What is the unit digit in the expansion of

(57242)^{9×7×5×3×1}           

(UPSC CSAT – 2023)

1. 2
2. 4
3. 6
4. 8

Solution: Ans.(1)

When 9×7×5×3×1 is divided by 4, remainder be 1.

So (57242)⁴ⁿ⁺¹ = (57242)⁴ⁿ × (57242)

                         = (……..6) × (…….2) = (……..2)