Let A be the set of all positive prime integers less than 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

Solution:

Clearly, A= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}. The total number of rational numbers whose numerator and denominator belong to A is equal to the number of arrangements of the numbers of set A by taking two at a time. Hence, required number of rational numbers $=^{10} C_{2} \times 2! = 90$

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