JEE Main202228 Jul 2022Morning ShiftMathematicsBinomial TheoremActual

The remainder when 7 2022 + 3 2022 is divided by 5 is

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Correct answer

C. 3

Step-by-step solution

Using the binomial expansion in the given expression we get, 7 2022 + 3 2022 = 50 - 1 1011 + 10 - 1 1011 = C 0 1011 50 1011 - 1 0 + C 1 1011 50 1010 - 1 1 + . . . . C 1011 1011 50 0 - 1 1011 + C 0 1011 10 1011 - 1 0 + C 1 1011 10 1010 - 1 1 + . . . . C 1011 1011 10 0 - 1 1011 = 5 k - 2 Using binomial expansion we get the remainder as - 2 + 5 = 3

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