Questions
If and then
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By Expert Faculty of Sri Chaitanya
a
X⊆Y
b
Y⊆X
c
X=Y
d
None of these
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Correct option is A
Since 8n-7n-1=(7+1)n-7n-1=7n+nC17n-1+nC27n-2+...+nCn-17+nCn-7n-1=nC272+nC373+..+nCn7n, (nC0, nC1=nCn-1etc.)=49[nC2+nC3(7)+...+nCn7n-2]∴8n-7n-1 is a multiple of 49 for n≥2For n=1, 8n-7n-1=8-7-1=0;For n=2, 8n-7n-1=64-14-1=49∴8n-7n-1 is a multiple of 49 for all n∈N.∴X contains elements which are multiples of 49 and clearly Y contains all multiplies of 49 ∴ X⊆Y.
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