InterviewSolution
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InterviewSolution
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If `k in I` such that `lim_(nrarroo) (cos.(kpi)/(4))^(2n)-(cos.(kpi)/(6))^(2n)=0,` thenA. k must bot be divisible by 24B. k is divisible by 24 or k is divisible neither by 4 nor by 6C. k must be divisible by 12 but not necessarity by 24D. none of these |
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Answer» Correct Answer - B `underset(nrarroo)(lim)(cos.(kpi)/(4))^(2n)-(cos.(kpi)/(6))^(2n)=0` holds good if `"Case I": cos .(kpi)/(4)=cos.(kpi)/(6)=1` i.e., `(kpi)/(4)=2mpi and (kpi)/(6)=2p pi,m,p in Z` i.e., k = 8m and k = 12 p i.e., k is divisible by both 8 and 12 i.e., k is divisible by 24. Case II: `-1 lt cos.(kpi)/(4),cos.(kpi)/(6) lt 1` i.e., k is not divisible by 4 and k is not divisible by 6. Case III: `cos.(kpi)/(4)=(2m+1)pi and (kpi)/(6)=(2p+1)pi` `k=4 (2m+1) and k=6(2p+1)` This is not possible. |
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