Import Question JSON

Current Question (ID: 20009)

Question:

$\text{The train blowing a whistle of frequency } 320 \text{ Hz is moving with a}$ $\text{velocity of } 36 \text{ km/h towards a hill from which an echo is heard by the}$ $\text{train driver. The frequency of echo will be:}$ $\text{(The velocity of sound in air is } 330 \text{ m/s.)}$

Options:

1. $430 \text{ Hz}$
2. $340 \text{ Hz}$
3. $120 \text{ Hz}$
4. $220 \text{ Hz}$

Solution:

$\text{Hint: } f = \left( \frac{v + v_s}{v - v_s} \right) f_0.$ $\text{Step 1: Find the frequency of the car w.r.t. the hill.}$ $f_1 = \left( \frac{v}{v - v_s} \right) f = \left( \frac{330}{320} \right) \times 320 = 330 \text{ Hz}$ $\text{Step 2: Find the frequency of the sound reflected by hill w.r.t. the car (echo).}$ $f_2 = \left( \frac{v + v_0}{v} \right) f_1 = \left( \frac{330 + 10}{330} \right) \times 330 = 340 \text{ Hz}$

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
}