Prove the converse of the mid-point theorem following the guidelines given below: Consider a triangle ABC with D as the midpoint of AB. Draw DE|| BC to intersect AC in E. Let E1 be the midpoint of AC. Use mid-point theorem to get DE1|| BC and DE1=12BC. Conclude E=E1 and hence E is the midpoint of AC.

How do you find the Maclaurin series for tanx?

Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the equation is not about the fifth postulate.)

The smallest composite number is ______.

(a) 2

(b) 4

(c) 1

(d) None of these

Find the arithmetic mean of the first ten odd natural numbers.

A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is

A. 10 km/hr

B. 4 km/hr

C. 14 km/hr

D. 6 km/hr