If the coefficient of ${x^7}$ in ${\left( {a{x^2} + \frac{1}{{bx}}} \right)^{11}}$ is equal to the coefficient of ${x^{ - 7}}$ in ${\left( {ax - \frac{1}{{b{x^2}}}} \right)^{11}}$, then $ab =$
$1$
$1\over2$
$2$
$3$
The ratio of the coefficient of the middle term in the expansion of $(1+x)^{20}$ and the sum of the coefficients of two middle terms in expansion of $(1+x)^{19}$ is $....$
The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of $\left(2 x^2+\frac{1}{2 x}\right)^{11}$ is equal to
If ${x^4}$ occurs in the ${r^{th}}$ term in the expansion of ${\left( {{x^4} + \frac{1}{{{x^3}}}} \right)^{15}}$, then $r = $
Coefficient of $x^3$ in the expansion of $(x^2 - x + 1)^{10} (x^2 + 1 )^{15}$ is equal to
If the coefficients of $x^7$ & $x^8$ in the expansion of ${\left[ {2\,\, + \,\,\frac{x}{3}} \right]^n}$ are equal , then the value of $n$ is :