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 term independent of $x$ in the expansion of ${\left( {2x - \frac{3}{x}} \right)^6}$ is
If $n$ is even positive integer, then the condition that the greatest term in the expansion of ${(1 + x)^n}$ may have the greatest coefficient also, is
The coefficient of middle term in the expansion of ${(1 + x)^{10}}$ is
If the $6^{th}$ term in the expansion of the binomial ${\left[ {\frac{1}{{{x^{\frac{8}{3}}}}}\,\, + \,\,{x^2}\,{{\log }_{10}}\,x} \right]^8}$ is $5600$, then $x$ equals to
The coefficients of three consecutive terms in the expansion of $(1+a)^{n}$ are in the ratio $1: 7: 42 .$ Find $n$