Import Question JSON

Current Question (ID: 17416)

Question:

$\text{Consider an oscillator which has a charged particle oscillating about its mean position with a frequency of } 300 \text{ MHz. The wavelength of electromagnetic waves produced by this oscillator would be:}$ $1. \ 1 \text{ m}$ $2. \ 10 \text{ m}$ $3. \ 100 \text{ m}$ $4. \ 1000 \text{ m}$

Options:

1. $1 \text{ m}$
2. $10 \text{ m}$
3. $100 \text{ m}$
4. $1000 \text{ m}$

Solution:

$\text{Hint: Use the relation } c = f \lambda.$ $\text{Step 1: Find wavelength from relation, } c = f \lambda$ $\text{Step 2: } \Rightarrow \lambda = \frac{c}{f}$ $= \frac{3 \times 10^8}{300 \times 10^6} = 1 \text{ m}$

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
}