Maharashtra Board Solutions for Chapter: Method of Induction and Binomial Theorem, Exercise 6: MISCELLANEOUS EXERCISE

Find tenth term in the expansion of

${\left(2x^2+\frac{1}{x}\right)}^{12}$

Find the middle term (s) in the expansion of

${\left(x-\frac{1}{2y}\right)}^{10}$

If the coefficient of $x^{16}$ in the expansion of ${\left(x^2+ax\right)}^{10}$ is $3360,$ find a.

If the constant term in the expansion of ${\left(x^3+\frac{k}{x^8}\right)}^{11}\text{ is }1320$. Find $\mathrm{k}$.

Find approximate value of $\frac{1}{4.08}$ up to four places of decimals.

Find the term independent of $x$ in the expansion of $\left(1-x^2\right){\left(x+\frac{2}{x}\right)}^6$.

The $3^{rd}$ term of $(1+x{)}^n$ is $36x^2$. And the $5^{th}$ term of $(1+x{)}^n$is $126x^p$, then find the value of $p$.

Suppose $(1+\mathrm{k}x{)}^n=1-12x+60x^2-\dots$find $k$ and $n$