Import Question JSON

Current Question (ID: 17011)

Question:

$\text{The number of turns in a coil of wire of fixed radius and length is } 600 \text{ and its self-inductance is } 108 \text{ mH.}$ $\text{The self-inductance of a coil of } 500 \text{ turns will be:}$

Options:

1. $74 \text{ mH}$
2. $75 \text{ mH}$
3. $76 \text{ mH}$
4. $77 \text{ mH}$

Solution:

$\text{Self-inductance } L \propto N^2 \text{ (where } N \text{ is the number of turns)}$ $\frac{L_1}{L_2} = \left(\frac{N_1}{N_2}\right)^2$ $\frac{108}{L_2} = \left(\frac{600}{500}\right)^2$ $L_2 = 75 \text{ mH}$

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
}