SATHEE: Permutations and Combinations 2 Question 12

Permutations and Combinations 2 Question 12

12. 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 $(p, q)$ is

(2006, 3M)

(a) 252

(b) 254

(d) 224

Show Answer

Answer:

Correct Answer: 12. (c)

Solution:

Since, $r, s, t$ are prime numbers.

$∴$ Selection of $p$ and $q$ are as under

$p$	$q$	Number of ways
$r^{0}$	$r^{2}$	1 way
$r^{1}$	$r^{2}$	1 way
$r^{2}$	$r^{0}, r^{1}, r^{2}$	3 ways

$∴$ Total number of ways to select, $r = 5$

Selection of $s$ as under

$∴$ Total number of ways to select $s = 9$ Similarly, the number of ways to select $t = 5$

$∴$ Total number of ways $= 5 \times 9 \times 5 = 225$

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Permutations and Combinations 2 Question 12

12. If r,s,t are prime numbers and p,q are the positive integers such that LCM of p,q is r2s4t2, then the number of ordered pairs (p,q) is

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12. 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 $(p, q)$ is