If N is the number of ways in which 3 distinct numbers can be selected from the set $\left\{3^1,3^2,3^3,\dots 3^{10}\right\}$ so that they form a G.P then the value of $\frac{\mathrm{N}}{5}$ is

To choose a,b,c from {1,2,3, .....,10} so that a,b,c forms an A.P and Consequently $3^{\mathrm{a}},3^{\mathrm{b}},3^{\mathrm{c}}$ forms a G.P

No. of A.Ps with c.d.s 1,2,3,4 are respectively 8,6,4,2 

$\mathrm{N}=\text{ Total no. of }\mathrm{A}\cdot \mathrm{P}\cdot \mathrm{s}=20\Rightarrow \frac{\mathrm{N}}{5}=4$