(719 + 2) is divided by 6. The remainder is :

Answer: Option C

$$\begin{array}{rl}& \left(7^{19}+2\right)÷6\\ & =\frac{{\left(6+1\right)}^{19}+2}{6}\\ & =\frac{1^{19}+2}{6}\\ & =3\text{remainder}\end{array}$$

Alternate
(xⁿ - aⁿ) is divisible by (x - a) for all values of n.
∴ (7¹⁹ - 1¹⁹) is divisible by (7 - 1)
⇒ (7¹⁹ - 1) is divisible by 6
⇒ On dividing (7¹⁹ + 2) by 6, remainder obtained = 3