$A$ coil of wire of radius $r$ has $600$ turns and a self-inductance of $108 \ mH$. The self-inductance of a coil with the same radius and $500$ turns is (in $mH$)

If $f(x) = \frac{x}{1+|x|}$, for $x \in \mathbb{R}$, then $f^{\prime}(0)$ is equal to :

In the following reaction,$A$ and $B$ respectively are:
$A$ $\xrightarrow{HBr} C_2H_5Br$ $\xrightarrow{B} A$

Give the correct order of initials $T$ or $F$ for the following statements. Use $T$ if the statement is true and $F$ if it is false.
$(I)$ Sulphide ions react with $Na_2[Fe(CN)_5(NO)]$ to form a purple-coloured compound $Na_4[Fe(CN)_5(NOS)]$. In the reaction,the oxidation state of iron changes.
$(II)$ $Pt(IV)$ compounds are relatively more stable than $Ni(IV)$ compounds.
$(III)$ The welding of magnesium can be done in an atmosphere of Helium.
$(IV)$ $LiAlH_4$ on hydrolysis will give $H_2$.

Two rigid boxes containing different ideal gases are placed on a table. Box $A$ contains one mole of nitrogen at temperature $T_0$,while box $B$ contains one mole of helium at temperature $(7/3) T_0$. The boxes are then put into thermal contact with each other,and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of the boxes). The final temperature of the gases $T_f$ in terms of $T_0$ is:

$A$ black body at a high temperature $T \ K$ radiates energy at the rate $E \ W/m^2$. When the temperature falls to $(T/2) \ K$,the radiated energy will be: