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Q. No.Which of the quantities below have the same dimensions?
(A)
\(\dfrac{\text{electric field }\times\text{ magnetic field}}{\mu_0}\)
(B)
\(\dfrac{\varepsilon_0\times\text{(electric potential)}^2\times\text{ velocity}}{\text{area}}\)
(C)
\(\dfrac{\text{power}}{\text{area}}\)
1. A, B
2. B, C
3. A, C
4. A, B, C
Subtopic: Dimensions |
Level 3: 35%-60%
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Match the units mentioned in List-I with the units in List-II.
| List-I | List-II | ||
| (a) | H/s | (i) | s2 |
| (b) | H×A | (ii) | Wb |
| (c) | H×F | (iii) | s |
| (d) | \(\Omega\)×F | (iv) | \(\Omega\) |
| 1. | (a)–(ii), (b)–(iv), (c)–(i), (d)–(iii) |
| 2. | (a)–(iv), (b)–(ii), (c)–(i), (d)–(iii) |
| 3. | (a)–(iv), (b)–(ii), (c)–(iii), (d)–(i) |
| 4. | (a)–(ii), (b)–(iii), (c)–(iv), (d)–(i) |
Subtopic: Dimensions |
62%
Level 2: 60%+
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Match the following quantities in List-I with their dimensions in List-II.
| List-I | List-II | ||
| (a) | acceleration | (i) | \([M^0L^0T^0 ]\) |
| (b) | torque | (ii) | \([ML^{-1}T^{-2} ]\) |
| (c) | absorptive power | (iii) | \([LT^{-2} ]\) |
| (d) | pressure | (iv) | \([ML^2T^{-2} ]\) |
| 1. | (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) |
| 2. | (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv) |
| 3. | (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv) |
| 4. | (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i) |
Subtopic: Dimensions |
86%
Level 1: 80%+
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Match the units of some physical quantities in List-I with their corresponding dimensions in List-II.
| List-I | List-II | ||
| (a) | Ohm | (i) | \([ML^2T^{-2}A^{-1}]\) |
| (b) | Farad | (ii) | \([ML^2T^{-2}A^{-2}]\) |
| (c) | Henry | (iii) | \([M^{-1}L^{-2}T^4A^2]\) |
| (d) | Weber | (iv) | \([ML^2T^{-3}A^{-2}]\) |
| 1. | (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) |
| 2. | (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii) |
| 3. | (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv) |
| 4. | (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) |
Subtopic: Dimensions |
63%
Level 2: 60%+
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Which of the following quantities have the same dimension?
1. B, C
2. A, B, C
3. B, D
4. A, B, C, D
| (A) | \(\dfrac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}\) | (B) | \(\text{Torque}\times\text{time}\) |
| (C) | \(\text{Momentum}\times\text{length}\) | (D) | \(\dfrac{\text{Power}}{\text{time}}\) |
2. A, B, C
3. B, D
4. A, B, C, D
Subtopic: Dimensions |
Level 3: 35%-60%
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Which of the following equations is dimensionally correct?
\((I)~~ v=\sqrt{\dfrac{P}{\rho}}~~~~~~(II)~~v=\sqrt{\dfrac{mgl}{I}}~~~~~~(III)~~v=\dfrac{Pr^2}{2\eta l}\)
(where \(v=\) speed, \(P=\) pressure; \(r,\) \(l\) are lengths; \(\rho=\) density, \(m=\) mass, \(g=\) acceleration due to gravity, \(I=\) moment of inertia, and \(\eta=\) coefficient of viscosity)
| 1. | \(I~ \text{and}~II\) |
| 2. | \(I~ \text{and}~III\) |
| 3. | \(II~ \text{and}~III\) |
| 4. | \(I,~II~\text{and}~III\) |
Subtopic: Dimensions |
63%
Level 2: 60%+
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Match List-I with List-II.
Choose from the given option from the given ones;
| List-I | List-II | ||
| (a) | \({h} \) (Planck's constant) | (i) | \([MLT^{-1}]\) |
| (b) | \({E} \) (kinetic energy) | (ii) | \([ML^2T^{-1}]\) |
| (c) | \(V\) (electric potential) | (iii) | \([ML^2T^{-2}]\) |
| (d) | \(p\) (linear momentum) | (iv) | \([ML^2A^{-1}T^{-3}]\) |
Choose from the given option from the given ones;
| 1. | (a) → (iii), (b) → (iv), (c) → (ii), (d) → (i) |
| 2. | (a) → (ii), (b) → (iii), (c) → (iv), (d) → (i) |
| 3. | (a) → (i), (b) → (ii), (c) → (iv), (d) → (iii) |
| 4. | (a) → (iii), (b) → (ii), (c) → (iv), (d) → (i) |
Subtopic: Dimensions |
89%
Level 1: 80%+
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The following is/are not a unit of time:
| (a) | second |
| (b) | parsec |
| (c) | year |
| (d) | light year |
Choose the correct option:
| 1. | (a, c, d) |
| 2. | (a, c) |
| 3. | (b, d) |
| 4. | (b, c) |
Subtopic: Dimensions |
78%
Level 2: 60%+
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Which of the following ratios, express pressure?
| (a) | force/area |
| (b) | energy/volume |
| (c) | energy/area |
| (d) | force/volume |
Choose the correct option:
| 1. | (a), (c) |
| 2. | (a), (d) |
| 3. | (b), (d) |
| 4. | (a), (b) |
Subtopic: Dimensions |
77%
Level 2: 60%+
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If Planck's constant \((h)\) and speed of light in a vacuum \((c)\) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass, and time in terms of the three chosen fundamental quantities?
| (a) | mass of the electron \((m_e)\) |
| (b) | universal gravitational constant \((G)\) |
| (c) | charge of an electron \((e)\) |
| (d) | mass of proton \((m_p)\) |
Choose the correct option from the given ones:
| 1. | (a), (c), and (d) only |
| 2. | (a), (b), and (d) only |
| 3. | (a), (b), and (c) only |
| 4. | (b), (c), and (d) only |
Subtopic: Dimensions |
61%
Level 2: 60%+
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