Q114 / 155 · WBJEE 2021 · Mathematics

The remainder when $7^{7^{7^{...7}}}(22$ times 7$)$ is divided by 48 is

A
21
Correct answer
B
7
C
47
D
1

Solution

$7^{7^{7-7}}=7^{2 \mathrm{~m}+1}=7(49)^{\mathrm{m}}=7(1+48)^{\mathrm{m}}=48 \mathrm{k}+7$

Hence, the correct answer is option: 'B'.

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