Import Question JSON

Current Question (ID: 20011)

Question:

$\text{A car is moving with speed of } 15 \text{ m/s towards a stationary wall. A person in the car press the horn and experience the change in frequency of } 40 \text{ Hz due to reflection from stationary wall. Find the frequency of horn. (Use } v_{\text{sound}} = 330 \text{ m/s)}$

Options:

1. $420 \text{ Hz}$
2. $400 \text{ Hz}$
3. $320 \text{ Hz}$
4. $500 \text{ Hz}$

Solution:

$f_{\text{echo}} = f_0 \left( \frac{v + v_0}{v - v_0} \right)$ $f_{\text{echo}} = 40 \text{ Hz}$ $v = 330 \text{ m/s}$ $v_0 = 15 \text{ m/s}$ $f_0 = \frac{f_{\text{echo}} \times (v - v_0)}{v + v_0}$ $f_0 = \frac{40 \times (330 - 15)}{330 + 15}$ $f_0 = 420 \text{ Hz}$

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
}