Consider a drop of rainwater having a mass of \(1~\text{gm}\) falling from a height of \(1~\text{km}\). It hits the ground with a speed of \(50~\text{m/s}\). Take \(g\)  as constant with a value \(10~\text{m/s}^2.\) The work done by the
(i) gravitational force and the
(ii) resistive force of air is:

1.	\((\text{i})~1.25~\text{J};\) \((\text{ii})~-8.25~\text{J}\)
2.	\((\text{i})~100~\text{J};\) \((\text{ii})~8.75~\text{J}\)
3.	\((\text{i})~10~\text{J};\) \((\text{ii})~-8.75~\text{J}\)
4.	\((\text{i})~-10~\text{J};\) \((\text{ii})~-8.75~\text{J}\)

A physical quantity of the dimensions of length that can be formed out of \(c, G,~\text{and}~\frac{e^2}{4\pi\varepsilon_0}\)is [\(c\) is the velocity of light, \(G\) is the universal constant of gravitation and \(e\) is charge]:
\(1. ~c^2\left[G \frac{e^2}{4 \pi \varepsilon_0}\right]^{\frac{1}{2}}\\ 2.~ \frac{1}{c^2}\left[\frac{e^2}{4 G \pi \varepsilon_0}\right]^{\frac{1}{2}}\\ 3. ~\frac{1}{c} G \frac{e^2}{4 \pi \varepsilon_0}\\ 4. ~\frac{1}{c^2}\left[G \frac{e^2}{4 \pi \varepsilon_0}\right]^{\frac{1}{2}}\)

Two rods \(A\) and \(B\) of different materials are welded together as shown in the figure. Their thermal conductivities are \(K_1\) and \(K_2.\) The thermal conductivity of the composite rod will be:
            

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system:

In a common-emitter transistor amplifier, the audio signal voltage across the collector is 3V. The resistance of the collector is 3k$\Omega$. If the current gain is 100 and the base resistance is 2k$\Omega$, the voltage and power gain of the amplifier are:

1. 15 and 200

2. 150 and 15000

3. 20 and 2000

4. 200 and 1000

Thermodynamic processes are indicated in the following diagram: 
   
Match the following: 

Suppose the charge of a proton and an electron differ slightly. One of them is \(-e\), the other is (\(e+\Delta e\)). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance \(d\) (much greater than atomic size) apart is zero, then$$ \(\Delta e\) is of the order of? (Given mass of hydrogen ${\mathrm{}}_{}$\(m_h = 1.67\times 10^{-27}~\text{kg}\)$$)
1. \(10^{-23}~\text{C}\)
2. \(10^{-37}~\text{C}\)
3. \(10^{-47}~\text{C}\)
4. \(10^{-20}~\text{C}\)

The given electrical network is equivalent to:
   

Which one of the following represents the forward bias diode?

1.
2.
3.
4.