) be a non-negative continuous function such that the area

bounded by the curve X–axis and the ordinates  and

  is  then  is

a)

b)

c)

d)

If

Then

a)

b)

c)

d)