The magnetic field $(B)$ inside a long solenoid having $n$ turns per unit length and carrying current $I$ when an iron core is kept in it is ($\mu_0 = $ permeability of vacuum,$\chi = $ magnetic susceptibility).

Find the points on the curve $\frac{x^2}{4} + \frac{y^2}{25} = 1$ at which the tangents are parallel to the $x$-axis.

If $\alpha, \beta, \gamma$ are the roots of $x^3-2x^2+3x-4=0$,then the value of $\alpha^2\beta^2+\beta^2\gamma^2+\gamma^2\alpha^2$ is

An artificial satellite of mass $m$ is moving along an elliptical path around the Earth. The areal velocity of the satellite is proportional to

The energy liberated on complete fission of $1\, kg$ of $_{92}U^{235}$ is (Assume $200\, MeV$ energy is liberated on fission of $1$ nucleus).

When an $AC$ source of $e.m.f. \ e = E_0 \sin(100t)$ is connected across a circuit,the phase difference between the $e.m.f. \ e$ and the current $i$ in the circuit is observed to be $\frac{\pi}{4}$ as shown in the diagram. If the circuit consists possibly only of $RC$,$RL$,or $LC$ in series,find the relationship between the two elements.