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lf r, s, t are prime numbers and p, q ar...

lf `r, s, t` are prime numbers and `p, q` are the positive integers such that their LCM of `p,q` is `r^2 t^4 s^2,` then the numbers of ordered pair of `(p, q)` is (A) `252` (B) `254` (C) `225` (D) `224`

A

252

B

254

C

225

D

224

Text Solution

Verified by Experts

The correct Answer is:
C
Since, r, s, t are prime numbers.
`therefore` Selection 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"):}`
`therefore` Total number of ways to select, r = 5
Selection of s as under
`{:(s^(0), s^(4), 1 " way"),(s^(1), s^(4), 1" way"),(s^(2), s^(4), 1" ways"),(s^(3), s^(4), 1" way"),(s^(4),,5" ways"):}`
`therefore` Total number of ways to select s = 9
Similarly, the number of ways to select t = 5
`therefore` Total number of ways `= 5 xx 9 xx 5 = 225`
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