The remainder when 7⁸⁴ is divided by 342 is :

A. 0

B. 1

C. 49

D. 341

Answer: Option B

Solution(By Examveda Team)

7⁸⁴ = (7³)²⁸ = (343)²⁸
Now, (xⁿ - aⁿ) is divisible by (x - a) for all values of n
∴ [(343)²⁸ - 1] is divisible by (343 - 1)
⇒ [(343)²⁸ - 1] is divisible by 342
⇒ (7⁸⁴ - 1) is divisible by 342
⇒ On dividing 7⁸⁴ by 342, we get 1 as remainder.