defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Binomial Theorem Binomial Expansion
If the coefficients of \( x^{3} \) and \( x^{4} \) in the expansion of \( (1+ax+bx^{2}) (1-2x)^{18} \) in powers of \( x \) are both zero, then \( \left ( a,b \right ) \) is equal to:
1
\( \left ( 16, \displaystyle \frac{251}{3} \right ) \)
2
\( \left ( 14, \displaystyle \frac{251}{3} \right ) \)
3
\( \left ( 14, \displaystyle \frac{272}{3} \right ) \)
4
\( \left ( 16, \displaystyle \frac{272}{3} \right ) \)