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Q. No.Match the LIST-I with LIST-II
Choose the correct answer from the options given below:
1. \(\mathrm{A\text-III, B\text-IV, C\text-I, D\text-II}\)
2. \(\mathrm{A\text-I, B\text-II, C\text-III, D\text-IV}\)
3. \(\mathrm{A\text-IV, B\text-III, C\text-I, D\text-II}\)
4. \(\mathrm{A\text-I, B\text-IV, C\text-III, D\text-II}\)
| List- I | List-II | ||
| \(\mathrm{(A)}\) | Planck's constant | \(\mathrm{(I)}\) | \([M L^2T^2]\) |
| \(\mathrm{(B)}\) | Stopping potential | \(\mathrm{(II)}\) | \([T^{-1}]\) |
| \(\mathrm{(C)}\) | Work function | \(\mathrm{(III)}\) | \([M L^2T^{-1}]\) |
| \(\mathrm{(D)}\) | Threshold frequency | \(\mathrm{(IV)}\) | \([M L^2 T^{-3}A^{-1}]\) |
1. \(\mathrm{A\text-III, B\text-IV, C\text-I, D\text-II}\)
2. \(\mathrm{A\text-I, B\text-II, C\text-III, D\text-IV}\)
3. \(\mathrm{A\text-IV, B\text-III, C\text-I, D\text-II}\)
4. \(\mathrm{A\text-I, B\text-IV, C\text-III, D\text-II}\)
Subtopic: Dimensions |
81%
Level 1: 80%+
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A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field \(\overrightarrow{{E}}_1={E}_0 \hat{x} .\) If another electric field \(\overrightarrow{{E}}_2=2 {E}_0(\hat{y}+\hat{z})\) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?
1. \(73\%\)
2. \(63\%\)
3. \(83\%\)
4. \(53\%\)
1. \(73\%\)
2. \(63\%\)
3. \(83\%\)
4. \(53\%\)
Subtopic: Errors |
59%
Level 3: 35%-60%
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Dimensions of universal gravitional constant \((G)\) in terms of Planck's constant \((h)\), distance \((L)\), mass \((M)\) and time \((T)\) are:
1. \([hTLM^{-2}]\)
2. \([hT^{-1}LM^{-2}]\)
3. \([hTL^{2}M^{-2}]\)
4. \([h^{-1}T^{-1}LM^{-2}]\)
1. \([hTLM^{-2}]\)
2. \([hT^{-1}LM^{-2}]\)
3. \([hTL^{2}M^{-2}]\)
4. \([h^{-1}T^{-1}LM^{-2}]\)
Subtopic: Dimensions |
87%
Level 1: 80%+
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In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \(100\) divisions in circular scale and pitch of screw gauge is \(0.1~\text{mm}.\) When diameter of a sphere is measured, the reading of main scale is \(5~\text{mm}\) and \(50^\text{th}\) division of circular scale coincides with the reference line of main scale. The diameter of sphere is: (in mm)
1. \(5.045\)
2. \(5.055\)
3. \(5.450\)
4. \(5.550\)
1. \(5.045\)
2. \(5.055\)
3. \(5.450\)
4. \(5.550\)
Subtopic: Measurement & Measuring Devices |
71%
Level 2: 60%+
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The percentage error in the calculated volume of a sphere, if there is \(2\%\) error in its diameter measurement, is:
1. \(1\)
2. \(2\)
3. \(6\)
4. \(8\)
1. \(1\)
2. \(2\)
3. \(6\)
4. \(8\)
Subtopic: Errors |
90%
Level 1: 80%+
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Match List-I with List-II.
