Three capacitors, each of capacitance \(0.3~\mu \text{F}\) are connected in parallel. This combination is connected with another capacitor of capacitance \(0.1~\mu \text{F}\) in series. Then the equivalent capacitance of the combination is:
1.
\(0.9~\mu\text{F}\)
2.
\(0.09~\mu\text{F}\)
3.
\(0.1~\mu\text{F}\)
4.
\(0.01~\mu\text{F}\)
A string of length \(l\) is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is \(2\) mm. The amplitude of a particle at a distance \(l/8\) from the fixed end is:
| 1. | \(2\sqrt2~\text{mm}\) | 2. | \(4~\text{mm}\) |
| 3. | \(\sqrt2~\text{mm}\) | 4. | \(2\sqrt3~\text{mm}\) |
The circuit represents a full wave bridge rectifier when switch \(S\) is open. The output voltage \((V_0)\) pattern across \(R_L\) when \(S\) is closed:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
| Assertion (A): | Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero. |
| Reason (R): | The magnetic monopoles do not exist. North and South poles occur in pairs, allowing vanishing net magnetic flux through the surface. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
An AC source given by \(V=V_m\sin(\omega t)\) is connected to a pure inductor \(L\) in a circuit and \(I_m\) is the peak value of the AC current. The instantaneous power supplied to the inductor is:
| 1. | \(\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\) | 2. | \(-\dfrac{V_mI_m}{2}\mathrm{sin}(2\omega t)\) |
| 3. | \({V_mI_m}\mathrm{sin}^{2}(\omega t)\) | 4. | \(-{V_mI_m}\mathrm{sin}^{2}(\omega t)\) |
The fraction of the original number of radioactive atoms that disintegrates (decays) during the average lifetime of a radioactive substance will be:
1. \(\frac{1}{e}\)
2. \(\frac{1}{1+e}\)
3. \(\frac{e-1}{e+1}\)
4. \(\frac{e-1}{e}\)
The figure given below shows the displacement and time, \((x\text -t)\) graph of a particle moving along a straight line:
The correct statement, about the motion of the particle, is:
| 1. | the particle moves at a constant velocity up to a time \(t_0\) and then stops. |
| 2. | the particle is accelerated throughout its motion. |
| 3. | the particle is accelerated continuously for time \(t_0\) then moves with constant velocity. |
| 4. | the particle is at rest. |
Air is pushed carefully into a soap bubble of radius \(r\) to double its radius. If the surface tension of the soap solution is \(T,\) then the work done in the process is:
| 1. | \(12\pi r^2T\) | 2. | \(24\pi r^2T \) |
| 3. | \(4\pi r^2T\) | 4. | \(8\pi r^2T\) |
| Statement I: | The magnetic field of a circular loop at very far away point on the axial line varies with distance as like that of a magnetic dipole. |
| Statement II: | The magnetic field due to magnetic dipole varies inversely with the square of the distance from the centre on the axial line. |
| 1. | Statement I is correct and Statement II is incorrect. |
| 2. | Statement I is incorrect and Statement II is correct. |
| 3. | Both Statement I and Statement II are correct. |
| 4. | Both Statement I and Statement II are incorrect. |
A positively charged particle \(+q\) is projected with speed \(v\) toward a fixed charge \(+Q,\) and rebounds after reaching a minimum distance \(r.\) What will be the new closest distance of approach if its initial velocity is doubled to \(2v\text{?}\)
| 1. | \(\dfrac{r}{4}\) | 2. | \(\dfrac{r}{2}\) |
| 3. | \(\dfrac{r}{16}\) | 4. | \(\dfrac{r}{8}\) |
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