A particle of charge \(16\times10^{-16}\, C\) moving with velocity \(10\, ms^{-1}\) along \(x-\) axis enters a region where magnetic field of induction \(\vec B\) is along the \(y-\) axis and an electric field of magnitude \(10^4\, Vm^{-1}\) is along the negative \(z-\) axis. If the charged particle continues moving along \(x-\) axis, the magnitude of \(\vec B\) is

A letter \('A'\) is constructed of a uniform wire with resistance \(1.0\,\Omega \) per \(cm\) , The sides of the letter are \(20\, cm\) and the cross piece in the middle is \(10\, cm\) long. The apex angle is \(60\) . The resistance between the ends of the legs is close to ................ \(\Omega\)

Three conductors of same length having thermal conductivity \(\mathrm{k}_1, \mathrm{k}_2\) and \(\mathrm{k}_3\) are connected as shown in figure.

Area of cross sections of \(1^{\text {st }}\) and \(2^{\text {nd }}\) conductor are same and for \(3^{\text {rd }}\) conductor it is double of the \(1^{\text {st }}\) conductor. The temperatures are given in the figure. In steady state condition, the value of \(\theta\) is _______ \({ }^{\circ} \mathrm{C}\).
(Given : \(\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1}\mathrm{~m}^{-1}\) \( \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}\) )

On the \(x-\)axis and a dsitance \(x\) from the origin, the gravitational field due to a mass distribution is given by \(\frac{A x}{\left(x^{2}+a^{2}\right)^{3 / 2}}\) in the \(x-\)direction. The magnitude of gravitational potential on the \(x-\)axis at a distance \(x,\) taking its value to be zero at infinity, is

For the circuit shown below, the current through the Zener diode is......\(mA\)

Two vectors \(\vec A\) and \(\vec B\) have equal magnitudes. The magnitude of \((\vec A + \vec B)\) is \(‘n’\) times the magnitude of \((\vec A - \vec B)\). The angle between \( \vec A\) and \(\vec B\) is

The dimension of \(\frac{\mathrm{B}^{2}}{2 \mu_{0}}\), where \(\mathrm{B}\) is magnetic field and \(\mu_{0}\) is the magnetic permeability of vacuum, is

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity \(3\, m / s\) (as shown in figure). Maximum height with respect to the initial position covered by it will be \(...........cm\).

Identify the logic operation performed by the given circuit.