$A$ magnetized wire of magnetic moment $M$ and length $L$ is bent into an arc of a circle subtending an angle of $60^{\circ}$ at the center. The new magnetic moment is:

$A$ and $B$ are two concentric circular loops carrying currents $i_1$ and $i_2$ as shown in the figure. If the ratio of their radii is $1:2$ and the ratio of the magnetic flux densities at the centre $O$ due to $A$ and $B$ is $1:3$,then the value of $\frac{i_1}{i_2}$ will be

$A$ variable circle passes through the fixed point $A(p, q)$ and touches the $X$-axis. The locus of the other end of the diameter through $A$ is

Let $f$ be a non-zero real-valued continuous function satisfying $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$. If $f(2)=9$,then $f(6)$ is equal to

Solid targets of different elements are bombarded by highly energetic electron beams. The frequency $(f)$ of the characteristic $X-$rays emitted from different targets varies with atomic number $(Z)$ as

The solution of the differential equation $\frac{dy}{dx} = \frac{x-2y+1}{2x-4y}$ is