Odisha Board Solutions for Chapter: Binomial Theorem, Exercise 1: EXERCISES 9 (a)

The number of terms in the expansion of ${\left(x^2-2+\frac{1}{x^2}\right)}^6$ is equal to $7.$

There is a term independent of both $x$ and $y$ in the expansion of ${\left(x^2+\frac{1}{y^2}\right)}^9$.

The highest power in the expansion of $x^{40}{\left(x^2+\frac{1}{x^2}\right)}^{20}$ is equal to $40 .$

The product of $K$ consecutive natural numbers is divisible by $K!$.

If $6^{th}$ term in the expansion of $(x+*{)}^n$ is equal to ${}^{n}C_5{x}^{n-10}$ and $*$$=\frac{m}{x}$, find $m$.

Find the coefficient of $\frac{1}{y^{10}}$ in the expansion of ${\left(y^3+\frac{a^7}{y^5}\right)}^{10}$.

Find the coefficient of $x^4$ in the expansion of $\left(1+3x+10x^2\right){\left(x+\frac{1}{x}\right)}^{10}$.

Find the term independent of $x$ in the expansion of $\left(1+3x+10x^2\right){\left(x+\frac{1}{x}\right)}^{10}$.