$A$ beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20 \; Vm^{-1}$ and $0.5 \; T$ at right angles to the direction of motion of the electrons. What is the velocity (in $m/s$) of the electrons?

To the free end of a spring hanging from a rigid support,a block of mass $m$ is hung and slowly allowed to come to its equilibrium position. Then the stretching in the spring is $d$. If the same block is attached to the same spring and allowed to fall suddenly,the amount of stretching is: (force constant,$k$)

The shadow of a tower standing on a level ground is found to be $60 \ m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $45^{\circ}$. The height of the tower is

For a binomial variate $X$ with $n=6$, if $P(X=2)=9 P(X=4)$, then its variance is

$A$ coil of wire of radius $r$ has $600$ turns and a self-inductance of $108 \ mH$. The self-inductance of a coil with the same radius and $500$ turns is (in $mH$)

$A$ magnetized wire of magnetic moment $M$ and length $l$ is bent into the form of a semicircle of radius $r$. Then its new magnetic moment is: