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  4. 3 × 722+2 × 1022-44 when divided by 18 leaves the remainder

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Q. $3 \times 7^{22}+2 \times 10^{22}-44$ when divided by 18 leaves the remainder _____

JEE MainJEE Main 2021Binomial Theorem

Solution:

$3(1+6)^{22}+2 \cdot(1+9)^{22}-44 $
$=(3+2-44)=18 . I $
$=-39+18 . I $
$=(54-39)+18( I -3) $
$=15+18 I _{1} $
$ \Rightarrow $ Remainder $=15$