jee-main 2014 Q66

jee-main · India · 06apr Binomial Theorem (positive integer n) Determine Parameters from Conditions on Coefficients or Terms

If the coefficients of $x ^ { 3 }$ and $x ^ { 4 }$ in the expansion of $\left( 1 + a x + b x ^ { 2 } \right) ( 1 - 2 x ) ^ { 18 }$ in powers of $x$ are both zero, then $( a , b )$ is equal to
(1) $\left( 14 , \frac { 272 } { 3 } \right)$
(2) $\left( 16 , \frac { 272 } { 3 } \right)$
(3) $\left( 16 , \frac { 251 } { 3 } \right)$
(4) $\left( 14 , \frac { 251 } { 3 } \right)$

If the coefficients of $x ^ { 3 }$ and $x ^ { 4 }$ in the expansion of $\left( 1 + a x + b x ^ { 2 } \right) ( 1 - 2 x ) ^ { 18 }$ in powers of $x$ are both zero, then $( a , b )$ is equal to\\
(1) $\left( 14 , \frac { 272 } { 3 } \right)$\\
(2) $\left( 16 , \frac { 272 } { 3 } \right)$\\
(3) $\left( 16 , \frac { 251 } { 3 } \right)$\\
(4) $\left( 14 , \frac { 251 } { 3 } \right)$

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