Import Question JSON

Current Question (ID: 19986)

Question:

$\text{A train is moving with a speed of } 10 \text{ m/s towards a platform and blows a horn with frequency } 400 \text{ Hz.}$ $\text{Find the frequency heard by a passenger standing on the platform.}$ $\text{Take speed of sound } = 310 \text{ m/s.}$

Options:

1. $405 \text{ Hz}$
2. $425 \text{ Hz}$
3. $380 \text{ Hz}$
4. $413 \text{ Hz}$

Solution:

$\text{Hint: } f = f' \left[ \frac{v - v_0}{v - v_s} \right]$ $f' = f \left[ \frac{v - v_0}{v - v_s} \right]$ $= 400 \left[ \frac{310 - 0}{310 - 10} \right]$ $= \frac{4}{3} (310) \text{Hz} \simeq 413 \text{ Hz}$

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
}