Import Question JSON

Current Question (ID: 19982)

Question:

$\text{When a car is approaching the observer, the frequency of the horn heard by observer is } 100 \text{ Hz.}$ $\text{After passing the observer, it is } 50 \text{ Hz.}$ $\text{If the observer moves with the car, the frequency will be } \frac{x}{3} \text{ Hz.}$ $\text{Then } x =$

Options:

1. $100$
2. $150$
3. $200$
4. $250$

Solution:

$\text{Hint: } f' = f \left( \frac{v}{v-v_s} \right)$ $\text{Step 1: Find the frequency.}$ $\left( \frac{v}{v-v_s} \right) f = 100 \quad \ldots (1)$ $\left( \frac{v}{v+v_s} \right) f = 50 \quad \ldots (2)$ $\text{from equations (1) \& (2).}$ $\frac{v+v_s}{v-v_s} = 2$ $\Rightarrow v_s = \frac{v}{3}$ $\text{from equation (1)-}$ $\frac{3v}{2} = 100$ $\text{Step 2: Find the value of } x.$ $f = \frac{200}{3} \text{ Hz} = \frac{x}{3}$ $\therefore x = 200 \text{ Hz}$

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
}