The upper half of an inclined plane with an angle of inclination \(\phi\), is smooth while the lower half is rough. A body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is

An \(n-p-n\) transistor power amplifier in \(C-E\) configuration gives

A wire of length \(50 \mathrm{~cm}\) and weighing \(10 \mathrm{gm}\) is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of \(50 \mathrm{~N} / \mathrm{m}\) and is stretched by \(1 \mathrm{~cm}\). If a wave pulse is produced on the string near the wall, then how much time will it take to reach the spring?

If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of \(2900 Å\), the intensity of radiation emitted by it is (Stefan-Boltzmann's constant \(=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}\) and Wein's constant \(=2.9 \times 10^{-3} \mathrm{mK}\) )

An air bubble of radius \(1 \mathrm{~cm}\) rises from the bottom portion through a liquid of density \(1.5 \mathrm{~g} / \mathrm{cc}\) at a constant speed of \(0.25 \mathrm{~cm} \mathrm{~s}^{-1}\). If the density of air is neglected, the coefficient of viscosity of the liquid is approximately, (In Pas) :

Consider the motion of a particle described by \(x=a \cos t, y=a \sin t\) and \(z=t\). The trajectory traced by the particle as a function of time is

In a travelling plane electromagnetic wave, the maximum magnetic field is \(1.26 \times 10^{-4} \mathrm{~T}\). The intensity of the wave is (Assume, \(\mu_0=1.26 \times 10^{-6} \mathrm{H} / \mathrm{m}\) )

The electrostatic force between two charges kept in air is F. If \(30 \%\) of the space between the charges is filled with a medium, then the electrostatic force between the charges becomes \(\frac{\mathrm{F}}{2.56}\). The dielectric constant of the medium is

A \(L-C-R\) series circuit is connected to a source of alternating current. At resonance, the applied voltage and the current flowing through the circuit will have a phase difference of

For a given truth table \(A, B\) and \(C\) are inputs and \(Y\) is the output, then the functional form of the circuit is

A plane electromagnetic wave of electric and magnetic fields \(E_0\) and \(B_0\) respectively incidents on a surface. If the total energy transferred to the surface in a time of ' \(t\) ' is ' \(U\), then the magnitude of the total momentum delivered to the surface for complete absorption is

Two identical bar magnets of magnetic moment \(M\) each, are placed along \(X\) and \(Y\)-axes, respectively at a distance \(d\) from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on \(X\)-axis and on the magnetic axis of magnet placed on \(Y\)-axis. If the magnitude of total magnetic field at the origin is \(B=\alpha\left[\frac{\mu_0}{4 \pi} \frac{M}{d^3}\right]\), then the value of constant \(\alpha\) will be \(\langle d>>l\), where \(l\) is the length of the bar magnets and direction of \(\mathrm{N}\) to \(\mathrm{S}\) in magnets is opposite with respect to each other)

A monochromatic radiation of wavelength \(\lambda\) is incident on a hydrogen sample in ground state. The sample subsequently emits radiation of six different wavelengths, then the value of \(\lambda\) is [Use ch \(=1242 \mathrm{eV}-\mathrm{m}\) ]