Embibe Experts Solutions for Exercise 6: Assignment

The expansion of ${\left(x^{\alpha }+\frac{1}{x^{\beta }}\right)}^n$ has constant term, if

The number of rational terms in the expansion of ${\left(\sqrt[3]{25}+\frac{1}{\sqrt[3]{25}}\right)}^{20}$ is

If in the expansion of $(1+kx{)}^4$ the coefficient of $x^3$ is $32$ , then the value of $k$ is equal to

If the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of ${\left(2^{\frac{1}{4}}+\frac{1}{3^{\frac{1}{4}}}\right)}^n$ is $\sqrt{6}:1$ then value of $n$ is equal to

The value of the coefficient of $x^4$ in the expansion of ${\left(2-x+3x^2\right)}^6$ is

The greatest value of $n$ for which $9^7+7^9$ is divisible by $2^n$ is equal to

If the coefficient of $x^n$ in the expansion of ${\left(1-9x+20x^2\right)}^{-1}$ is $a^{n+1}-b^{n+1}$ (where $a, b$ are coprime) then $\frac{a}{b}$ is equal to $(a>b)$.

The coefficient of $x^9$ in the expansion of $\prod _{r=1}^{100}\left(1+x^r\right)$ is equal to