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Q.
If the coefficients of $x^2$ and $x^3$ are both zero, in the expansion of the expression $(1 + ax + bx^2) (1 - 3x)^{15}$ in powers of $x$, then the ordered pair $(a, b)$ is equal to :
Coefiicient of $x^{2}={ }^{15} C_{2} \times 9-3 a\left({ }^{15} C_{1}\right)+b=0$
$\Rightarrow -45 a+b+{ }^{15} C_{2} \times 9=0$
Also, $-27 \times{ }^{15} C _{3}+9 a \times{ }^{15} C _{2}-3 b \times{ }^{15} C _{1}=0$
$\Rightarrow 9 \times 15 C _{2} a -45 b -27 \times 15 C _{3}=0$
$\Rightarrow 21 a - b -273=0 \quad \ldots$
(i) $+$ (ii) $-24 a +672=0$
$\Rightarrow a =28$
$So , b =315$