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The remainder when $\left ( 11 \right )^{1011}+\left ( 1011 \right )^{11}$ is divided by $9$ is
Option: 1
$1$

Option: 2
$4$

Option: 3
$6$

Option: 4
$8$

Answers (1)

best_answer

$(11)^{1011} \\$

$=(9+2)^{1011} \\$

$=92+2^{1011} \\$

$=92+(8)^{337}$

$=9 \lambda+(9-1)^{337} \\$

$=9 \lambda+9 k-1 \\$

$=9 k^{\prime}+8$

And $(1011)^{11} \\$

$=(9 k+3)^{11} \\$ $= 9 \lambda+3^{11} \\$

$= 9\lambda+9 k \\$

$= 9 \mu$

$\therefore$ Required remainder $=8$

Hence correct option is 4

Posted by

Kuldeep Maurya

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