Question

Let $A=$ { $x|x$ 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

The correct option is C 91

The number of primes in A $=10$ as $2,3,5,7,11,13,17,19,23,29$
The different rational no. is of the form $\frac{p}{q}$ where $p\ne q$ except when the rational no.$=1$
Hence the total no. of different rational no.$=\left(\begin{array}{c}10\\ 2\end{array}\right)\times 2!+1=91$
$1$ is being added because the rational no. 1 was not counted.
Hence, option 'C' is correct.