$A$ conducting rod of length $\ell$ is moving with velocity $v$ in a uniform magnetic field $B$ directed into the plane of the paper,as shown in the diagram. Which end of the rod is at a lower potential?

In a potentiometer, a wire of length $10 \, m$ having resistance $50 \, \Omega$ is used. $A$ battery of $5 \, V$ and a resistor of $450 \, \Omega$ are connected in series to the wire. If an unknown battery of emf $E$ balances the potentiometer at $450 \, cm$, then the value of $E$ is (in $V$)

If $x=a\left\{\cos \theta+\log \tan \left(\frac{\theta}{2}\right)\right\}$ and $y=a \sin \theta$,then $\frac{d y}{d x}$ is equal to

The eccentricity of the ellipse $x^2+4y^2+2x+16y+13=0$ is

In Kranz anatomy,the bundle sheath cells have

$A$ body of mass $1 ~g$ and carrying a charge $10^{-8} ~C$ passes through two points $P$ and $Q$. $P$ and $Q$ are at electric potentials $600 ~V$ and $0 ~V$,respectively. The velocity of the body at $Q$ is $20 ~cm/s$. Its velocity in $m/s$ at $P$ is: