Q. If 3^2019 is divided by 10, then what is the remainder?

Explanation : 

Problem: Find the remainder when 3^2019 is divided by 10

Let’s solve this step by step:

1) To find 3^2019 mod 10, examine the pattern of remainders when successive powers of 3 are divided by 10:
3^1 = 3
3^2 = 9
3^3 = 27 ≡ 7 (mod 10)
3^4 = 81 ≡ 1 (mod 10)
3^5 = 243 ≡ 3 (mod 10)
3^6 = 729 ≡ 9 (mod 10)
3^7 ≡ 7 (mod 10)
3^8 ≡ 1 (mod 10)

2) The pattern of remainders is: 3, 9, 7, 1, 3, 9, 7, 1, …
This forms a cycle of length 4

3) For 3^2019:
2019 = 504 × 4 + 3
Thus 3^2019 will have the same remainder as 3^3

4) Since 3^3 ≡ 7 (mod 10)

Therefore, when 3^2019 is divided by 10, the remainder is 7.

The answer is (c) 7.