Import Question JSON

Current Question (ID: 16026)

Question:

$\text{Two sound waves given by the equations } y = A \sin 122\pi t \text{ and } y = A \sin 128\pi t \text{ pass through a point simultaneously. The number of beats per second is:}$

Options:

1. $6$
2. $5$
3. $4$
4. $3$

Solution:

$\text{Hint: The beat frequency is equal to the absolute value of the difference in frequency of the two waves.}$ $\text{Step 1: Use the standard equation of wave } y = A \sin(2\pi ft)$ $\text{Step 2: Compare the given equation and find the frequencies.}$ $f_1 = 61 \text{ Hz}$ $f_2 = 64 \text{ Hz}$ $\text{The beat frequency is given by:}$ $\text{Beat} = f_2 - f_1 = 3 \text{ Hz}$ $\text{Hence, option (4) is the correct answer.}$

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
}