A spring of force constant \(k\) is cut into lengths of ratio \(1:2:3\). They are connected in series and the new force constant is \(k'\). Then they are connected in parallel and the force constant is \(k''\). Then \(k':k''\) is:
1.
\(1:9\)
2.
\(1:11\)
3.
\(1:14\)
4.
\(1:6\)
The ratio of resolving powers of an optical microscope for two wavelengths =4000 and is:
1. 9:4
2. 3:2
3. 16:81
4. 8:27
The two nearest harmonics of a tube closed at one end and open at the other end are \(220\) Hz and \(260\) Hz. What is the fundamental frequency of the system?
| 1. | \(20\) Hz | 2. | \(30\) Hz |
| 3. | \(40\) Hz | 4. | \(10\) Hz |
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 \(c, G,~\text{and}~\dfrac{e^2}{4\pi\varepsilon_0}\)is:
(\(c\) is the velocity of light, \(G\) is the universal constant of gravitation and \(e\) is charge)
| 1. | \(c^2\left[G \dfrac{e^2}{4 \pi \varepsilon_0}\right]^{\dfrac{1}{2}}\) | 2. | \(\dfrac{1}{c^2}\left[\dfrac{e^2}{4 G \pi \varepsilon_0}\right]^{\dfrac{1}{2}}\) |
| 3. | \(\dfrac{1}{c} G \dfrac{e^2}{4 \pi \varepsilon_0}\) | 4. | \(\dfrac{1}{c^2}\left[G \dfrac{e^2}{4 \pi \varepsilon_0}\right]^{\dfrac{1}{2}}\) |
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:
| 1. | \(\dfrac{3(K_1+K_2)}{2}\) | 2. | \(K_1+K_2\) |
| 3. | \(2(K_1+K_2)\) | 4. | \(\dfrac{(K_1+K_2)}{2}\) |
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. | decreases by a factor of \(2\) |
| 2. | remains the same |
| 3. | increases by a factor of \(2\) |
| 4. | increases by a factor of \(4\) |
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 | ||
| \(\mathrm{(P)}\) | Process I | \(\mathrm{(a)}\) | Adiabatic |
| \(\mathrm{(Q)}\) | Process II | \(\mathrm{(b)}\) | Isobaric |
| \(\mathrm{(R)}\) | Process III | \(\mathrm{(c)}\) | Isochoric |
| \(\mathrm{(S)}\) | Process IV | \(\mathrm{(d)}\) | Isothermal |
| 1. | \(\mathrm{P → c, Q → a, R → d, S→ b}\) |
| 2. | \(\mathrm{P→ c, Q → d, R → b, S → a}\) |
| 3. | \(\mathrm{P → d, Q → b, R → b, S → c}\) |
| 4. | \(\mathrm{P → a, Q → c, R → d, S → b}\) |
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 the 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. \(10^{-20}~\text{C}\)
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