For the reactions:
$2NO + O_2 \rightleftharpoons 2NO_2 ; K_1$
$4NO + 2Cl_2 \rightleftharpoons 4NOCl ; K_2$
$NO_2 + 1/2 Cl_2 \rightleftharpoons NOCl + 1/2 O_2 ; K_3$
where $K_1, K_2, K_3$ are equilibrium constants,then $K_3^2$ is equal to:

What does the part labeled as "$X$" represent in the given figure?

Assertion $(A)$: Equal moles of different substances contain the same number of constituent particles.
Reason $(R)$: Equal weights of different substances contain the same number of constituent particles.
The correct answer is

$1+\frac{1+2}{2 !}+\frac{1+2+2^2}{3 !}+\ldots$ is equal to

In a triangle $ABC$,if the midpoints of sides $AB, BC, CA$ are $(3,0,0), (0,4,0), (0,0,5)$ respectively,then $AB^2 + BC^2 + CA^2 = $

In the figure,suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also,let the center disk be rotated on the common axis with an angular speed $\omega$. If unpolarized light is incident on the left disk with an intensity $I_{max}$,the intensity of the beam emerging from the right disk is given by: