For the reaction $SnO_{2(s)} + 2H_{2(g)} \rightleftharpoons 2H_2O_{(g)} + Sn_{(l)}$,calculate $K_p$ at $900 \ K$ where the equilibrium steam-hydrogen mixture was $45\%$ $H_2$ by volume.

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = Young's modulus,$\rho$ = density,$\alpha$ = coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

The set $\{x \in R: \cos 2x + 2 \cos^2 x = 2\}$ is equal to

One mole of $N_2H_4$ loses $10$ moles of electrons to form a new compound $Z$. Assuming that all the nitrogen atoms appear in the new compound,what is the oxidation state of nitrogen in $Z$? (There is no change in the oxidation state of hydrogen.)

$A$ patient who excretes a large quantity of sodium in urine has:

Planet $M$ orbits around its sun,$S$,in an elliptical orbit with the sun at one of the foci. When $M$ is closest to $S$,it is $2 \ unit$ away. When $M$ is farthest from $S$,it is $18 \ unit$ away. Assuming $S$ is at the origin $(0, 0)$ and the other focus lies on the negative $y$-axis,find the equation of the elliptical orbit of planet $M$.