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JEE Main · 2009 · 12 Apr 2009 · Offline · Binomial Theorem

The remainder left out when

8^{2 n} - (62)^{2 n + 1}

is divided by 9 is

(A)0
(B)2✓ Correct
(C)7
(D)8

Answer: (B)

Solution

Work modulo 9, where

8 \equiv - 1

and

62 \equiv - 1

. Then

8^{2 n} \equiv (- 1)^{2 n} = 1

and

6 2^{2 n + 1} \equiv (- 1)^{2 n + 1} = - 1

, so

8^{2 n} - 6 2^{2 n + 1} \equiv 1 - (- 1) = 2 (mod 9)

. The remainder left on division by 9 is therefore 2.

JEE Main · 2009 · 12 Apr 2009 · Offline · Single correct option

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