Choose the correct answer from the option given below:
| List-I | List-II | ||
| \(\mathrm{A.}\) | Boltzmann constant | \(\mathrm{I.}\) | \({\left[{M}^{-1} {~L}^3 {~T}^{-2}\right]}\) |
| \(\mathrm{B.}\) | Stefan's constant | \(\mathrm{II.}\) | \({\left[{M} {~L}^2 {~T}^{-1}\right]} \) |
| \(\mathrm{C.}\) | Planck's constant | \(\mathrm{III.}\) | \({\left[{M} {~L}^2 {~T}^{-2} {~K}^{-1}\right]}\) |
| \(\mathrm{D.}\) | Gravitational constant | \(\mathrm{IV.}\) | \( {\left[{M} {~L}^0 {~T}^{-3} {~K}^{-4}\right]}\) |
| 1. | \(\mathrm{A\text-I, B\text-II, C\text-III, D\text-IV} \) |
| 2. | \(\mathrm{A\text-IV, B\text-III, C\text-II, D\text-I} \) |
| 3. | \(\mathrm{A\text-III, B\text-IV, C\text-II, D\text-I} \) |
| 4. | \(\mathrm{A\text-II, B\text-I, C\text-IV, D\text-III}\) |
Subtopic: Dimensions |
91%
Level 1: 80%+
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The density \(\rho\) of a uniform cylinder is determined by measuring its mass \(m,\) length \(l\) and diameter \(d.\) The measured values of \(m,l\) and \(d\) are \(97.42 \pm 0.02 ~\text{g},\) \(8.35 \pm 0.05 ~\text{mm} \text { and } 20.20 \pm 0.02 ~\text{mm} \text {,}\) respectively. Calculated percentage fractional error in \(\rho\) is:
1. \(0.63\%\)
2. \(0.82\%\)
3. \(0.72\%\)
4. \(0.25\%\)
1. \(0.63\%\)
2. \(0.82\%\)
3. \(0.72\%\)
4. \(0.25\%\)
Subtopic: Errors |
62%
Level 2: 60%+
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The potential energy of a particle changes with distance \(x\) from a fixed origin as \(V=\dfrac{A \sqrt{x}}{x+B},\) where \(A\) and \(B\) are constant with appropriate dimensions. The dimensions of \(AB\) are:
1. \({\left[{M}^1{~L}^{5 / 2}{~T}^{-2}\right]} \)
2. \({\left[{M}^{3 / 2}{~L}^{5 / 2} {~T}^{-2}\right]}\)
3. \({\left[{M}^1{~L}^2 {~T}^{-2}\right]}\)
4. \({\left[{M}^1 {~L}^{7 / 2} {~T}^{-2}\right]}\)
1. \({\left[{M}^1{~L}^{5 / 2}{~T}^{-2}\right]} \)
2. \({\left[{M}^{3 / 2}{~L}^{5 / 2} {~T}^{-2}\right]}\)
3. \({\left[{M}^1{~L}^2 {~T}^{-2}\right]}\)
4. \({\left[{M}^1 {~L}^{7 / 2} {~T}^{-2}\right]}\)
Subtopic: Dimensions |
74%
Level 2: 60%+
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The dimensional formula of \(\dfrac{1}{2}\varepsilon_0 E^2\) (\(\varepsilon_0\)=permittivity of vacuum and \(E\)=electric field) is \({M}^{a} {~L}^{{b}} {~T}^{{c}} .\) The value of \(2a-b+c\) is:
1. \(0\)
2. \(1\)
3. \(-1\)
4. \(2\)
1. \(0\)
2. \(1\)
3. \(-1\)
4. \(2\)
Subtopic: Dimensions |
91%
Level 1: 80%+
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In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \(7^{\text{th}}\) Vernier division coincides with a main scale reading. If the value of \(1\) main scale division is \(1\) mm and there are \(10\) Vernier scale divisions, then the Vernier caliper has:
1. \(0.07\) cm negative zero error
2. \(0.7\) cm negative zero error
3. \(0.07\) cm positive zero error
4. \(0.7\) cm positive zero error
1. \(0.07\) cm negative zero error
2. \(0.7\) cm negative zero error
3. \(0.07\) cm positive zero error
4. \(0.7\) cm positive zero error
Subtopic: Measurement & Measuring Devices |
83%
Level 1: 80%+
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