Question

Let A = {x I x is a prime number and x < 30}. The number of different rational numbers whose numerator and denominator belong to A is

(A)  90

(B)  180

(C)  91

(D)  None of these 

Answer 1

Correct option  (C) 91

A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}.

A rational number is made by taking any two in any order. So, the required number of rational numbers is (including 1)

¹⁰P₂ + 1 = 10!/8! + 1 = 90 + 1 = 91