Embibe Experts Solutions for Chapter: Binomial Theorem, Exercise 1: NDA & NA EE 2019 Paper 1 Mathematics

The term independent of $x$ in the binomial expansion of ${\left(\frac{2}{x^2}-\sqrt{x}\right)}^{10}$ is equal to

If ${\left(1+2x-x^2\right)}^6=a_0+a_{1}x+a_2{x}^2$ $+\dots +a_{12}{x}^{12},$ then what is $a_0-a_1$ $+a_2-a_3+a_4-\dots +a_{12}$ equal to?

If $C\left(20, n+2\right)=C\left(20, n-2\right),$ then what is $n$ equal to?

What is the sum of the last five coefficients in the expansion of $(1+x{)}^9$ when it is expanded in ascending powers of $x?$

If the constant term in the expansion of ${\left(\sqrt{x}-\frac{k}{x^2}\right)}^{10}$ is $405,$ then what can be the values of $k?$

What is $C\left(47, 4\right)+C\left(51, 3\right)+C\left(50, 3\right)+C\left(49, 3\right)+C\left(48, 3\right)+C\left(47, 3\right)$ equal to?

What is the number of terms in the expansion of ${\left[(2x-3y{)}^2(2x+3y{)}^2\right]}^2?$

In the expansion of $(1+ax{)}^n,$ the first three terms are respectively $1,12 x$ and $64x^2.$ What is $n$ equal to?