Correct Option: B

Using the Binomial expansion , we have
(x + 1)ⁿ = xⁿ + ⁿc₁ x^n–1 +
ⁿc₂ x^{n– 2} + ..... + ⁿc_n–1 x +1
Here, each term except the last term contains x. Obviously, each term except the last term is exactly divisible by x.
Following the same logic,
∴ 7¹⁹ = (6 + 1)¹⁹ has each term except last term divisible by 6.
Hence, 7¹⁹ + 2 when divided by 6 leaves remainder
⇒ 7¹⁹ + 2 = 1 + 2 = 3
Hence the remainder is 3.