MCA Entrance Previous Year Question Bank

Let $k$ be the sum of the coefficients of the odd powers of $x$ in the expansion of $(1+x{)}^{99}$. Let $a$ be the middle term in the expansion of ${\left(2+\frac{1}{\sqrt{2}}\right)}^{200}$. If $\frac{{}^{200}{C}_{99}k}{a}=\frac{2^{l}m}{n}$, where $m$ and $n$ are odd numbers, then the ordered pair $(l,n)$ is equal to:

If the coefficient of $x^9$ in ${\left(\alpha x^3+\frac{1}{\beta x}\right)}^{11}$ and the coefficient of $x^{-9}$ in ${\left(\alpha x-\frac{1}{\beta x^3}\right)}^{11}$ are equal, then $(\alpha \beta {)}^2$ is equal to

Let the coefficients of three consecutive terms in the binomial expansion of $(1+2x{)}^n$ be in the ratio $2:5:8$. Then the coefficient of the term, which is in the middle of these three terms, is?