If f (θ) = sinθ (sinθ + sin3θ) then f (θ)

a) ≥ 0 only when θ ≥ 0

b) ≤ 0 for all real θ

c) ≥ 0 for all real θ

d) ≤ θ only when θ ≤ 0

Given A =  and f (x) = cosx – x (x + 1). Find the range of f (A).

a)

b)

c)

d)

If f (x) =  and  

then (gof)(x) = …………

a) 0

b) 1

c) 2

d) 3

The number of solutions of the pair of equations

in the interval [ 0, 2π ] is

a) 0

b) 1

c) 2

d) 4

The equation  has

a) no real solutions

b) one real solution

c) two real solutions

d) infinite real solutions

If  satisfies ,
find the value of

Given A =  for all values of θ, then

a) 1 ≤ A ≤ 2

b)  ≤ A ≤ 1

c)  ≤ A ≤ 1

d)  ≤ A ≤

 is equal to

a)

b)

c)

d)

The expression
 
 is equal to

a) 0

b) 1

c) 3

d) sin4α + cosα

The value of the expression  is equal to

a) 2

b)

c) 4

d)

If the lengths of the sides of a triangle are 3, 5, 7 then the largest angle of the triangle is

a)

b)

c)

d)

Let  then  equals

a) tan

b) tan

c) tan

d) tan²

a) 11

b) 12

c) 13

d) 14

 is true if

a) x + y= 0

b) x = y, x ≠ 0

c) x = y

d) x ≠ 0, y ≠ 0

Given both θ and Ф are acute angles and sinθ =  , cos Ф =  then the value of θ + Ф belongs to

a)

b)

c)

d)

 and
where α, β ε [π, π]. Values of α, β which satisfy both the equations is/are

a) 0

b) 1

c) 2

d) 4

If  and α, β lie between 0 and  find  

a)

b)

c)

d) 2

If , then  

a) True

b) False

a) True

b) False

a) True

b) False

Suppose  is an identity in x where  are constants and . Then the value of n = ……….

a) 4

b) 5

c) 6

d) 7

The set of all values of x in the interval (0, π) for which
 is

a) (0, )

b) {  }

c) ( , π)

d) (0,   ) U {  } U ( , π)

If k =  then the numerical value of k is ……….

a)

b)

c)

d)