Question

Remainder when $2^{30}{3}^{30}$ is divided by 7 is

• A. $1$
• B. $2$
• C. $4$
• D. $6$

Answer 1

Answer: (A)

$1$

$2^{30}\times 3^{30}=6^{30}=(7-1{)}^{30}$

Using Binomial expansion. all terms are divided by $7$ except last term where power of $7$ in $0$

$\Rightarrow$ Coeff remainder $=1$

$\frac{(7-1{)}^{30}}{7}=\frac{{}^{30}{C}_0}{7}{7}^{30}-------\frac{{}^{30}{C}_4}{7}{7}^{14}.......\frac{{}^{30}{C}_{30}}{7}$