List of top Mathematics Questions on Binomial theorem

The coefficient of $x^5$ in the expansion of $(1 + x^2)^5(1 + x)^4$ is

The value of the sum $(\,^nC_1)^2+(\,^nC_2)^2+(\,^nC_3)^2+...+(\,^nC_n)^2$ is

The value of $\frac{1}{81^n}-\frac{10}{81^n}\,^{2n}C_1+\frac{10^2}{81^n}\,^{2n}C_2-\frac{10^3}{81^n}\,^{2n}C_3+.....+\frac{10^{2n}}{81^n}is$

The term independent of $x$ in the expansion of $(x- \frac {3} {x^2})^{18}$

If $x = 99^{50} + 100^{50}$ and $y = \left(101\right)^{50}$ then

If the coefficients of $x^7$ and $x^8$ in $\left( 2 + \frac{x}{3} \right)^n$ are equal, then n is

If n is a positive integer, then the number of terms in the expansion of $[x + a]^n$ is

If $(2x^2 - x - 1)^5 = a_0 + a_1x + a_2x^2 + ... + a_{10}x^{10}$, then, $a_2 + a_4 + a_6 + a_8 + a_{10} =$

Expand $(1 - x + x^2)^4$.

After simplification, what is the number of terms in the expansion of $[(3x + y)^5]^4 - [(3x-y)^4]^5$ ?

A set contains (2n + 1) elements. If the number of subsets of this set which contain at most n elements is 4096, then the value of n is

If $\left(1+x+x^{2}\right)^{n} =1+a_{1}x+a_{2}x^{2} +\cdots+a_{2n}x^{2n}$, $2a_{1} -3a_{2} +\cdots-\left(2n+1\right)a_{2n}$ is equal to