Import Question JSON

Current Question (ID: 17442)

Question:

$\text{An electromagnetic wave going through the vacuum is described by}$ $E = E_0 \sin(kx - \omega t).$ $\text{Which is the following is/are independent of the wavelength?}$

Options:

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

Solution:

$k = \frac{2\pi}{\lambda}$ $\text{and}$ $\omega = \frac{2\pi c}{\lambda}$ $\text{Hence,}$ $\frac{k}{2\pi} = \frac{\omega}{2\pi c}$ $\Rightarrow \frac{k}{\omega} \text{ independent of wavelength.}$

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
}