Number of rational terms in the expansion of ${\left( {\sqrt 2 \,\, + \,\,\sqrt[4]{3}} \right)^{100}}$ is :
$25$
$26$
$27$
$28$
The greatest coefficient in the expansion of ${(1 + x)^{2n + 1}}$ 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 $(a > 0, b > 0)$
The term independent of $x$ in ${\left( {\sqrt x - \frac{2}{x}} \right)^{18}}$ is
If the coefficents of ${x^3}$ and ${x^4}$ in the expansion of $\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \right)^{18}}$ in powers of $x$ are both zero, then $ (a,b) $ is equal to
In the binomial $(2^{1/3} + 3^{-1/3})^n$, if the ratio of the seventh term from the beginning of the expansion to the seventh term from its end is $1/6$ , then $n =$