Two finite sets have $m$ and $n$ elements respectively. If the number of subsets of the first set is $56$ more than the number of subsets of the second set,then the values of $m$ and $n$ are:

Justify that the following reactions are redox reactions:
$a$. $CuO_{(s)} + H_{2(g)} \rightarrow Cu_{(s)} + H_2O_{(g)}$
$b$. $Fe_2O_{3(s)} + 3CO_{(g)} \rightarrow 2Fe_{(s)} + 3CO_{2(g)}$
$c$. $4BCl_{3(g)} + 3LiAlH_{4(s)} \rightarrow 2B_2H_{6(g)} + 3LiCl_{(s)} + 3AlCl_{3(s)}$
$d$. $2K_{(s)} + F_{2(g)} \rightarrow 2K^{+}F^{-}_{(s)}$
$e$. $4NH_{3(g)} + 5O_{2(g)} \rightarrow 4NO_{(g)} + 6H_2O_{(g)}$

$A$ particle of mass $m$ moves with a velocity $v$ along the line $PC$ (as shown in the figure). The angular momentum of the particle about point $O$ is:

The skull of a frog is:

Under which one of the following conditions do real gases approach the ideal gas behaviour?

Solar radiation emitted by the sun resembles that emitted by a black body at a temperature of $6000\, K$. Maximum intensity is emitted at a wavelength of about $4800\, \mathring{A}$. If the sun was cooled down from $6000\, K$ to $3000\, K$,then the peak intensity would occur at a wavelength of ......... $\mathring{A}$.