Q. No.Plane angle and solid angle have:
1.
both units and dimensions
2.
units but no dimensions
3.
dimensions but no units
4.
no units and no dimensions
1. \(14\times10^{2}\)
2. \(138\times10^{1}\)
3. \(1382\)
4. \(1382.5\)
| List-I | List-II | ||
| (a) | Gravitational constant (\(G\)) | (i) | \([{L}^2 {~T}^{-2}] \) |
| (b) | Gravitational potential energy | (ii) | \([{M}^{-1} {~L}^3 {~T}^{-2}] \) |
| (c) | Gravitational potential | (iii) | \([{LT}^{-2}] \) |
| (d) | Gravitational intensity | (iv) | \([{ML}^2 {~T}^{-2}]\) |
| (a) | (b) | (c) | (d) | |
| 1. | (iv) | (ii) | (i) | (iii) |
| 2. | (ii) | (i) | (iv) | (iii) |
| 3. | (ii) | (iv) | (i) | (iii) |
| 4. | (ii) | (iv) | (iii) | (i) |
| 1. | wavelength of light |
| 2. | size of an atom |
| 3. | astronomical distance |
| 4. | height of a building |
Here, \(k\) is the permeability of the medium. The unit of \(k\) is (SI units):
1. m
2. m2
3. m2/s
4. m/s2
The acceleration due to gravity on the surface of the Earth is \(g=10~\text{m/s}^2\) . The value in \(\text {km/minute}^2\) is:
| 1. | \(36\) | 2. | \(0.6\) |
| 3. | \(\dfrac{10}{6}\) | 4. | \(3.6\) |
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. | \(I,~II~\text{and}~III\) |
The radius of a circle is stated as \(2.12\) cm. Its area should be written as:
| 1. | \(14\mathrm{~cm^2}\) | 2. | \(14.1\mathrm{~cm^2}\) |
| 3. | \(14.11\mathrm{~cm^2}\) | 4. | \(14.1124\mathrm{~cm^2}\) |
The dimensions of \(\left [ML^{-1} T^{-2} \right ] \) may correspond to:
| (a) | Work done by a force |
| (b) | Linear momentum |
| (c) | Pressure |
| (d) | Energy per unit volume |
Choose the correct option from the given ones:
| 1. | (a) and (b) only |
| 2. | (b) and (c) only |
| 3. | (c) and (d) only |
| 4. | none of the above |
Given: \(\int \frac{{dx}}{\sqrt{2{ax}-{x}^{2}}}={a}^{{n}} \sin ^{-1}\left[\frac{{x}}{{a}}-1\right]\)
The value of \(n\) is:
1. \(0\)
2. \(-1\)
3. \(1\)
4. none of these
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