Sequences and S...

Find: $$6,25,62,123,(?),341$$

Find the missing factor among the given figure ?

The numbers $${\log _{180}}12,{\log _{2160}}12,{\log _{25920}}12$$ are in

If $$[x]$$ denotes the greates integer $$\le x$$, then $$\left[\dfrac{2}{3} \right] + \left[\dfrac{2}{3} + \dfrac{1}{99} \right] + \left[\dfrac{2}{3} + \dfrac{2}{99} \right] + .... + \left[\dfrac{2}{3} + \dfrac{98}{99} \right] =$$

$$\sum _{ r=0 }^{ n }{ \dfrac { { 2 }^{ r+2 }\cdot ^{ n }C_{ r } }{ (r+1)(r+2) }  } $$ is equal to 

If $$S={1}^{2}-{2}^{2}+{3}^{2}-{4}^{2}....$$ upto $$n$$ terms and $$n$$ is even, then $$S$$ equals _____

The value of $$\sum\limits_{n = 2}^\infty  {\left( {1 - \frac{1}{{{n^2}}}} \right)} $$ equals 

If $$x$$ and $$y$$ are the number of possibilities that $$A$$ can assume such that the unit digit of A and $$A^3$$ are same and the unit digit of $$A^2$$ and $$A^3$$ are same respectively ,then the value of $$x-y$$ is (where $$A$$ is a single digit number)

$$\begin{bmatrix} 12 & 47 & 21 \\ 10 & 52 & 4 \\ 64 & ? & 24 \end{bmatrix}$$ 

If $$(1+ax)^{n }=1+8x+24x^{2}+...;$$ then $$\cfrac {a-n}{a+n}$$ is equal to