A pole is vertically submerged in swimming pool, such that it gives a length of shadow \(2.15 \,m\) within water when sunlight is incident at an angle of \(30^{\circ}\) with the surface of water. If swimming pool is filled to a height of \(1.5\,m\), then the height of the pole above the water surface in centimetres is \(\left(\eta_W=4 / 3\right)........\)

Match the List\(-I\) with List\(-II\).

List \(I\)	List \(II\)
\(A\) \(AC\) generator	\(I\) Presence of both \(L\) and \(C\)
\(B\) Transformer	\(II\) Electromagnetic Induction
\(C\)Resonance phenomenon to occur	\(III\) Quality factor
\(D\)Sharpness of resonance	\(IV\) Mutual Inductance

Choose the correct answer from the options given below:

An infinite number of point charges, each carrying \(1 \,\mu C\) charge, are placed along the y-axis at \(y=1\, m , 2\, m , 4 \,m , 8\, m \ldots \ldots \ldots \ldots \ldots\) The total force on a \(1 \,C\) point charge, placed at the origin, is \(x \times 10^{3}\, N\). The value of \(x\), to the nearest integer, is ......... [Take \(\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,Nm ^{2} / C ^{2}\right]\)

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \(P_1\) and \(P_2\) are orthogonal to each other. The polarizer \(P_3\) covers both the slits with its transmission axis at \(45^{\circ}\) to those of \(P_1\) and \(P_2\). An unpolarized light of wavelength \(\lambda\) and intensity \(I_0\) is incident on \(P_1\) and \(P_2\). The intensity at a point after \(P_3\) where the path difference between the light waves from \(s_1\) and \(s_2\) is \(\frac{\lambda}{3}\), is _______.

An electric field \(\overrightarrow{\mathrm{E}}=4 \mathrm{x} \hat{\mathrm{i}}-\left(\mathrm{y}^{2}+1\right) \hat{\mathrm{j}}\; \mathrm{N} / \mathrm{C}\) passes through the box shown in figure. The flux of the electric field through surfaces \(A B C D\) and \(BCGF\) are marked as \(\phi_{I}\) and \(\phi_{\mathrm{II}}\) respectively. The difference between \(\left(\phi_{\mathrm{I}}-\phi_{\mathrm{II}}\right)\) is (in \(\left.\mathrm{Nm}^{2} / \mathrm{C}\right)\)

A wire of density \(8 \times 10^3\,kg / m ^3\) is stretched between two clamps \(0.5\,m\) apart. The extension developed in the wire is \(3.2 \times 10^{-4}\,m\). If \(Y =8 \times 10^{10}\,N / m ^2\), the fundamental frequency of vibration in the wire will be \(......\,Hz\).

Mobility of electron in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an \(n-\) type semiconductor, the density of electrons is \(10^{19}\, m^{-3}\) and their mobility is \(1.6\, m^2\,/(V.s)\) then the resistivity of the semiconductor(since it is an \(n-\) type semiconductor contribution of holes is ignored) is close to ................ \(\Omega  m\)

The top of a water tank is open to air and its water level is maintained. It is giving out \(0.74\,m^3\) water per minute through a circular opening of \(2\,cm\) radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to........ \(m\)

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of \(10\, mV\) is added to the base-emitter voltage, the base current changes by \(10 \mu A\) and the collector current changes by \(1.5 \,mA\). The load resistance is \(5 \,k \Omega\). The voltage gain of the transistor will be

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is \(6\,V\) and the load resistance is \(R_L= 4\,k\Omega .\) The series resistance of the circuit is \(R_i = 1\,k\Omega .\) If the battery voltage \(V_B\) varies from \(8\,V\) to \(16\,V,\) what are the minimum and maximum values of the current through Zener diode?

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

An ice cube of dimensions \(60\,cm \times 50\,cm \times 20\,cm\) is placed in an insulation box of wall thickness \(1\,cm\). The box keeping the ice cube at \(0^{\circ}\,C\) of temperature is brought to a room of temperature \(40^{\circ}\,C\). The rate of melting of ice is approximately. (Latent heat of fusion of ice is \(3.4 \times 10^{5}\,J\,kg ^{-1}\) and thermal conducting of insulation wall is \(0.05\,Wm ^{-10} C ^{-1}\) )