JEE Math Practice Question

If the coefficints of $${x^3}$$ and $${x^4}$$ in the expansion of $$\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \right)^{18}}$$ in powers of $$x$$ are both zero, then $$\left( {a,\,b} \right)$$ is equal to:

1. A.$$\left( {14,{{272} \over 3}} \right)$$
2. B.$$\left( {16,{{272} \over 3}} \right)$$
3. C.$$\left( {16,{{251} \over 3}} \right)$$
4. D.$$\left( {14,{{251} \over 3}} \right)$$