Import Question JSON

Current Question (ID: 20003)

Question:

$\text{The velocity of sound in a gas in which two wavelengths } 4.08 \text{ m and } 4.16 \text{ m produce } 40 \text{ beats in } 12 \text{ s, will be:}$

Options:

1. $282.8 \text{ ms}^{-1}$
2. $175.5 \text{ ms}^{-1}$
3. $353.6 \text{ ms}^{-1}$
4. $707.2 \text{ ms}^{-1}$

Solution:

$\text{Hint: } f_b = f_1 - f_2$ $\text{Step: Find the velocity of sound in the gas.}$ $f_b = f_1 - f_2$ $\frac{v}{4.08} - \frac{v}{4.16} = \frac{40}{12}$ $\Rightarrow v = 707.2 \text{ m/s}$ $\text{Hence, option (4) is the correct answer.}$

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
}