Let A₁,A₂,....,A_m be m sets such that O(A_i)=p for all i=1,2,...,m and B₁,B₂,..,B_n be n sets such that O(B_j )=q for all j=1,2,..,n. If U^m_i=1 A_i=Uⁿ_j=1 B_j=S and each element of S belongs to exactly a number of A_i ’s and b number of B_j ‘s, then

(1)pm=nq

(2)apm=bnq

(3)bpm=anq

(4)(pm)^b =(nq)^a

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