If sin θ +cos θ =p and sec θ +cosec θ =q, show that q(p²-1)=2 p

Two dice are thrown together once. Find the probability of getting a sum of more than 9.

500 persons are taking dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04m³ ?

Prove that, a tangent to a circle is perpendicular to the radius through thepoint of contact.

OR

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

On dividing x³-3 x²+x+2 by a polynomial a cos. the quotient and remainder were x-2 and -2 x+4 respectively. Find g(x).

OR

If the sum of the squares of zeros of the quadratic polynomial f(x)=x²-8 x+k is 40, find the value of k