KVPY SA Exam 19-Nov-2017 Question Paper

Question : 7 of 80

Marks: +1, -0

Let S be the set of all ordered pairs (x,y) of positive integers, with HCF (x,y) = 16 and LCM (x,y) = 48000. The number of elements in S is

Solution:

48000 = 16 × 3000
= 16 ×

[3^1× 2^3 × 5^3]

As H.C.F. is 16 So 23 can be selected in 1 way & 31 × 53 can be seleted in (1+ 1) (3 +1) = 8 ways
No of ordred pairs = 8

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