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 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. |
When a particle with charge \(+q\) is thrown with an initial velocity \(v\) towards another stationary change \(+Q,\) it is repelled back after reaching the nearest distance \(r\) from \(+Q.\) The closest distance that it can reach if it is thrown with an initial velocity \(2v,\) is:
| 1. | \(\dfrac{r}{4}\) | 2. | \(\dfrac{r}{2}\) |
| 3. | \(\dfrac{r}{16}\) | 4. | \(\dfrac{r}{8}\) |
The determination of the value of acceleration due to gravity \((g)\) by simple pendulum method employs the formula,
\(g=4\pi^2\frac{L}{T^2}\)
The expression for the relative error in the value of \(g\) is:
| 1. | \(\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\Big(\frac{\Delta T}{T}\Big)\) | 2. | \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}-2\frac{\Delta T}{T}\Big]\) |
| 3. | \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}+2\frac{\Delta T}{T}\Big]\) | 4. | \(\frac{\Delta g}{g}=\frac{\Delta L}{L}-2\Big(\frac{\Delta T}{T}\Big)\) |
A monochromatic light of frequency \(500\) THz is incident on the slits of a Young's double slit experiment. If the distance between the slits is \(0.2\) mm and the screen is placed at a distance \(1\) m from the slits, the width of \(10\) fringes will be:
1. \(1.5\) mm
2. \(15\) mm
3. \(30\) mm
4. \(3\) mm
In a meter bridge experiment, the null point is at a distance of \(30~\text{cm}\) from \(\mathrm{A}\). If a resistance of \(16~\Omega\) is connected in parallel with resistance \(Y\), the null point occurs at \(50~\text{cm}\) from \(\mathrm{A}\). The value of the resistance \(Y\) is:
| 1. | \(\dfrac{112}{3}~\Omega\) | 2. | \(\dfrac{40}{3}~\Omega\) |
| 3. | \(\dfrac{64}{3}~\Omega\) | 4. | \(\dfrac{48}{3}~\Omega\) |
The temperature at which the rms speed of atoms in neon gas is equal to the rms speed of hydrogen molecules at \(15^{\circ} \mathrm{C}\) is: (Atomic mass of neon \(=20.2\) u, molecular mass of hydrogen \(=2\) u)
| 1. | \(2.9\times10^{3}\) K | 2. | \(2.9\) K |
| 3. | \(0.15\times10^{3}\) K | 4. | \(0.29\times10^{3}\) K |
Two planets are in a circular orbit of radius \(R\) and \(4R\) about a star. At a specific time, the two planets and the star are in a straight line. If the period of the closest planet is \(T,\) then the star and planets will again be in a straight line after a minimum time:
2. \((4)^{\frac13}T\)
3. \(2T\)
4. \(8T\)
The correct order for boiling points of the following compounds is:
| 1. | AsH3 > PH3 > NH3 > SbH3 > BiH3 |
| 2. | BiH3 > SbH3 > NH3 > AsH3 > PH3 |
| 3. | NH3 > PH3 > AsH3 > SbH3 > BiH3 |
| 4. | PH3 > NH3 > AsH3 > SbH3 > BiH3 |
Match List-I with List-II:
| List-I | List-II | ||
| (a) | 4.48 litres of O2 at STP | (i) | 0.2 moles |
| (b) | 12.022 × 1022 molecules of H2O | (ii) | 12.044 × 1023 molecules |
| (c) | 96 g of O2 | (iii) | 6.4 g |
| (d) | 88 g of CO2 | (iv) | 67.2 litres at STP |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (i) | (iii) | (iv) | (ii) |
| 2. | (iii) | (i) | (iv) | (ii) |
| 3. | (iv) | (i) | (ii) | (iii) |
| 4. | (iii) | (i) | (ii) | (iv) |
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