Question

$3^{2n}$ when divided by $8$ will leave the remainder.

• A. $1$
• B. $0$
• C. A multiple of $3$
• D. $5$

Answer 1

Answer: (A)

$1$

$3^{2n}=9^n=(1+8{)}^n=1+n8{+}^n{C}_2{8}^2+.......{+}^n{C}_n{8}^n=1+8[n{+}^n{C}_{2}8+........{+}^n{C}_n{8}^{n-1}]Clearlywhendividedby8,remainderwillbe1.$