Binomial Theore...

The coefficient of $$x^{2012}$$ in $$\dfrac{1+x}{(1+x^2)(1-x)}$$ is.

Let $$n$$ be a positive integer and, $${ \left( 1+x \right)  }^{ n }={ a }_{ 0 }+{ a }_{ 1 }x+{ a }_{ 2 }{ x }^{ 2 }+\dots +{ a }_{ n }{ x }^{ n }$$. What is $${ a }_{ 0 }+{ a }_{ 1 }+{ a }_{ 2 }+\dots +{ a }_{ n }$$ equal to?

$$5^{th}$$ term from the end in the expansion of $$\left( \dfrac{x^2}{2} - \dfrac{2}{x^2} \right )^{12}$$ is

The value of $${ }^nC_0 - { }^nC_1 + { }^n C_2 - .... + (-1)^{n^n}C_n$$ is:

Consider the expansion of $$(1+x)^{2n+1}$$
The average of the coefficients of the two middle terms in the expansion is

In the expansion of $$\left( x^3 - \dfrac{1}{x^2} \right )^n , n \in N$$, if the sum of the coefficient of $$x^5$$ and $$x^{10}$$ is $$0$$, then $$n$$ is :

Consider the expansion of $$(1+x)^{2n+1}$$
The sum of the coefficients of all the terms in the expansion is

How many terms are there in the expansion of $${ \left( 1+2x+{ x }^{ 2 } \right)  }^{ 10 }$$?

The value of the expression $${ _{  }^{ k-1 }{ C } }_{ k-1 }+{ _{  }^{ k }{ C } }_{ k-1 }+....{ _{  }^{ n+k-2 }{ C } }_{ k-1 }$$ is given by :

What is n equal to ?