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(A) $1$. Analyze the observations: The bulb glows $(ON)$ only if both materials connected at $X$ and $Y$ are conductors. If the bulb is $OFF$,it means

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$II$ and $III$

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(A) $1$. Analyze the observations: The bulb glows $(ON)$ only if both materials connected at $X$ and $Y$ are conductors. If the bulb is $OFF$,it means at least one of the materials is an insulator.$2$. From observation $2$,$I$ and $IV$ result in $ON$,so both $I$ and $IV$ are conductors.$3$. From observation $4$,$III$ and $V$ result in $ON$,so both $III$ and $V$ are conductors.$4$. From observation $1$,$I$ and $II$ result in $OFF$. Since $I$ is a conductor,$II$ must be an insulator.$5$. For the third row,the bulb is $OFF$. This means at least one of the materials must be an insulator. Since $II$ is the only identified insulator,the pair must contain $II$.$6$. Looking at the options,option $A$ ($II$ and $III$) contains $II$,which is an insulator. Therefore,the bulb will remain $OFF$.

Sample	$A$	$B$	$C$
Resistivity	$1.6 \times 10^{-8} \Omega \cdot m$	$5.2 \times 10^{-8} \Omega \cdot m$	$100 \times 10^{-6} \Omega \cdot m$

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$S.No.$	Material at $X$	Material at $Y$	Electric Bulb ($ON$/$OFF$)
$1$	$I$	$II$	$OFF$
$2$	$I$	$IV$	$ON$
$3$	-	-	$OFF$
$4$	$III$	$V$	$ON$