Sequences and S...

If $$(1+x+x^{2})^{n}=a_{0}+a_{1}+a_{2}x^{2n}$$, then $$a_{0}+a_{2}+a_{4}+........+a_{2n}x^{2n},$$ is equal to :

In the sum $$3+33+333+3333+.........2015$$ terms the number formed by taking the last four digits in that order is 

$$^{(2n+1)}C_{0}+^{(2n+1)}C_{1}+^{(2n+1)}C_{2}+...+^{(2n+1)}C_{n}=$$

Sum of the series $$\dfrac{1^2}{1!}+\dfrac{2^2}{2!}+\dfrac{3^2}{3!}+\dfrac{4^2}{4!}+.....$$(infinite terms) is?

I for $$n\in I, n> I0;1+(1+x)+(1+x)^{2}+....+(1+)^{n}=\displaystyle \sum_{k=0}^{n}a_{k}.x^{k},x\neq 0$$ then

If $$(3x-1)^{}=a_{7}x^{7}+a_{6}x^{6}+....+a_{0}$$, then $$a_{7}+a_{6}+...+a_{0}$$ is

$$\dfrac { 7 } { 11 } : \dfrac { 336 } { 110 } : ? \quad : \quad \dfrac { 720 } { 272 }$$

Find the number .

$$ABCDEFGHIJKLMZYXWVUTSRQPON$$

From the above letter series find the letter which is at the  $$6th$$  position to the right side of the letter which is at the centre position of the letters which are at the  $$11th$$  place form the left and  $$14th$$  place from the right.

 There is a specific relationship between the numbers that are given in the following figures. On the basis of the relationship choose the correct alternative to replace the question mark.