Import Question JSON

Current Question (ID: 19979)

Question:

$\text{In an experiment to determine the velocity of sound in air at room temperature, a resonance is observed when the air column has a length of } 20.0 \text{ cm for a tuning fork of frequency } 400 \text{ Hz is used. The velocity of the sound at room temperature is } 336 \text{ ms}^{-1}. \text{ The third resonance is observed when the air column has a length of:}$ $1. \ 100 \text{ cm}$ $2. \ 110 \text{ cm}$ $3. \ 104 \text{ cm}$ $4. \ 120 \text{ cm}$

Options:

1. $100 \text{ cm}$
2. $110 \text{ cm}$
3. $104 \text{ cm}$
4. $120 \text{ cm}$

Solution:

$\text{Hint: } l_1 + e = \frac{\lambda}{4}$ $\text{For first resonance}$ $\ell_1 + e = \frac{\lambda}{4}$ $\lambda = \frac{336}{400} \times 100 \text{ cm} = 84 \text{ cm} \Rightarrow \frac{\lambda}{4} = 21 \text{ cm}$ $e = 21 - 20 = 1 \text{ cm}$ $\text{For third resonance}$ $\ell_3 + e = \frac{5\lambda}{4} = 105 \text{ cm} \Rightarrow \ell_3 = 104 \text{ cm}$

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
}