Binomial Theore...

The number of terms in the expansion of $$( 1 + 5\sqrt 2 x)^9 + ( 1 -5\sqrt 2 x)^9$$ is

The sum of all the coefficients in the binomial expansion of $$(x^2 + x^3)^{319}$$ is

Which term in the expansion of $$\left (\displaystyle \frac {x}{3}-\frac {2}{x^2}\right )^{10}$$ contains $$x^4$$?

If $$C_0 , C_1 , C_2 .... C_n$$ denote the binomial coefficients in the expansion of $$(1 + x)^n$$ , then the value of $$\displaystyle \sum_{r=0}^n(r+1)C_r$$ is

If $$C_0, C_1, C_2, ..............C_n$$ are binomial coefficients then $$\displaystyle \frac {1}{n!0!}+\frac {1}{(n-1)!1!}+\frac {1}{(n-2)!2!}+ ....+\frac {1}{0!n!}$$ is equal to

If $$(1+x-2x^2)^8= a_0 + a_1x + a_2x^2 +....+ a_{16}x^{16}$$ then the sum $$a_1+a_3+a_5+ .... +a_{15}$$ is equal to

The number of terms which are free from radical signs in the expansion of $$(y^{\frac 15} + x^{\frac 1{10}})^{55}$$ are

If the sum of the coefficients in the expansion of $$(1 -3x + 10x^2)^n$$ is $$a$$ and if the sum of the coefficients in the expansion of $$(1 + x^2)^n$$ is $$b$$, then

$$\binom{n}{0}+2\binom{n}{1}+2^2\binom{n}{2}+ .... +2^n\binom{n}{n}$$ is equal to

If $$(2x+3x^2)^6 = a_0 + a_1x + a_2x^2+.....+ a_{12} x^{12}$$, then values of $$a_0$$ and $$a_6$$ are