Quantitative analysis of an organic compound (X) shows following % composition.
C : $14.5 \%$
Cl : 64.46%
H: 1.8 %
(Empirical formula mass of the compound $(\mathrm{X})$ is _________ $\times 10^{-1}$
(Given molar mass in $\mathrm{g} \mathrm{~mol}^{-1}$ of $\mathrm{C}: 12, \mathrm{H}: 1, \mathrm{O}: 16, \mathrm{Cl}: 35.5$)
Let $\mathrm{A}(x, y, z)$ be a point in $x y$-plane, which is equidistant from three points $(0,3,2),(2,0,3)$ and $(0,0,1)$.
Let $\mathrm{B}=(1,4,-1)$ and $\mathrm{C}=(2,0,-2)$. Then among the statements
(S1) : $\triangle \mathrm{ABC}$ is an isosceles right angled triangle, and
(S2) : the area of $\triangle \mathrm{ABC}$ is $\frac{9 \sqrt{2}}{2}$,
If $f(x)=\frac{2^x}{2^x+\sqrt{2}}, \mathrm{x} \in \mathbb{R}$, then $\sum_\limits{\mathrm{k}=1}^{81} f\left(\frac{\mathrm{k}}{82}\right)$ is equal to
The sum, of the squares of all the roots of the equation $x^2+|2 x-3|-4=0$, is