Import Question JSON

Current Question (ID: 19975)

Question:

$\text{The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from } 420 \text{ Hz to } 490 \text{ Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is } 330 \text{ ms}^{-1}.$

Options:

1. $61 \text{ kmh}^{-1}$
2. $81 \text{ kmh}^{-1}$
3. $71 \text{ kmh}^{-1}$
4. $91 \text{ kmh}^{-1}$

Solution:

$\text{Use } f = f_0 \left[ \frac{v + v_0}{v - v_s} \right]$ $f_1 = \left( \frac{330}{330 - v_B} \right) 420$ $f_2 = \left( \frac{330 + v_0}{330} \right) \left( \frac{330}{330 - v_B} \right) 420$ $490 = \left( \frac{330 + v_B}{330 - v_B} \right) 420$ $\frac{7}{6} = \frac{330 + v_B}{330 - v_B}$ $v_B = \frac{330 \times 1}{13} \approx 91 \text{ km/hr}$

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
}