Question(s) from Search: IIT

If  then  is equal to

a)

b)

c)

d)

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

a)

b)

c)

d)

If  then the value of f(1) is

a)

b) 0

c) 1

d)

Given  find

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

a)

b)

c)

d)

If y =  

Prove that  

The value of  is

a) π

b) aπ

c)

d) 2π

Let F(x) = f (x) g (x) h (x) for all real x, where f (x), g (x) and h (x) are differentiable functions. At some point x₀

 and

 then k is equal to

a) 12

b) 20

c) 24

d) 28

If  then f

a)

b)

c) 3

d) None

If G(x) then  is

a)

b)

c)

d)

Show that

If

Where [x] denotes the greatest integer less than or equal to x then  equals

a) 1

b) 0

c) – 1

d) None of these

Evaluate

a)

b)

c)

d)

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)

Evaluate

a)

b)

c)

d)

 is

a) 2

b) – 2

c)

d)

Evaluate

a)

b)

c)

d)

For x ε R,  is equal to

a) e

b)

c)

d)

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

a) Yes

b) No

Prove that  Hence or otherwise evaluate the integral .

given that  and

a) does not exist

b) is equal to

c) is equal to

d) is equal to 3

Multiple choices

The function

a) continuous at x = 1

b) differentiable at x = 1

c) continuous at x = 3

d) differentiable at x = 3

The value of  is

a) 0

b) 1

c) 2

d) 4

For n > 0,  is

a)

b) π

c)

d)

Evaluate

a) 0

b)

c)

d) 1