Import Question JSON

Current Question (ID: 16027)

Question:

$\text{A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency of } 250 \ \text{Hz.}$ $\text{The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of } 513 \ \text{Hz.}$ $\text{The unknown frequency will be:}$

Options:

1. $246 \ \text{Hz}$
2. $240 \ \text{Hz}$
3. $260 \ \text{Hz}$
4. $254 \ \text{Hz}$

Solution:

$\text{Hint: Beat frequency per second } = |f_1 - f_2|$ $\text{Step: Find the unknown frequency.}$ $\text{Given: Known frequency } = 250 \ \text{Hz, Beats per second } = 4$ $\text{The frequency of the unknown source can be } 250 - 4 \text{ or } 250 + 4 \ \text{Hz}$ $= 246 \text{ or } 254.$ $\text{Let unknown frequency } = v$ $\text{Frequency of other sources } = 513 \ \text{Hz}$ $\text{Beats per second with this } = 5$ $\text{Frequency } = 513 + 5, 513 - 5 = 518, 508$ $2v = 508$ $v = 254 \ \text{Hz}$ $\text{Therefore, the unknown frequency is } 254 \ \text{Hz.}$ $\text{Hence, option (4) is the correct answer.}$

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
}