$A$ particle $A$ has charge $+q$ and particle $B$ has charge $+4q$,with each of them having the same mass $m$. When allowed to fall from rest through the same electrical potential difference,the ratio of their speeds $V_A : V_B$ will be:

$A$ cylindrical conductor of radius $R$ carries a current $i$. The value of the magnetic field at a point which is $R/4$ distance inside from the surface is $10 \ T$. Find the value of the magnetic field at a point which is $4R$ distance outside from the surface.

If $\cos ^{-1}\left(\frac{x^2-y^2}{x^2+y^2}\right)=k$ (a constant),then $\frac{d y}{d x}$ is equal to

An electron is projected along the axis of a circular conductor carrying current $I$. The electron will experience:

Two slits separated by a distance of $1\, mm$ are illuminated with red light of wavelength $6.5 \times 10^{-7}\, m$. The interference fringes are observed on a screen placed $1\, m$ from the slits. Find the distance between the third dark fringe and the fifth bright fringe on the same side of the central maxima.

The network shown in the figure is part of a complete circuit. If at a certain instant,the current $I$ is $5 \ A$ and it is decreasing at a rate of $10^3 \ A \ s^{-1}$,and if $I$ is reversed in direction,then $V_B - V_A$ equals .......... $V$.