Which of the following liquid mixtures shows a positive deviation from Raoult's law?

If $N$ denotes the set of all positive integers and if $f: N \rightarrow N$ is defined by $f(n) =$ the sum of positive divisors of $n$,then $f(2^k \cdot 3)$,where $k$ is a positive integer,is

$A$ Carnot engine absorbs an amount $Q$ of heat from a reservoir at an absolute temperature $T$ and rejects heat to a sink at a temperature of $T/3$. The amount of heat rejected 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

Light of wavelength $4000 \, \mathring A$ is incident on a sodium surface for which the threshold wavelength of photoelectrons is $5420 \, \mathring A$. The work function of sodium is .......... $eV$.

The pair of compounds which cannot exist together in aqueous solution is
$I$. $NaH_2PO_4$ and $NaHCO_3$
$II$. $Na_2CO_3$ and $NaHCO_3$
$III$. $NaOH$ and $NaH_2PO_2$
$IV$. $NaHCO_3$ and $NaOH$