The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?

If a tower 30 m high, casts a shadow 10 3m long on the ground, then what is the angle of elevation of the sun?

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP.

What is the common difference of an A.P. in which a₂₁- a₇= 84?

5.

A circle touches all the four sides of a quadrilateral ABCD. Prove that 

AB + CD = BC + DA

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q.

If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that  3x = 2y.

Find the value of p, for which one root of the quadratic equation px² – 14x + 8= 0 is 6 times the other.

For what value of n, are the n^th terms of two A.Ps.  63, 65, 67,…. and 3, 10, 17,….. equal?