Import Question JSON

Current Question (ID: 20524)

Question:

$\text{Magnetic flux (in weber) in a closed circuit of resistance } 20 \, \Omega \text{ varies with time } t(s) \text{ as } \phi = 8t^2 - 9t + 5.$ $\text{The magnitude of the induced current at } t = 0.25 \, s \text{ will be:}$

Options:

1. $150 \, \text{mA}$
2. $300 \, \text{mA}$
3. $250 \, \text{mA}$
4. $100 \, \text{mA}$

Solution:

$I = \frac{\varepsilon}{R}$ $\varepsilon = \left| \frac{d\phi}{dt} \right|$ $\varepsilon = 16t - 9$ $I = \frac{16 \times 0.25 - 9}{20} = 0.25 \, \text{A} = 250 \, \text{mA}$

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
}