A series \(LCR\) circuit is designed to resonate at an angular frequency \(\omega_{0}=10^{5} \,rad / s\). The circuit draws \(16\, W\) power from \(120\, V\) source at resonance. The value of resistance \('R'\) in the circuit is ...... \(\Omega\).

Match the LIST-I with LIST-II.

LIST-I	LIST-II
(A) \(_0^1n + _{92}^{235}U \rightarrow _{54}^{140}Xe + _{38}^{94}Sr + 2_0^1n\)	(I) Chemical reaction
(B) \(2H_2 + O_2 \rightarrow 2H_2O\)	(II) Fusion with +ve Q value
(C) \(_1^2H + _1^2H \rightarrow _2^3He + _0^1n\)	(III) Fission
(D) \(_1^1H + _1^3H \rightarrow _1^2H + _1^2H\)	(IV) Fusion with -ve Q value

Choose the correct answer from the options given below :

A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration \(a_{0}.\) The angle between the inclined plane and ground is \(\theta\) and its base length is L. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is ___________.

Match List \(− I\) (Event) with List \(−II \) (Order of the time interval for happening of the event) and select the correct option from the options given below the lists

List \(- I\)	List \(- II\)
\((1)\) Rotation period of earth	\((i)\) \(10^5\, s\)
\((2)\) Revolution period of earth	\((ii)\) \(10^7\, s\)
\((3)\) Period of light wave	\((iii)\) \(10^{-15}\, s\)
\((4)\) Period of sound wave	\((iv)\) \(10^{-3}\, s\)

Figure shows a circuit that contains four identical resistors with resistance \(R =2.0\, \Omega,\) two identical inductors with inductance \(L =2.0 \,mH\) and an ideal battery with \(e m f E =9 \,V .\) The current \('i'\) just after the switch \('S'\) is closed will be .... \(A\)

A steam engine intakes \(50\, g\) of steam at \(100^{\circ} C\) per minute and cools it down to \(20^{\circ} C\). If latent heat of vaporization of steam is \(540 \,cal g ^{-1}\), then the heat rejected by the steam engine per minute is .........\(\times 10^{3}\)\(cal.\)

The threshold frequency of a metal with work function \(6.63\  \mathrm{eV}\) is:

There are \(100\) divisions on the circular scale of a screw gauge of pitch \(1 \mathrm{~mm}\). With no measuring quantity in between the jaws, the zero of the circular scale lies \(5\) divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the \(4\) linear scale divisions are clearly visible while \(60\) divisions on circular scale coincide with the reference line. The diameter of the wire is _______.

Two cells of emf \(2\, E\) and \(E\) with internal resistance \(r _{1}\) and \(r _{2}\) respectively are connected in series to an external resistor \(R\) (see \(figure\)). The value of \(R ,\) at which the potential difference across the terminals of the first cell becomes zero is

The following logic gate is equivalent to

The typical transfer characteristic of a transistor in \(CE\) configuration is shown in figure. A load resistor of \(2\,k\Omega\) is connected in the collector branch of the circuit used. The input resistance of the transistor is \(0.50\,k \Omega\). The voltage gain of the transistor is.

A bar magnet of length \(14 \,cm\) is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of \(18\, cm\) from the center of the magnet. If \(B _{ H }=0.4 \,G ,\) the magnetic moment of the magnet is \(\left(1\, G =10^{-4} T \right)\)