If tan θ =  then sin θ is

a)  but not  

b)  or

c)  but not −

d) None of these

If  then

tan

a) True

b) False

The equation  has

a) No solution

b) One solution

c) More than one real solution

d) Cannot be said

The solution of is

a)

b)

c)

d) None of these

The general solution of
 is

a)

b)

c)

d)

In a triangle ABC, angle A is greater than angle B. If the measures of angle A and B satisfy the equation , then the measure of angle C is

a)

b)

c)

d)

The number of solutions of the equation

a) 0

b) 1

c) 2

d) Infinitely many

If n be a positive integer such that
 then

a)

b)

c)

d)

The general value of θ satisfying the equation
 is

a)

b)

c)

d)

The number of values of x in the interval (0, 5π) satisfying the equation  is

a) 0

b) 5

c) 6

d) 10

Which of the following are rational?

a)

b)

c)

d)

In ΔPQR, angle R . If tan  and tan  are roots of the equation

a)

b)

c)

d)

The maximum value of cos₁ cos₂ cos_{3 ……} cos_nunder the restriction 0  _{1 , 2} , ₃ …. , _n   and cot₁ cot₂ cot_{3 ……} cot_n= 1 is

a)

b)

c)

d)

If α + β =  and β + γ = α, then tanα equals

a) 2(tanβ + tanγ)

b) tanβ + tanγ

c) tanβ + 2tanγ

d) 2tanβ + tanγ

The number of integral values of k for which the equation  has a solution is

a) 4

b) 8

c) 10

d) 12

The values of θ ε (0, 2π) for which  are

a)

b)

c)

d)

If   are altitudes of a triangle from the vertices A, B, C and Δ the area of the triangle then  

a) True

b) False

Let   are the perpendiculars from the vertices of a triangle to the opposite sides, then  

a) True

b) False

In a ΔABC,  then find the other sides and angles

a) A = 60°, B = 60°, c =

b) A = 45°, B = 75°, c =

c) A = 75°, B = 45°, c =

d) A = 15°, B = 105°, c =

Find the coordinates of the point of intersection of the curves
y = cosx and y = sin3x if .

a) (((

b) ((

c) (

d) (

Find the number of solutions of  

a) 0

b) 1

c) 2

d) Infinitely many

Find all the values of θ in the interval  satisfying the equation .

a)

b)

c)

d)

Prove that the value of the function  do not lie between  and 3 for any real x.

a) True

b) False