NCERT Solutions for Chapter: Binomial Theorem, Exercise 1: EXERCISE

Find the coefficient of $x^{15}$ in the expansion of ${\left(x-x^2\right)}^{10}$.

Find the coefficient of $\frac{1}{x^{17}}$ in the expansion of ${\left(x^4-\frac{1}{x^3}\right)}^{15}$.

Find the sixth term of the expansion ${\left({\mathrm{y}}^{1/2}+{\mathrm{x}}^{1/3}\right)}^{\mathrm{n}}$, if the binomial coefficient of the third term from the end is $45$.

Find the value of $\mathrm{r}$ if the coefficients of $(2\mathrm{r}+4{)}^{th}$ and $(\mathrm{r}-2{)}^{th}$ terms in the expansion of $(1+\mathrm{x}{)}^{18}$ are equal.

Find the coefficient of ${\mathrm{x}}^4$ in the expansion of ${\left(1+\mathrm{x}+{\mathrm{x}}^2+{\mathrm{x}}^3\right)}^{11}$.

Find $\mathrm{n}$ in the binomial ${\left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)}^n$ if the ratio of $7^{\mathrm{th}}$ term from the beginning to the $7^{\mathrm{th}}$ term from the end is $\frac{1}{6}$.

The largest coefficient in the expansion of $(1+\mathrm{x}{)}^{30}$ is _____.

Middle term in the expansion of ${\left({\mathrm{a}}^3+\mathrm{ba}\right)}^{28}$ is _____.