Import Question JSON

Current Question (ID: 17439)

Question:

$\text{A lamp radiates power } P_0 \text{ uniformly in all directions. The amplitude of electric field strength } E_0 \text{ at a distance } r \text{ from it is:}$

Options:

1. $E_0 = \frac{P_0}{2\pi \varepsilon_0 c r^2}$
2. $E_0 = \sqrt{\frac{P_0}{2\pi \varepsilon_0 c r^2}}$
3. $E_0 = \sqrt{\frac{P_0}{4\pi \varepsilon_0 c r^2}}$
4. $E_0 = \sqrt{\frac{P_0}{8\pi \varepsilon_0 c r^2}}$

Solution:

$S_{\text{av}} = \frac{P}{4\pi r^2} = \frac{1}{2} \varepsilon_0 E_0^2 c$ $E_0 = \sqrt{\frac{P}{2\pi \varepsilon_0 c r^2}}$

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
}