Joseph has a recurring deposit account in a bank for 3 years at 10% p.a. simple interest. If he gets ₹ 16,650 as interest at the time of maturity, find his monthly deposit and the maturity value.

If a, b and c are in continued proportion, prove that :

abc(a + b + c)³ = (ab + bc + ca)³.

The given figure shows a semicircle with center at point O and AE as diameter. Chord AB = chord BC and angle CEO = 50°.

(i) Find angle AOB.

(ii) Show that OB is parallel to EC.