The fundamental frequency of vibration of a string stretched between two rigid support is \(50\,Hz\). The mass of the string is \(18\,g\) and its linear mass density is \(20\,g / m\). The speed of the transverse waves so produced in the string is \(..........\,ms ^{-1}\)

Statement \(I :\) When a Si sample is doped with Boron, it becomes \(P\) type and when doped by Arsenic it becomes \(N-\)type semi conductor such that \(P-\)type has excess holes and N-type has excess electrons. Statement \(II\) : When such \(P-\)type and \(N-\)type semi-conductors, are fused to make a junction, a current will automatically flow which can be detected with an externally connected ammeter. In the light of above statements, choose the most appropriate answer from the options given below.

The position co-ordinates of a particle moving in a \(3-D\) coordinates system is given by \(x = a\,cos\,\omega t\) , \(y = a\,sin\,\omega t\) and \(z = a\omega t\) The speed of the  particle is

A charge \(Q\) is moving \(\overrightarrow{dl}\) distance in the magnetic field \(\overrightarrow{ B }\). Find the value of work done by \(\overrightarrow{ B }\).

If wattless current flows in the \(AC\) circuit, then the circuit is

A physical quantity \(z\) depends on four observables \(a,\) \(b,\) \(c\) and \(d ,\) as \(z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}} .\) The percentage of error in the measurement of \(a, b, c\) and \(d\) are \(2 \%, 1.5 \%, 4 \%\) and \(2.5 \%\) respectively. The percentage of error in \(z\) is\(......\%\)

A stationary particle breaks into two parts of masses \(m_A\) and \(m_B\) which move with velocities \(v_A\) and \(V_B\) respectively. The ratio of their kinetic energies \(\left(\mathrm{K}_B: \mathrm{K}_{\mathrm{A}}\right)\) is _______.

Find out the surface charge density at the intersection of point \(x =3\, m\) plane and \(x\) -axis, in the region of uniform line charge of \(8\, nC / m\) lying along the \(z\) -axis in free space.

A concave mirror for face viewing has focal length of \(0.4\,m.\) The distance at which you hold the mirror from your face in order to see your image upright with a magnification of \(5\) is......\(m\)