The possible number of ordered triplets (m, n, p) where `m,np in N` is (6250K) such that `1ltmlt100,1ltnlt50,1ltplt25` and `2^(m)+2^(n)+2^(p)` is divisible by 3 then k is

Answer

5

Explanation

Here `2^(m)+2^(n)+2^(p)=(3-1)^(m)+(3-1)^(n)+(3-1)^(p)=3k+(-1)^(m)+(-1)^(n)+(-1)^(p)`
So that `2^(m)+2^(n)+2^(p)` is divisible by `3` if `m,n,p` all are odd or all are even
`implies` Number of possible ordered triplets
`=50xx25xx12+50xx25xx13=31250=6250xx5`