The possible number of ordered triplets (m, n, p) where `m,np in N` is (6250K) such that `1ltmlt100,1ltnlt50,1ltplt25` and `2^(m)+2n^(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)` (`k in 1`)
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 triples
`=50xx25xx12+50xx25xx13=31250=6250xx5`