The value of  is

a)

b)

c) 1

d) 2

If for non-zero x, where a ≠ b thenis equal to

a)

b)

c)

d)

For n > 0,  is

a)

b) π

c)

d)

Interval containing the value of the integral

Multiple correct answers

Area of the region bounded by the curves y = e^x and curves x = 0 and y = e is

a) e – 1

b)

c)

d)

, then the value of  is

The value of

 is equal to

a) sec⁻¹ (secx + cosx) + c

b) sec⁻¹ (cosx − tanx) + c

c) sec⁻¹ (secx − cosx) + c

d) none of the above

If then the value of u₁₀ + 90u₈ is equal to

a)

b)

c)

d)

If f and g are continuous on [0, π] satisfying f (x) + f (π – x) = g (x) + g (π – x) then  is equal to

a) π

b) 2 π

c)

d)

If x > 0 and  where [.] denotes the greatest integer function, then

a) A = [x] – 1

b) B = − x − [x]

c) A = [x] + 1

d) B = x + [x]

The area above X – axis, bounded by the line x = 4 and the curve y = f (x) where f (x) = x², 0 ≤ x ≤ 1 and  is

a) 2 square units

b) 5 square units

c) 4 square units

d) 9 square units

If , f (0) = 0, then f (1) is equal to

a)

b)

c)

d) None of these

Determine whether the following statements are true or false.
Statement 1
 
Statement 2
f (x) is continuous in [0, 2]

a) True, True

b) True, False

c) False True

d) False, False

The area enclosed between y = x³ and  is

a)  square units

b)  square units

c)  square units

d)  square units

The value of  is

a)

b)

c) 3

d) 5

The area of the figure bounded by the straight line x = 0, x = 2 and the curves y = 2^x, y = 2x – x² is

a)  square units

b)  square units

c)  square units

d)  square units

The value of the integral  is

a)

b)

c) – sin2x + c

d)

The value of  is

a) – 1

b) 1

c) 0

d) None of the above

In (- 4, 4) the function  has

a) No extrema

b) One extrema

c) Two extremas

d) None of the above

If  then

a) a = e, b = − 2

b) a = e, b = 2

c) a = − e, b = 2

d) none of these

The area contained between the curve  and X – axis is

a) πa² square units

b) 3πa² square units

c) 2πa² square units

d) None of these