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| 1. | \(\text{tan}^{-1}(0.750)\) | 2. | \(\text{sin}^{-1}(0.500)\) |
| 3. | \(\text{sin}^{-1}(0.750)\) | 4. | \(\text{tan}^{-1}(0.500)\) |
| 1. | \(2~\text{A}\) | 2. | \(0.25~\text{A}\) |
| 3. | \(1.5~\text{A}\) | 4. | \(1~\text{A}\) |
| 1. | do not play any significant role. |
| 2. | should be approximately equal to \(2X\). |
| 3. | should be approximately equal and are small. |
| 4. | should be very large and unequal. |

| 1. | \(\dfrac{1}{{R}^{6}}\) | 2. | \(\dfrac{1}{{R}^{2}}\) |
| 3. | \(\dfrac{1}{{R}^{3}}\) | 4. | \(\dfrac{1}{{R}^{4}}\) |
| 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. | \(\nu=100 ~\text{Hz} ; ~\nu_0=\dfrac{100}{\pi} ~\text{Hz}\) |
| 2. | \(\nu_0=\nu=50~\text{Hz}\) |
| 3. | \(\nu_0=\nu=\dfrac{50}{\pi} ~\text{Hz}\) |
| 4. | \(\nu_{0}=\dfrac{50}{\pi}~ \text{Hz}, \nu=50 ~\text{Hz}\) |
| 1. | \(10~\text{m/s}\) | 2. | zero |
| 3. | \(5\sqrt{3}~\text{m/s}\) | 4. | \(5~\text{m/s}\) |
What is the pH of a solution prepared by mixing equal volumes (50 mL each) of 0.10 M sodium acetate and 0.01 M acetic acid?
[Given pKa of CH3COOH = 4.57]
1. 2.57
2. 5.57
3. 3.57
4. 4.57