Binomial Theore...

If the coefficients of $$2^{nd}, 3^{rd},$$ and $$4^{th}$$ terms in the expansion of $${(1 + x)^n},n \in N$$ are in A.P.,then $$n=$$

The coefficient of $${ x }^{ n }$$ in $$(1-x+\frac { { x }^{ 2 } }{ 2! } -\frac { { x }^{ 3 } }{ 3! } +.....+\frac { { (-1) }^{ n }{ x }^{ n } }{ n! } )^{ 2 }$$ is 

The middle term in the expansion of $$\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^{20}$$ is 

The coefficient of $$x^8$$ in the expansion of $$(1+x+x^3+x^5+x^9)(1+x^2)^5(1_x^4)^6$$ is equal to

If coefficient of $$2^{nd}, 3^{rd}$$ and $$4^{th}$$ term in the expansion of $$\left(1+x\right)^{2n}$$ are in A.P. then :

The coefficient of $$a^3b^4c$$ in the expansion of $$(1+a+b-c)^9$$ is

If the fourth term in the expansion of $$\left(px+\dfrac{1}{x}\right)^{n}$$ is independent of $$x$$, then the value of term is :

If in the expansion of $$\left(2^{1/3}+\dfrac {1}{3^{1/3}}\right)^{n}$$, the ratio of $$6^{th}$$ term from beginning and from the end is $$1/6$$, then the value of $$n$$ is

Find the number of terms in expansion of $$(1+x)^{2}+(1-x)^{8}$$

Middle term in the expansion of $$(1+3x+3x^2+x^3)^6$$ is