JEE Main 2022 · 24 Jun · Shift 1 · Mathematics Q2

MathematicsSingle correct+4 / -1Question 2 of 90

The remainder when $3^{2022}$ is divided by 5 is :

Answer and worked solution

Official answer: D

Cycle of last digit. Powers of 3 mod 5 repeat with period 4: $3,4,2,1$ .

Reduce. $2022=4\cdot505+2$ , so $3^{2022}\equiv3^2=9\equiv4\pmod5$ .

(D)

Topics:Binomial expansion Number systems

JEE Main 2022 · 24 Jun · Shift 1, Mathematics question 2