Prove that the diagonals of a rectangle ABCD, with vertices A (2, -1), B (5, -1), C (5, 6) and D (2, 6) are equal and bisect each other.

The sum of the 2^nd and the 7^th terms of an AP is 30. If its 15^th term is 1 less than twice its 8^th term, find the AP.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Solve for x:

; x ≠ 4, 6

Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is

(i) of red color

(ii) a queen

(iii) an ace

(iv) a face card