If  then  

a) True

b) False

2sinx + tanx > 3x where 0 ≤ x ≤

a) True

b) False

Prove that  = 2[cosx + cos3x + cos5x + … + cos(2k−1)x] for any positive integer k. Hence prove that  =

Determine the smallest positive value of x (in degrees) for which  

a) 30°

b) 50°

c) 55°

d) 60°

Find the smallest possible value of p for which the equation
 

a)

b)

c)

d)

Find the larger of cos(lnθ) and ln(cosθ) if  < θ < .

a) cos(lnθ)

b) ln(cosθ)

c) Neither is larger throughout the interval

The real roots of the equation x +  = 1 in the interval (−π, π) are …...........

a) x = 0

b) x = ±  

c) x = 0 , x = ±  

If are in harmonic progression then  …………

a) 1

b)

c)

d)

If

then x equals

a)

b) 1

c)

d) –1

Let a, b, c be three positive real numbers and
 
Then tan θ = ………..

a) 0

b) 1

c) 2

d) 3

The greater of the two angles
 and  is

a) A

b) B

c) Both are equal

Match the following

Let (x, y) be such that

 =

One angle of an isosceles triangle is 120 and the radius of its incircle = . Then the area of the triangle in square units is

a)

b)

c)

d) 2π

Let O (0, 0), P (3, 4), Q (6, 0) be the vertices of the triangle OPQ. The point inside the triangle OPQ is such that OPR, PQR, OQR are of equal area. The coordinates of R are

a)

b)

c)

d)

Multiple choice

There exists a triangle ABC satisfying the conditions

a) bsinA = a, A <

b) bsinA > a, A >

c) bsinA > a, A <

d) bsinA < a, A <, b > a

e) bsinA < a, A >, b = a

One or more correct answers
In a triangle the length of the two larger sides are 10 and 9 respectively. If the angles are in arithmetic progression then the length of the third side can be

a)

b)

c) 5

d)

e) None of these

One or more correct answers
In triangle ABC the internal angle bisector of ∠A meets the side BC in D. DE is a perpendicular to AD which meets AC in E and AB in F. Then

a) AE is harmonic mean of b and c

b) AD

c)

d) Δ AEF is isosceles

For a triangle ABC it is given that  , then Δ ABC is equilateral.

a) True

b) False

With usual notation if in a triangle ABC,  then

 .

a) True

b) False

A ladder rests against a wall at an angle α to the horizontal. If its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal, then .

a) True

b) False

Find the set of all values of a such that  are sides of a triangle.

a) (0, 3)

b) (3, ∞)

c) (0, 5)

d) (5, ∞)

If in a triangle ABC, cosA cosB + sinA sinB sin C = 1 then show that  a : b : c = 1 : 1 :

a) True

b) False

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of triangle.

a) 3, 4, 5

b) 4, 5, 6

c) 4, 5, 7

d) 5, 6, 7