Import Question JSON

Current Question (ID: 16029)

Question:

$\text{Two wires, } A \text{ and } B, \text{ of a musical instrument 'Sitar' produce } 3 \text{ beats per second. If the tension of } B \text{ is raised, the number of beats becomes } 1 \text{ beat per second. If the frequency of } A \text{ is } 450 \text{ Hz, then the original frequency of } B \text{ will be:}$ $1. \ 447 \ \text{Hz}$ $2. \ 453 \ \text{Hz}$ $3. \ 449 \ \text{Hz}$ $4. \ 451 \ \text{Hz}$

Options:

1. $447 \ \text{Hz}$
2. $453 \ \text{Hz}$
3. $449 \ \text{Hz}$
4. $451 \ \text{Hz}$

Solution:

$\text{Hint: } v \propto \sqrt{T}$ $\text{Step 1: Identify which wire has more frequency.}$ $f_A - f_B = 3$ $\text{If the tension of } B \text{ is raised, the number of beats becomes } 1 \text{ beat per second.}$ $f_B < f_A$ $\text{Step 2: Find the original frequency of the wire } B.$ $f_A = 450 \ \text{Hz}$ $f_A - f_B = 3$ $f_B = 450 - 3 = 447 \ \text{Hz}$ $\text{Therefore, the original frequency of the wire } B \text{ is } 447 \ \text{Hz.}$ $\text{Hence, option (1) is the correct answer.}$

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
}