JEE Main2009MathematicsBinomial TheoremActual

The remainder left out when 8^ 2 n -(62)^ 2 n+1 is divided by 9 is

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Correct answer

B. 2

Step-by-step solution

aligned & 8^ 2 n -(62)^ 2 n+1 =(1+63)^n-(63-1)^ 2 n+1 & =(1+63)^n+(1-63)^ 2 n+1 = (1+ ^n c₁ 63+ ^n c₂(63)^2+ .+(63)^n )+ (1- ^ (2 n+1) c₁ 63+ ^ (2 n+1) c₂(63)^2+ .+(-1)(63)^ (2 n+1) ) & =2+63 ( ^n c₁+ ^n c₂(63)+ .+(63)^ n-1 - ^ (2 n+1) c₁+ ^ (2 n+1) c₂(63)+ .(63)^ (2 n) ) aligned Reminder is 2

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