If R(x, y) is a point on the line segment joining the point P(a, b) and Q(b, a) then prove that x + y = a + b.

A bookseller buys a number of books for ₹ 1760. If he had bought 4 more books for the same amount, each book would have cost ₹ 22 less. How many books did he buy?

OR

A two-digit number is such that product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2.5 m apart. What is the length of the wood required for the rungs?

If x = cot A + cos A and y = cot A – cos A, prove that

OR

If a cos θ – b sin θ = c, prove that .

In the given figure, PQSR represents a flower bed. If OP = 21 m and OR = 14 m, find the area of the flower bed.