JEE Main 2021 — Binomial Theorem Question with Solution
From: JEE Main 2021 (Online) 25th February Evening Shift
Question
If the remainder when x is divided by 4 is 3, then the remainder when (2020 + x)2022 is divided by 8 is __________.
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Show full solutionCorrect answer: 1
Correct answer
1
Step-by-step explanation
Let x = 4k + 3
(2020 + x)2022
= (2020 + 4k + 3)2022
= (4(505) + 4k + 3)2022
= (4P + 3)2022
= (4P + 4 1)2022
= (4A 1)2022
2022C0(4A)0(1)2022 + 2022C1(4A)1(1)2021 + ......
= 1 + 2022(4A)(-1) + .....
= 1 + 8
Reminder is 1.
(2020 + x)2022
= (2020 + 4k + 3)2022
= (4(505) + 4k + 3)2022
= (4P + 3)2022
= (4P + 4 1)2022
= (4A 1)2022
2022C0(4A)0(1)2022 + 2022C1(4A)1(1)2021 + ......
= 1 + 2022(4A)(-1) + .....
= 1 + 8
Reminder is 1.
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