Import Question JSON

Current Question (ID: 19993)

Question:

$\text{Two cars } A \text{ and } B \text{ are moving away from each other in opposite directions.}$ $\text{Both the cars are moving with a speed of } 20 \text{ ms}^{-1} \text{ with respect to the ground.}$ $\text{If an observer in car } A \text{ detects a frequency } 2000 \text{ Hz of the sound coming from car } B,$ $\text{what is the natural frequency of the sound source in car } B? \text{ (speed of sound in air } = 340 \text{ ms}^{-1})$

Options:

1. $2060 \text{ Hz}$
2. $2150 \text{ Hz}$
3. $2300 \text{ Hz}$
4. $2250 \text{ Hz}$

Solution:

$\text{Using the Doppler effect formula:}$ $f' = \frac{f(v + v_o)}{v + v_s}$ $\text{where } f' = 2000 \text{ Hz, } v = 340 \text{ ms}^{-1}, v_o = 20 \text{ ms}^{-1}, v_s = -20 \text{ ms}^{-1}$ $\text{Solving for } f:$ $2000 = \frac{f(340 + 20)}{340 - 20}$ $f = \frac{2000 \times 320}{360} = 2250 \text{ Hz}$

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
}