If  is the number of ways in which 3 distinct numbers can be selected from the set  so that they form a G.P. then the value of  is

(4)

If three numbers are in G.P., then their exponent must be in A.P.

If a,b,c are selected number in G.P., then the exponent of a and  both are either odd or even, ot otherwise exponent  will not be integer  will not be integer

Now two odd exponent (from 1,2,3,…,10) can be selected in  ways and two even exponent can be selected in  ways

Hence number of G.P.’s are