In the circuit shown below $E_1 = 4.0 \, V$,$R_1 = 2 \, \Omega$,$E_2 = 6.0 \, V$,$R_2 = 4 \, \Omega$ and $R_3 = 2 \, \Omega$. The current $I_1$ is ............... $A$

In which of the following,ortho/para substitution by an electrophile is very facile?

$A$ family of curves has the differential equation $x y \frac{d y}{d x}=2 y^2-x^2$. Then,the family of curves is

In an astronomical telescope in normal adjustment,a straight black line of length $L$ is drawn on the objective lens. The eyepiece forms a real image of this line. The length of this image is $l$. The magnification of the telescope is

The solution of $\frac{dx}{dy} + \frac{x}{y} = x^2$ is:

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is: