Import Question JSON

Current Question (ID: 17422)

Question:

$\text{If an electromagnetic wave propagating through vacuum is described by}$ $E_y = E_0 \sin(kx - \omega t); \quad B_z = B_0 \sin(kx - \omega t), \text{ then:}$

Options:

1. $E_0 k = B_0 \omega$
2. $E_0 B_0 = \omega k$
3. $E_0 \omega = B_0 k$
4. $E_0 B_0 = \frac{\omega}{k}$

Solution:

$\text{Hint: Speed of the wave = } \frac{\omega}{K}$ $\text{Step 1:}$ $\text{Use relation between amplitude}$ $\frac{E_0}{B_0} = C = \frac{\omega}{k}$ $E_0 k = \omega B_0$

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
}