A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60º at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30º. The height of the tower is

The value of 

• i

• 1

• -i

• -i

If 0 < x < π and cosx + sinx = 1/2 , then tanx is

• 
• 

• tan 1

• tan 1

In a triangle PQR, ∠R =π/2. If (P/2) and tan (Q/2) are the roots of ax² +bx+ c = 0, a ≠ 0 then 

• a = b + c

• c = a + b

• b = c

• b = c

In a triangle, ABC, let ∠C = π/2 . If r is the in radius and R is the circumradius of the triangle ABC, then 2 (r + R) equals

• b + c

• a+b

• a + b + c

• a + b + c

• I₂ > I₁

• I₁ > I₂

• I₃ = I₄

• I₃ = I₄

Let α, β be such that π < α - β < 3π. If sinα + sinβ = -21/65 and cosα + cosβ = -27/65, then the value of cos α-β/2 is

• 
• 

• 6/65

• 6/65

19.

If  then the difference between the maximum and minimum values of 2 u is given by

• 2(a² + b²)

• 2(a²-b²)

• (a+b)²

• (a+b)²

The sides of a triangle are sinα, cosα and  for some 0 < α < π/2 . Then the greatest angle of the triangle is

• 60^o

• 120^o

• 360^o

• 360^o