The number of integral terms in the expansion of ${({5^{1/2}} + {7^{1/6}})^{642}}$ is
$106$
$108$
$103$
$109$
If the term without $x$ in the expansion of $\left( x ^{\frac{2}{3}}+\frac{\alpha}{ x ^3}\right)^{22}$ is $7315$ , then $|\alpha|$ is equal to $...........$.
The ratio of the coefficient of terms ${x^{n - r}}{a^r}$and ${x^r}{a^{n - r}}$ in the binomial expansion of ${(x + a)^n}$ will be
If the second term of the expansion ${\left[ {{a^{\frac{1}{{13}}}}\,\, + \,\,\frac{a}{{\sqrt {{a^{ - 1}}} }}} \right]^n}$ is $14a^{5/2}$ then the value of $\frac{{^n{C_3}}}{{^n{C_2}}}$ is :
In the expansion of ${\left( {\frac{a}{x} + bx} \right)^{12}}$,the coefficient of $x^{-10}$ will be
The middle term in the expansion of ${\left( {3x - \frac{{{x^3}}}{6}} \right)^9}$ are :-