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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 |
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Answer» Correct Answer - 5 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` |
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