In the following circuit,find $I_1$ and $I_2$.

Planet $M$ orbits around its sun,$S$,in an elliptical orbit with the sun at one of the foci. When $M$ is closest to $S$,it is $2 \ unit$ away. When $M$ is farthest from $S$,it is $18 \ unit$ away. Assuming $S$ is at the origin $(0, 0)$ and the other focus lies on the negative $y$-axis,find the equation of the elliptical orbit of planet $M$.

$A$ constant voltage of $25 ~V$ is applied to a series $L-R$ circuit at $t=0$,by closing a switch. What is the potential difference across the resistor and the inductor at time $t=0$?

In an $A.C.$ circuit,$V$ and $I$ are given by $V = 100 \sin(100t) \ V$ and $I = 100 \sin(100t + \frac{\pi}{3}) \ mA$. The power dissipated in the circuit is ...... $W$.

$A$ number $n$ is chosen at random from $S=\{1, 2, 3, \ldots, 50\}$. Let $A=\{n \in S: n+\frac{50}{n} > 27\}$,$B=\{n \in S: n \text{ is a prime}\}$ and $C=\{n \in S: n \text{ is a square}\}$. Then,the correct order of their probabilities is