A certain quantity of water cools from \(70~^{\circ}\text{C}\) to \(60~^{\circ}\text{C}\) in the first \(5\) minutes and to \(54~^{\circ}\text{C}\) in the next \(5\) minutes. The temperature of the surroundings is:
1. \(45~^{\circ}\text{C}\)
2. \(20~^{\circ}\text{C}\)
3. \(42~^{\circ}\text{C}\)
4. \(10~^{\circ}\text{C}\)
| 1. | \(64P\) | 2. | \(32P\) |
| 3. | \(\frac{P}{64}\) | 4. | \(16P\) |
A thermodynamic system undergoes a cyclic process \(ABCDA\) as shown in Fig. The work done by the system in the cycle is:
| 1. | \( P_0 V_0 \) | 2. | \( 2 P_0 V_0 \) |
| 3. | \(\dfrac{P_0 V_0}{2} \) | 4. | zero |
The mean free path of molecules of a gas (radius \(r\)) is inversely proportional to:
| 1. | \(r^3\) | 2. | \(r^2\) |
| 3. | \(r\) | 4. | \(\sqrt{r}\) |
If \(n_1\), \(n_2\), and \(n_3\) are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency \(n\) of the string is given by:
| 1. | \( \frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}\) |
| 2. | \( \frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}\) |
| 3. | \( \sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}\) |
| 4. | \( n=n_1+n_2+n_3\) |
The number of possible natural oscillations of the air column in a pipe closed at one end of length \(85\) cm whose frequencies lie below \(1250\) Hz are:
(velocity of sound= \(340~\text{m/s}\)
| 1. | \(4\) | 2. | \(5\) |
| 3. | \(7\) | 4. | \(6\) |
A speeding motorcyclist sees a traffic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the honk as heard by him will be:
1. 1332 Hz
2. 1372 Hz
3. 1412 Hz
4. 1454 Hz
Two thin dielectric slabs of dielectric constants \(K_1\) and \(K_2\) \((K_1<K_2)\) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field \('E'\) between the plates with distance \('d'\) as measured from the plate \(P\) is correctly shown by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A conducting sphere of the radius \(R\) is given a charge \(Q.\) The electric potential and the electric field at the centre of the sphere respectively are:
| 1. | zero and \(\frac{Q}{4 \pi \varepsilon_0 {R}^2}\) | 2. | \(\frac{Q}{4 \pi \varepsilon_0 R}\) and zero |
| 3. | \(\frac{Q}{4 \pi \varepsilon_0 R}\) and \(\frac{Q}{4 \pi \varepsilon_0{R}^2}\) | 4. | both are zero |
| 1. | \(6\sqrt{5}~\text{N}\) | 2. | \(30~\text{N}\) |
| 3. | \(24~\text{N}\) | 4. | \(4\sqrt{35}~\text{N}\) |
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