At temperature $T \ K$,the $rms$ speed of $CO_2$ gas is $x \ cm/s$. At what temperature (in $Kelvin$) will the $rms$ speed of nitrous oxide $(N_2O)$ be $4x \ cm/s$ (in $T$)?

$A$ carrier signal $60 \sin(2\pi \times 10^6 t)$ is used to modulate an audio signal $15 \sin(300\pi t)$. The depth of modulation is .........$\%$.

Two particles which are initially at rest,move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of the centre of mass of the system will be

$A$ parallel plate capacitor with plate area $A$ and separation between the plates $d$ is charged by a constant current $I$. Consider a plane surface of area $A/2$ parallel to the plates and drawn between the plates. The displacement current through the area is

The major products obtained from the reactions in List$-II$ are the reactants for the named reactions mentioned in List$-I.$ Match each entry in List$-I$ with the appropriate entry in List$-II$ and choose the correct options.

List$-I$	List$-II$
$(P)$ Stephen reaction	$(1)$ Toluene $\xrightarrow{\substack{\text { (i) } CrO _2 Cl _2 / CS _2 \\ \text { (ii) } H _3 O +}}$
$(Q)$ Sandmeyer reaction	$(2)$ Benzoic acid $\xrightarrow{\substack{\text { (i) } PCl _5 \\ \text { (iii) } NH _3 \\ \text { (iii) } P _4 O _{10}, \Delta}}$
$(R)$ Hoffmann bromamide degradation reaction	$(3)$ Nitrobenzene $\xrightarrow{\begin{array}{l}\text { (i) } Fe , HCl \\ \text { (ii) } HCl , NaNO _2 \\ \text { (273-278 K), } H _2 O \end{array}}$
$(S)$ Cannizzaro reaction	$(4)$ Toluene $\xrightarrow{\begin{array}{l}\text { (i) } Cl _2 / hv , H _2 O \\ \text { (ii) } \text {Tollen 's reagent } \\ \text { (iii) } SO _2 Cl _2 \\ \text { (iv) } NH _3\end{array}}$
	$(5)$ Aniline $\xrightarrow{\substack{\text { (i) }\left( CH _3 CO \right)_2 O , \text { Pyridine } \\ \text { (ii) } HN O _3 H _{2} SO _4, 288 K \\ \text { (iii) } aq . NaOH }}$

$A$ photon of energy $E$ ejects a photoelectron from a metal surface whose work function is $W_0$. If this electron enters into a uniform magnetic field of induction $B$ in a direction perpendicular to the field and describes a circular path of radius $r,$ then the radius $r$ is given by: (in the usual notation)