Embibe Experts Solutions for Chapter: Binomial Theorem, Exercise 1: AP EAPCET 2019 (21-Apr Shift-2)

If the term independent of $x$ in the expansion of ${\left(\sqrt{x}-\frac{k}{x^2}\right)}^{10}$ is $405,$ then $k=$

The index of the power of $x$ occurring in the $5^{\text{th }}$ term from the end in the expansion of ${\left(\frac{x^3}{2}-\frac{2}{x^2}\right)}^{12}$ is

If $\left[x\right]$ represents the greatest integer not greater than $x,$ then $\left[{\left(1+\frac{1}{10000}\right)}^{10000}\right]=$

If $\text{'}a\text{'}$ is the middle term in the expansion of $(2x-3y{)}^8$ and $b, c$ are the middle terms in the expansion of $(3x+4y{)}^7,$ then the value of $\frac{b+c}{a},$ when $x=2$ and $y=3,$ is

$\frac{1}{4}-\frac{5}{4·8}+\frac{5·9}{4·8·12}-\dots =$

The first negative coefficient in the terms occurring in the expansion of $(1+x{)}^{\frac{21}{5}}$ is

When $\left|x\right|<\frac{1}{2},$ the coefficient of $x^4$ in the expansion of $\frac{3x^2-5x+3}{(x-1)(2x+1)(x+3)}$ is

The number of rational terms in the expansion of ${\left(3^{\frac{1}{4}}+7^{\frac{1}{6}}\right)}^{144}$ is