If the number of integral terms in the expansion of $\left(3^{\frac{1}{2}}+5^{\frac{1}{8}}\right)^{\text {n }}$ is exactly $33,$ then the least value of $n$ is
$264$
$256$
$128$
$248$
If the sum of the coefficients in the expansion of $(x - 2y + 3 z)^n,$ $n \in N$ is $128$ then the greatest coefficie nt in the exp ansion of $(1 + x)^n$ is
If the coefficients of ${T_r},\,{T_{r + 1}},\,{T_{r + 2}}$ terms of ${(1 + x)^{14}}$ are in $A.P.$, then $r =$
Find the term independent of $x$ in the expansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{6}$
In the expansion of ${\left( {2{x^2} - \frac{1}{x}} \right)^{12}}$, the term independent of x is
If $a^3 + b^6 = 2$, then the maximum value of the term independent of $x$ in the expansion of $(ax^{\frac{1}{3}}+bx^{\frac{-1}{6}})^9$ is, where $(a > 0, b > 0)$