Import Question JSON

Current Question (ID: 20675)

Question:

$\text{In the given electromagnetic wave } E_y = 600 \sin(\omega t - kx) \text{ Vm}^{-1},$ $\text{intensity of the associated light beam is (in W/m}^2\text{): (Given }$ $\varepsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2})$

Options:

1. 729
2. 243
3. 972
4. 486

Solution:

$\text{The intensity of an electromagnetic wave is given by } I = \frac{1}{2} \varepsilon_0 c E_0^2.$ $\text{Here, } E_0 = 600 \text{ Vm}^{-1}, \varepsilon_0 = 9 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}, \text{ and } c = 3 \times 10^8 \text{ m/s}.$ $I = \frac{1}{2} \times 9 \times 10^{-12} \times 3 \times 10^8 \times (600)^2 = 486 \text{ W/m}^2.$

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
}