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Solution


Q.

The remainder when 4282024 is divided by 21 is ______ .             [2024]

Ans.

(1)

4282024=(420+8)2024

=C02024(420)2024+C12024(420)2023(8)1+…+C20232024(420)(8)2023+C20242024(8)2024

=420 [Some integer] +641012

=21×20 [Some integer] +(63+1)1012

=21×20 [Some integer] +63×Some integer + 1

=21×20 [Some integer]  +21×3×Some integer + 1 

Hence, remainder = 1