The number of common tangents, to the circles

$x^{2}+y^{2}-18 x-15 y+131=0$

and $x^{2}+y^{2}-6 x-6 y-7=0$, is :

Let $[x]$ denote the greatest integer function and

$f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2$. Let $m$ be the number of

points in $[0,2]$, where $f$ is not continuous and $n$ be the number of points in

$(0,2)$, where $f$ is not differentiable. Then $(m+n)^{2}+2$ is equal to :

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is :

Let $\left(a+b x+c x^{2}\right)^{10}=\sum\limits_{i=0}^{20} p_{i} x^{i}, a, b, c \in \mathbb{N}$.

If $p_{1}=20$ and $p_{2}=210$, then $2(a+b+c)$ is equal to :