$A$ tiny air bubble in a glass slab $(\mu = 1.5)$ appears from one side to be $6\, cm$ from the glass surface and from the other side,$4\, cm$. The thickness of the glass slab is......$cm$

If the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and the hyperbola $\frac{x^2}{4}-\frac{y^2}{b^2}=1$ coincide,then $b^2$ is equal to

Which of the following minerals is not remobilized in plants?

$\begin{aligned} & \frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3} \\ & \Rightarrow A+C= \end{aligned}$

For the gaseous reactions $(I)$ and $(II)$,the equilibrium constants are $X$ and $Y$ respectively.
$I$. $\frac{1}{2} N_{2(g)} + O_{2(g)} \rightleftharpoons NO_{2(g)}$
$II$. $2 NO_{2(g)} \rightleftharpoons N_2 O_{4(g)}$
Using the above reactions,the equilibrium constant $Z$ for the reaction $(III)$ given below is:
$III$. $N_2 O_{4(g)} \rightleftharpoons N_{2(g)} + 2 O_{2(g)}$

$\frac{12}{3 + \sqrt{5} - 2\sqrt{2}} = $