QJEEM21Maf6e4: JEE Main 2021 Mathematics - Class 11 JEEM21Maf6e4 Solution: If the remainder when x is divided by 4 is 3, then the…

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)<sup>2022

2022</sup>C₀(4A)⁰( $-$ 1)²⁰²² + ²⁰²²C₁(4A)¹( $-$ 1)²⁰²¹ + ......

= 1 + 2022(4A)(-1) + .....

= 1 + 8 $\lambda$

$\therefore$ Reminder is 1.