12l+3m+5n
=2l+(4-1)m+(4+1)n
=2l+ multiple of 4+(-1)m+1n
here for l=1 m=2,4,6,8
4x8=32ways
for l≠1 m=1,3,5,7
7x4x8=224 ways
so option d
NUMBER OF ORDERED TRIPLETS l,m,n ( l,m.n are positive integers and 1≤ l,m,n≤ 8 ) such that 2l + 3m + 5nis divisible by 4 is _______________
[94] a> 224 b>288 c> 60 d> 256
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5 Answers
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1well i didnt get >>>
for l≠1 m=1,3,5,7
7x4x8=224 ways
<<<
please make me understAND dis step [76]
1observe dat l,m,n ε [1,8]
in d first case when l=1, m can take 4 values viz., 2,4,6,8... and n can take 8 values viz.,1 to 8... so no. of ordered triplets = 4x8 = 32
in d second case when l≠1, l can take 7 values viz., 2 to 7... m can take 4 values viz., 1,3,5,7... and n can take 8 values viz., 1 to 8... so no. of ordered triplets = 7x4x8 =224
hence answer is 224+32=256... option D........