Import Question JSON

Current Question (ID: 19996)

Question:

$\text{A student is performing the experiment of resonance column. The diameter of the column tube is } 6 \text{ cm. The frequency of the tuning fork is } 504 \text{ Hz. Speed of the sound at the given temperature is } 336 \text{ m/s.}$ $\text{The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column, when the first resonance occurs is:}$

Options:

1. $13 \text{ cm}$
2. $16.6 \text{ cm}$
3. $18.4 \text{ cm}$
4. $14.8 \text{ cm}$

Solution:

$\text{Hint: End correction } (e) = 0.6 \times r$ $d = 6 \text{ cm}, f = 504, v = 336 \text{ m/s}$ $e = 0.3 \text{ cm}$ $l + e = \frac{\lambda}{4} = \frac{v}{4f} = \frac{336}{4 \times 504} = 16.66 - 0.3 \times 6$ $l = 14.866 \text{ cm} \approx 14.8 \text{ cm}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}