When two sound waves travel in the same direction in a medium, the displacements of a particle located at \('x'\) at time \('t'\) is given by \({y_1} = 0.05\,\cos \,\left( {0.50\,\pi x - 100\,\pi t} \right)\) \({y_2} = 0.05\,\cos \,\left( {0.46\,\pi x - 92\,\pi t} \right)\) then velocity is..... \(m/s\)

Four resistances of \(15\; \Omega, 12\; \Omega, 4 \;\Omega\) and \(10\; \Omega\) respectively in cyclic order to form Wheats tone's network. The resistance that is to be connected in parallel with the resistance of \(10\; \Omega\) to balance the network is .................. \(\Omega\)

The work function of a substance is \(3.0\ \mathrm{eV}\). The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately _______.

Given below are two statements: Statement \(I :\) Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an \(AC\) source, when resonance occurs Statement \(II :\) Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below :

The speed verses time graph for a particle is shown in the figure. The distance travelled (in \(m\) ) by the particle during the time interval \(t=0\) to \(t=5\, s\) will be

A slender uniform rod of mass \(M\) and length \(l\) is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle \(\theta\) with the vertical is

The total number of turns and cross-section area in solenoid is fixed. However, its length \(L\) is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to

A \(1\,m\) long metal rod \(XY\) completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \(0.15\,T\). If the resistance of the circuit is \(5\,\Omega\), the force needed to move the rod in direction, as indicated, with a constant speed of \(4\,m / s\) will be \(................\,10^{-3}\,N\)

The activity of a radioactive material is \(6.4 \times 10^{-4}\) curie. Its half life is \(5\; days\). The activity will become \(5 \times 10^{-6}\) curie after \(.......day\)

A shown in the figure, a battery of \(emf \;\varepsilon\) is connected to an inductor \(L\) and resistance \(R\) in series. The switch is closed at \(t=0 .\) The total charge that flows from the battery, between \(\mathrm{t}=0\) and \(\mathrm{t}=\mathrm{t}_{\mathrm{c}}\;( \mathrm{t}_{\mathrm{c}}\) is the time constant of the circuit) is

A particle of mass \(m\) projected with a velocity ' \(u\) ' making an angle of \(30^{\circ}\) with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height \(\mathrm{h}\) is _______.

A thin convex lens of focal length \('f'\) is put on a plane mirror as shown in the figure. When an object is kept at a distance \('a'\) from the lens - mirror combination, its image is formed at a distance \(\frac{a}{3}\) in front of the combination. The value of \('a'\) is

The current gain of a common emitter amplifier is \(69\). If the emitter current is \(7.0\,mA\), collector current is.....\(mA\)