AIEEE 2013 PYQ Mock Test

In an LCR circuit as shown below both switches are open initially. Now switch $S_1$ is closed, $S_2$ kept open. ($q$ is charge on the capacitor and $\tau =RC$ is capacitive time constant). Which of the following statement is correct?

A diode detector is used to detect an amplitude modulated wave of $60\%$ modulation by using a condenser of capacity $250\text{pF}$ in parallel with a load resistance $100\text{k}\Omega$. Find the maximum modulated frequency which could be detected by it.

The supply voltage to a room is $120\text{V}$. The resistance of the lead wires is $6\Omega$. A $60\text{W}$ bulb is already switched on. What is the decrease of voltage across the bulb, when a $240\text{W}$ heater is switched on in parallel to the bulb?

A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is:

Two charges, each equal to $q$, are kept at $x=-a$ and $x=a$ on the $x$ -axis. A particle of mass $m$ and charge $q_0=\frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $y$ ($y\ll a$) along the $y$ -axis, the net force acting on the particle is proportional to: