The magnetic field at the centre of a circular current-carrying conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the centre is $B_a$. The value of $B_c : B_a$ will be:

The solution set of $(5+4 \cos \theta)(2 \cos \theta+1)=0$ in the interval $[0, 2 \pi]$ is:

An ammeter gives full scale deflection when a current of $1.0 \ A$ is passed through it. To convert it into a $10 \ A$ range ammeter,the ratio of its resistance $(G)$ to the shunt resistance $(S)$ will be:

Let $k$ be a non-zero real number. If $f(x) = \begin{cases} \frac{(e^x - 1)^2}{\sin(\frac{x}{k}) \log(1 + \frac{x}{4})} & x \neq 0 \\ 12 & x = 0 \end{cases}$ is a continuous function,then the value of $k$ is:

If the wavelength of an electromagnetic radiation is $2000 \ \mathring{A}$,what is its energy in ergs?

$A$ ball of mass $1.2 \ kg$ moving with a velocity of $12 \ ms^{-1}$ makes a one-dimensional collision with another stationary ball of mass $1.2 \ kg$. If the coefficient of restitution is $\frac{1}{\sqrt{2}}$,then the ratio of the total kinetic energy of the balls after collision to the initial kinetic energy is: