If $r,\;s,\;t$ are prime numbers and $p,q$ are the positive integers such that LCM of $p,\;q$ is ${r^2}{s^4}{t^2}$, then the number of ordered pairs $\left( {p,\;q} \right)$ is

JEE MATHEMATICS MCQ: PERMUTATIONS

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Application +4 | -1

r,\;s,\;t

are prime numbers and

p,q

are the positive integers such that LCM of

p,\;q

{r^2}{s^4}{t^2}

, then the number of ordered pairs

\left( {p,\;q} \right)

View answer and explanation

Correct option: C

225

Option C (225) is correct because the number of ordered pairs (p, q) is found by considering all possible combinations of the prime factors' exponents in the LCM.

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