Import Question JSON

Current Question (ID: 17432)

Question:

$\text{The speed of an electromagnetic wave in a medium of dielectric constant } 2.25$ $\text{ and relative permeability } 4 \text{ is approximately:}$

Options:

1. $1 \times 10^8 \text{ m/s}$
2. $2.5 \times 10^8 \text{ m/s}$
3. $3 \times 10^8 \text{ m/s}$
4. $2 \times 10^8 \text{ m/s}$

Solution:

$\text{The speed of an electromagnetic wave in a medium is given by } v = \frac{c}{\sqrt{\varepsilon_r \mu_r}}$ $\text{where } c = 3 \times 10^8 \text{ m/s is the speed of light in vacuum, } \varepsilon_r \text{ is the dielectric constant,}$ $\text{and } \mu_r \text{ is the relative permeability.}$ $v = \frac{3 \times 10^8}{\sqrt{2.25 \times 4}} = \frac{3 \times 10^8}{3} = 1 \times 10^8 \text{ m/s}$

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
}