For one mole of a van der Waals gas,when $b = 0$ and $T = 300 \ K$,the plot of $PV$ versus $1/V$ is shown below. The value of the van der Waals constant $a \ (atm \ L^2 \ mol^{-2})$ is:

$A$ parallel plate capacitor with air between the plates has a capacitance of $9 \, pF$. The separation between its plates is $d$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $d/3$,while the other one has dielectric constant $K_2 = 6$ and thickness $2d/3$. The new capacitance of the capacitor is .... $pF$.

Three positive charges of equal value $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in

$y=A e^x+B e^{2 x}+C e^{3 x}$ satisfies the differential equation

$A$ square is inscribed in the circle $x^{2} + y^{2} - 2x + 4y - 93 = 0$ such that its sides are parallel to the coordinate axes. The coordinates of its vertices are: