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:
1. \(\frac{3(K_1+K_2)}{2}\)
2. \(K_1+K_2\)
3. \(2(K_1+K_2)\)
4. \(\frac{(K_1+K_2)}{2}\)
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:
1. | \(2\) | decreases by a factor of
2. | remains the same |
3. | \(2\) | increases by a factor of
4. | \(4\) | increases by a factor of
In a common-emitter transistor amplifier, the audio signal voltage across the collector is 3V. The resistance of the collector is 3k. If the current gain is 100 and the base resistance is 2k, 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:
Column-I | Column-II | ||
P. | Process I | a. | Adiabatic |
Q. | Process II | b. | Isobaric |
R. | Process III | c. | Isochoric |
S. | Process IV | d. | Isothermal |
P | Q | R | S | |
1. | c | a | d | b |
2. | c | d | b | a |
3. | d | b | a | c |
4. | a | c | d | b |
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 \(m_h = 1.67\times 10^{-27}~\text{kg}\))
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:
1. \(\mathrm{OR}\) gate
2. \(\mathrm{NOR}\) gate
3. \(\mathrm{NOT}\) gate
4. \(\mathrm{AND}\) gate
Which one of the following represents the forward bias diode?
1. | |
2. | |
3. | |
4. |
A long solenoid of diameter \(0.1\) m has \(2 \times 10^4\) turns per meter. At the center of the solenoid, a coil of \(100\) turns and radius \(0.01\) m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to \(0\) A from \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\) then the total charge flowing through the coil during this time is:
1. \(16~\mu \text{C}\)
2. \(32~\mu \text{C}\)
3. \(16\pi~\mu \text{C}\)
4. \(32\pi~\mu \text{C}\)
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1\). On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk upon the moving escalator will be:
1. \(\frac{t_1t_2}{t_2-t_1}\)
2. \(\frac{t_1t_2}{t_2+t_1}\)
3. \(t_1-t_2\)
4. \(\frac{t_1+t_2}{2}\)