Coefficient of ${x^2}$ in the expansion of ${\left( {x - \frac{1}{{2x}}} \right)^8}$ is
$\frac{1}{7}$
$\frac{{ - 1}}{7}$
$-7$
$7$
The first $3$ terms in the expansion of ${(1 + ax)^n}$ $(n \ne 0)$ are $1, 6x$ and $16x^2$. Then the value of $a$ and $n$ are respectively
If the term independent of $x$ in the exapansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{9}$ is $k,$ then $18 k$ is equal to
If coefficients of $2^{nd}$, $3^{rd}$ and $4^{th}$ terms in the binomial expansion of ${(1 + x)^n}$ are in $A.P.$, then ${n^2} - 9n$ is equal to
The middle term in the expansion of ${\left( {3x - \frac{{{x^3}}}{6}} \right)^9}$ are :-
The term independent of $' x '$ in the expansion of ${\left( {9\,x\,\, - \,\,\frac{1}{{3\,\sqrt x }}} \right)^{18}}, x > 0$ , is $\alpha$ times the corresponding binomial co-efficient . Then $' \alpha '$ is :