When a ruler falls vertically, \(5\) different persons catch it with different reaction times. (\(g = 9.8 \text{ m s}^{-2}\))
What is the correct order of the distance travelled by the ruler for each person?
1. \(B>E>A>C>D~\)
2. \(C>D>A>E>B~\)
3. \(C>D>A>B>E~\)
4. \(B>E>A>D>C~\)
| A. | Person \(A\) has reaction time of \(0.20\) s. |
| B. | Person \(B\) has reaction time of \(0.22\) s. |
| C. | Person \(C\) has reaction time of \(0.18\) s. |
| D. | Person \(D\) has reaction time of \(0.19\) s. |
| E. | Person \(E\) has reaction time of \(0.21\) s. |
What is the correct order of the distance travelled by the ruler for each person?
1. \(B>E>A>C>D~\)
2. \(C>D>A>E>B~\)
3. \(C>D>A>B>E~\)
4. \(B>E>A>D>C~\)
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The power of a crane, which lifts a mass of \(1000\) kg to a height of \(20\) m in \(10\) s is: (\(g=9.8~\) m/s2)
1. \(19.6\) kW
2. \(19.6\) W
3. \(39.2\) kW
4. \(39.2\) W
1. \(19.6\) kW
2. \(19.6\) W
3. \(39.2\) kW
4. \(39.2\) W
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Consider two uncharged capacitors of equal capacitance \(200~\text{pF}.\) One of them is charged by a \(100~\text{V}\) supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of electrostatic energy lost in the process is:
1. \(0.5~\text{J}~\)
2. \(1.0\times 10^{-6}~\text{J}\)
3. \(0.5\times 10^{-6}~\text{J}\)
4. \(1.0~\text{J}~\)
1. \(0.5~\text{J}~\)
2. \(1.0\times 10^{-6}~\text{J}\)
3. \(0.5\times 10^{-6}~\text{J}\)
4. \(1.0~\text{J}~\)
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An AC circuit contains a resistance of \(1~\text{k}\Omega,\) a capacitor of \(0.1~\mu \text{F}\) and an inductor of \(1~\text{mH}\) connected in series. The resonance frequency of the circuit is approximately the following:
1. \(15.9\) kHz
2. \(20.7\) kHz
3. \(10.1\) kHz
4. \(13.5\) kHz
1. \(15.9\) kHz
2. \(20.7\) kHz
3. \(10.1\) kHz
4. \(13.5\) kHz
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The figure given below shows a long, straight, solid wire of circular cross-section of radius \(a\) carrying a steady current \(I.\) The current \(I\) is uniformly distributed across its cross-section. The plot which correctly represents the variation of the magnetic field \((B)\) with distance \((r)\) from the axis of the conductor in the region is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Level 4: Below 35%
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An electric heater supplies heat to a system at a rate of \(100\) W. If the system performs work at a rate of \(75\) J/s, then the rate at which internal energy increases will be:
1. \(75~\text{W}~\)
2. \(25~\text{W}\)
3. \(100~\text{W}\)
4. \(125~\text{W}\)
1. \(75~\text{W}~\)
2. \(25~\text{W}\)
3. \(100~\text{W}\)
4. \(125~\text{W}\)
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The peak value of an alternating current is \(5\) A and frequency is \(60\) Hz. How long will the current, starting from zero, take to reach the peak value?
1. \(\dfrac{1}{120} ~\text{s}\)
2. \(\dfrac{1}{240} ~\text{s}\)
3. \(\dfrac{1}{30}~\text{s}\)
4. \(\dfrac{1}{60} ~\text{s}~\)
1. \(\dfrac{1}{120} ~\text{s}\)
2. \(\dfrac{1}{240} ~\text{s}\)
3. \(\dfrac{1}{30}~\text{s}\)
4. \(\dfrac{1}{60} ~\text{s}~\)
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In Young's double-slit experiment, using monochromatic light of wavelength \(\lambda,\) the intensity of light at a point on the screen where the path difference is \(\lambda,\) is \(K\) units. The intensity of light at a point where the path difference is \(\dfrac{\lambda}{3}\) will be:
1. \(K\)
2. \(2K\)
3. \(\dfrac{K}{2}\)
4. \(\dfrac{K}{4}\)
1. \(K\)
2. \(2K\)
3. \(\dfrac{K}{2}\)
4. \(\dfrac{K}{4}\)
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Four statements are given (\(A\) is mass numbers):
Choose the correct answer from the options given below.
| \((\mathrm{A})\) | The volume of a nucleus is proportional to \(A^{1/3}.\) |
| \((\mathrm{B})\) | The volume of a nucleus is proportional to \(A.\) |
| \((\mathrm{C})\) | The difference in mass of an atom and its nucleus is called the mass defect. |
| \((\mathrm{D})\) | The difference in mass of a nucleus and its constituents is called the mass defect. |
| 1. | \((\mathrm{A})\) and \((\mathrm{D})\) are True, but \((\mathrm{B})\) and \((\mathrm{C})\) are False |
| 2. | \((\mathrm{B})\) and \((\mathrm{D})\) are True but \((\mathrm{A})\) and \((\mathrm{C})\) are False |
| 3. | \((\mathrm{B})\) and \((\mathrm{C})\) are True but \((\mathrm{A})\) and \((\mathrm{D})\) are False |
| 4. | \((\mathrm{A})\) and \((\mathrm{C})\) are True, but \((\mathrm{B})\) and \((\mathrm{D})\) are False |
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In interference and diffraction, the light energy is redistributed. It reduces in one region, producing a dark fringe; it increases in another region, producing a bright fringe.
Choose the correct answer from the options given below:
| \((\mathrm{A})~\) | As there is no gain or loss of energy, these phenomena are consistent with the principle of conservation of energy. |
| \((\mathrm{B})~\) | Diffraction and interference are characteristics exhibited only by light waves. |
| 1. | \((\mathrm{A})\) is False, but \((\mathrm{B})\) is True |
| 2. | \((\mathrm{A})\) is True, but \((\mathrm{B})\) is False |
| 3. | \((\mathrm{A})\) is True and \((\mathrm{B})\) is also True |
| 4. | Both \((\mathrm{A})\) and \((\mathrm{B})\) are False |
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