Carbon cannot be used in the reduction of $Al_2O_3$ because :

$A$ conducting bar is pulled with a constant speed $v$ on a smooth conducting rail. The region has a steady magnetic field of induction $B$ as shown in the figure. If the speed of the bar is doubled then the rate of heat dissipation will

List-$I$ shows reactions involved in the metallurgy of $Pb$ (lead) and List-$II$ shows the names of the processes. Match List-$I$ with List-$II$ and select the correct code for your answer.

List-$I$	List-$II$
$(P). PbS + 2PbO \xrightarrow{\Delta} 3Pb + SO_2 \uparrow$	$(1).$ Smelting
$(Q). PbS + \frac{3}{2}O_2 \xrightarrow{\Delta} PbO + SO_2 \uparrow$	$(2).$ Self reduction
$(R). PbCO_3 \xrightarrow{\Delta} PbO + CO_2 \uparrow$	$(3).$ Calcination
$(S). PbO + C \xrightarrow{\Delta} Pb + CO \uparrow$	$(4).$ Roasting

Two substances $A$ and $B$ of equal mass $m$ are heated at a uniform rate of $6 \, cal \, s^{-1}$ under similar conditions. $A$ graph between temperature and time is shown in the figure. The ratio of heat absorbed $H_A/H_B$ by them for complete fusion is

If the slope of one of the lines in the pair of lines $8x^2 + axy + y^2 = 0$ is thrice the slope of the other line,then $a =$

The oxidation states of $S$ atoms in Caro's and Marshall's acids are