The sum of the rational terms in the binomial expansion of ${\left( {{2^{\frac{1}{2}}} + {3^{\frac{1}{5}}}} \right)^{10}}$ is

 Suppose $2-p, p, 2-\alpha, \alpha$ are the coefficient of four consecutive terms in the expansion of $(1+x)^n$. Then the value of $p^2-\alpha^2+6 \alpha+2 p$ equals

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

In the expansion of ${\left( {3x - \frac{1}{{{x^2}}}} \right)^{10}}$ then $5^{th}$ term from the end is :-

If the coefficients of the three successive terms in the binomial expansion of $(1 + x)^n$ are in the ratio $1 : 7 : 42,$ then the first of these terms in the expansion is

Find the middle terms in the expansion of $\left(\frac{x}{3}+9 y\right)^{10}$