Import Question JSON

Current Question (ID: 20656)

Question:

$\text{A radio can tune to any station in } 6 \text{ MHz to } 10 \text{ MHz band. The value of corresponding wavelength bandwidth will be:}$

Options:

1. $4 \text{ m}$
2. $20 \text{ m}$
3. $30 \text{ m}$
4. $50 \text{ m}$

Solution:

$\text{Hint: } f = \frac{c}{\lambda}$ $f_1 = 6 \text{ MHz} = 6 \times 10^6 \text{ Hz}$ $f_2 = 10 \text{ MHz} = 10 \times 10^6 \text{ Hz}$ $\lambda_1 = \frac{c}{f_1} = \frac{3 \times 10^8}{6 \times 10^6} = 50 \text{ m}$ $\lambda_2 = \frac{c}{f_2} = \frac{3 \times 10^8}{10 \times 10^6} = 30 \text{ m}$ $\text{Bandwidth} = \lambda_1 - \lambda_2 = 50 - 30 = 20 \text{ m}$

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
}