Let $\alpha=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\ldots \infty$ and

$\beta=\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\ldots \infty$. Then the value of

$(0.2)^{\log _{\sqrt{5}}(\alpha)}+(0.04)^{\log _5(\beta)}$ is equal to :

For 10 observations $x_1, x_2, \ldots, x_{10}$, if $\sum\limits_{i=1}^{10}\left(x_i+2\right)^2=180$ and $\sum\limits_{i=1}^{10}\left(x_i-1\right)^2=90$, then their standard deviation is :

In the expansion of $\left(9 x-\frac{1}{3 \sqrt{x}}\right)^{18}, x>0$, if the term independent of $x$ is (221)k, then k is equal to:

Let $\mathrm{P}(3 \cos \alpha, 2 \sin \alpha), \alpha \neq 0$, be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1, \mathrm{Q}$ be a point on the circle $x^2+y^2-14 x-14 y+82=0$ and R be a point on the line $x+y=5$ such that the centroid of the triangle PQR is $\left(2+\cos \alpha, 3+\frac{2}{3} \sin \alpha\right)$. Then the sum of the ordinates of all possible points R is: