Let  be a differentiable function having . Then,   is equal to

a) 18

b) 12

c) 36

d) 24

, then  equals

a)

b) 1

c)

d) 0

Let f : R → R be a function defined by f(x) = min(x + 1, |x| + 1) then which of the following is true?

a) f(x) ≥ 1 for all x  R

b) f(x) is not differentiable at x = 1

c) f(x) is differentiable everywhere

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

The function f : R – {0} → R given by  can be made continuous by defining f(0) as

a) 2

b) -1

c) 0

d) 1

Suppose f(x) is differentiable at x = 1 and
 

a) 6

b) 5

c) 4

d) 3

If f is a real differentiable function satisfying |f(x) – f(y)| ≤ (x – y)², x, y  R and f(0) = 0, then f(1) equals

a) 1

b) 2

c) 0

d) – 1

Let α, β be the distinct roots of ax² + bx + c = 0 then  is equal to

a)

b)

c)

d)

If  then the values of a, b are

a) a  R, b  R

b) a = 1, b  R

c) a  R, b = 2

d) a = 1, b = 2

Let . If f(x) is continuous in  then  is

a) 1

b)

c)

d) 1

 is

a)

b) 0

c)

d) ∞

If  then the value of k is

a) 0

b)

c)

d)

 is equal to

a) e⁴

b) e²

c) e³

d) e

For x ε R,  is equal to

a) e

b) e⁻¹

c) e⁻⁵

d) e⁵

Let f(2) = 4 and  then  is given by

a) 2

b) – 2

c) – 4

d) 3

If α, β be the roots of the equation ax² + bx + c = 0 then  is

a) ln|a(α – β)|

b) e^{a(β – α)}

c) e^{a(α – β)}

d) None of these

The values of constants a, b so that  is

a) a = 0, b = 0

b) a = 2, b = −1

c) a = −1, b = 1

d) a = 1, b = −1

Let f(x) = (x+|x|) |x| then for all x

a) f  is not continuous

b)  is differentiable for all x

c)  is continuous

d) None ofthe above

The value of  is

a) 2asina + a²cosa

b) 2asina − a²cosa

c) 2acosa + a²sina

d) None of these

If f(x) = sign(x³), then

a) f(x) is continuous but not differentiable at x = 0

b)

c)

d) f is not differentiable at x = 0

The function defined by
   is

a) Continuous at x = 1

b) Continuous at x = 3

c) Differentiable at x = 1

d) All of the above

Let  and  

where a, b are non–negative real numbers. The value of a, if (gof)x is continuous for all values of x, is

a) – 1

b) 0

c) 1

d) 2

If the function  

be continuous at , then k is equal to

a) 3

b) 6

c) 12

d) None of these

If α and β be the roots of ax² + bx + c = 0 then

 is

a) ln a(α – β)

b)

c)

d) None of these