The sum of all rational terms in the expansion of $\left(2^{\frac{1}{5}}+5^{\frac{1}{3}}\right)^{15}$ is equal to :
$3133$
$633$
$931$
$6131$
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 :
In the expansion of ${\left( {\frac{a}{x} + bx} \right)^{12}}$,the coefficient of $x^{-10}$ will be
The value of $x$, for which the 6th term in the expansion of ${\left\{ {{2^{{{\log }_2}\sqrt {({9^{x - 1}} + 7)} }} + \frac{1}{{{2^{(1/5){{\log }_2}({3^{x - 1}} + 1)}}}}} \right\}^7}$ is $84$, is equal to
In the expansion of ${\left( {x - \frac{3}{{{x^2}}}} \right)^9},$ the term independent of $x$ is
The number of integral terms in the expansion of ${({5^{1/2}} + {7^{1/6}})^{642}}$ is