Evaluate   dx,  a>0

a) 2π

b)

c)

d) aπ

If  dx =Ax + B ln sin(x

Then value of (A, B) is

a) (sinα, cosα)

b) (cosα, sinα)

c) (sinα, cosα)

d) (cosα, sinα)

 =

a)  ln  + c

b)  ln  + c

c)  ln  + c

d)  ln  + c

a)

b)

c)

d)

If   

then A is equal to

a) 0

b)

c)

d)

If

Then the value of  is

a) 2

b)  

c)  

d)  

If  and   then

a)

b)

c)

d)

If  then  is equal to

a)

b)

c)

d)

 is

a)

b) 0

c)

d)

Let  If  then

one of the possible values of k is

a) 15

b) 16

c) 63

d) 64

Let  be a function satisfying  with  and  be a function that satisfies  then the value of the integral  is

a)

b)

c)

d)

 is

a) 20

b) 8

c) 10

d) 18

, then  equals

a)

b) 1

c)

d) 0

dx is

a)

b)

c)

d)

Evaluate  dx

a)

b)

c) 0

d) 1

a)

b)

c)

d) None of the above

Let f(x) be differentiable for all x. If f (1) = − 2 and  for x [1, 6] then

a) f(6)=5

b) f(6) < 5

c) f(6) < 8

d) f(6) ≥ 8

The value of the definite integral  is

a) – 1

b) 2

c)

d)

The area bounded by the curve y = f(x), the X–axis and the ordinate x = 1 and x = b is (b – 1) sin (3b + 4). Then f(x) is

a) (x – 1) cos (3x + 4)

b) sin(3x + 4)

c) sin(3x + 4) + 3(x – 1) cos (3x + 4)

d) none of these

The slope of the tangent to the curve y = f(x) at [x, f(x)] is 2x + 1. The curve passes through (1, 2), then the area bounded by the curve and X–axis, and the line x = 1 is

a)

b)

c)

d) 6

Let   then the real roots of the equation

 are

a) ± 1

b)

c)

d) 0 and 1

The area bounded by the curves  

and the X–axis in the first quadrant is

a) 9

b)

c) 36

d) 18

The area enclosed between y = ax² and x = ay² (a > 0)

is one square unit. Then the value of a is

a)

b)

c) 1

d)