An ideal gas follows a process $PT = \text{constant}$. The correct graph between pressure $(P)$ and volume $(V)$ is:

If $\alpha, \beta, \gamma$ are the roots of $x^3+4x+1=0$,then the equation whose roots are $\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}, \frac{\gamma^2}{\alpha+\beta}$ is

If $f(2)=4$ and $f^{\prime}(2)=1$,then $\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$ is equal to

The force between the plates of a parallel plate capacitor of capacitance $C$ and distance of separation of the plates $d$ with a potential difference $V$ between the plates,is

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is:

$A$ small source of sound moves on a circle as shown in the figure and an observer is standing at $O$. Let $n_1, n_2$ and $n_3$ be the frequencies heard when the source is at $A, B$ and $C$ respectively. Then