JEE Main202125 Feb 2021Evening ShiftMathematicsBinomial TheoremActual

If the remainder when x is divided by 4 is 3 , then the remainder when 2020 + x 2022 is divided by 8 is ___ .

Correct answer

Step-by-step solution

x = 4 k + 3 ∴ 2020 + x 2022 = 2020 + 4 k + 3 2022 = 4 505 + k + 3 2022 = 4 λ + 3 2022 = 16 λ 2 + 24 λ + 9 1011 = 8 2 λ 2 + 3 λ + 1 + 1 1011 = 8 p + 1 1011 ∴ Remainder when divided by 8 = 1 .

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