Among the following compounds $(I-III)$,the correct order of reactivity towards electrophilic substitution is:

$A$ long straight rod of diameter $4 \ mm$ carries a steady current '$i$'. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances $1 \ mm$ and $4 \ mm$ from the axis of the rod is

An infinitely long conductor $PQR$ is bent to form a right angle as shown. $A$ current $I$ flows through $PQR$. The magnetic field due to this current at the point $M$ is $H_1$. Now,another infinitely long straight conductor $QS$ is connected at $Q$ such that the current in $PQ$ remains unchanged. The magnetic field at $M$ is now $H_2$. The ratio $H_1/H_2$ is given by

If $A$ and $B$ are two sets,then $A \cup B = A \cap B$ if and only if

If $y=(1+x)(1+x^2)(1+x^4) \dots (1+x^{2^n})$,then $(\frac{dy}{dx})_{x=0}$ is equal to

If a gas expands at constant temperature,it indicates that