Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax +2ay +c= 0 and 5bx +2by +d = 0 lies in the fourth quadrant and is equidistant from the two axes, then

• 2bc-3ad =0 

• 2bc+3ad =0

• 2ad-3bc =0

• 2ad-3bc =0

The locus of the foot of perpendicular drawn from the centre of the ellipse x²+3y² =6 on any tangent to it is

• (x²-y²)² = 6x²+2y²

• (x²-y²)² = 6x² -2y²

• (x²+y²)² = 6x²+2y²

• (x²+y²)² = 6x²+2y²

Let C be the circle with centre at(1,1) and radius 1. If T is the circle centred at (0,y) passing through origin and touching the circle externally, then the radius of T is equal to

• 
• 

• 1/2

• 1/2

The slope of the line touching both the parabolas y² = 4x and x²-32y is 

• 1/2

• 3/2

• 1/8

• 1/8

The image of line  in the plane 2x-y+z+3 =0 is the line

The statement ~ (p↔ ~q) is 

• equivalent to p ↔ q

• equivalent to ~ p ↔q

• a tautology

• a tautology

A bird is sitting on the top of a vertical pole 20m high and its elevation from a point O n the ground is 45^o. It flies off horizontally straight away from the point O. After 1s, the elevation of the bird from O is reduced to 30^o. Then, the speed (in m/s of the bird is

• (

• 
• 
• 

The variance of first 50 even natural number is

• 833/4

• 833

• 437

• 437

If [a x b b x c c x a] = λ[a b c]², then λ is equal to 

• 0

• 1

• 2

• 2

20.

If α, β ≠ 0 and f(n) = αⁿ+ βⁿ and 


= K(1-α)²(1-β)²(α- β)², then K is equal to 

• αβ 

• 1/αβ 

• 1

• 1