A \(LCR\) circuit behaves like a damped harmonic oscillator. Comparing it with a physical springmass damped oscillator having damping constant \(\mathrm{b}\), the correct equivalence would be:

An inclined plane making an angle of \(30^{\circ}\) with the horizontal is placed in a uniform horizontal electric field \(200 \, \frac{ N }{ C }\) as shown in the figure. A body of mass \(1\, kg\) and charge \(5\, mC\) is allowed to slide down from rest at a height of \(1\, m\). If the coefficient of friction is \(0.2,\) find the time (in \(s\) )taken by the body to reach the bottom. \(\left[ g =9.8 \,m / s ^{2}, \sin 30^{\circ}=\frac{1}{2}\right.\); \(\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]\)

Figure shown a \(DC\) voltage regulator circuit, with a Zener diode of breakdown voltage \(= 6\,V\). If the unregulated input voltage varies between \(10\, V\) to \(16\, V\), then what is the maximum Zener current ?.......\(mA\)

In case of vertical circular motion of a particle by a thread of length \(r\) if the tension in the thread is zero at an angle \(30^{\circ}\) shown in figure, the velocity at the bottom point (A) of the circular path is ( \(g =\) gravitational acceleration)

A telescope has an objective lens of focal length \(150\,\,cm\) and an eyepiece of focal length \(5 \,\,cm.\) If a \(50\,\,m\) tall tower at a distance of \(1\,\,km\) is observed through this telescope in normal setting, the angle formed by the image of the tower is \(\theta \), then \(\theta \) is close to.....\(^o\)

A wheel is rotaing freely with an angular speed \(\omega\) on a shaft. The moment of inertia of the wheel is \(I\) and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia \(3I\) initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

Three identical resistors with resistance \(R=12 \Omega\) and two identical inductors with sell inductance \(L=5 mH\) are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _________ A.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below :

From the given transfer characteristic of a transistor in \(CE\) configuration, the value of power gain of this configuration is \(10^{ x }\), for \(R_B=10\,k \Omega\), and \(R _C=1\,k \Omega\). The value of \(x\) is \(.....\).

In photoelectric experiment energy of \(2.48 \mathrm{eV}\) irradiates a photo sensitive material. The stopping potential was measured to be \(0.5 \mathrm{~V}\). Work function of the photo sensitive material is _______.

Diameter of a plano-convex lens is \(6 \,cm\) and thickness at the centre is \(3\, mm\). If the speed of light in the material of the lens is \(2  \times  10^8 m/sec\), the focal length of the lens is.......\(cm\)