Import Question JSON

Current Question (ID: 16951)

Question:

$\text{The current in a coil varies with time } t \text{ as } I = 3t^2 + 2t. \text{ If the inductance of coil be } 10 \text{ mH, the value of induced emf at } t = 2 \text{ s will be:}$

Options:

1. $0.14 \text{ V}$
2. $0.12 \text{ V}$
3. $0.11 \text{ V}$
4. $0.13 \text{ V}$

Solution:

$\text{Induced emf } (\varepsilon) = -L \frac{dI}{dt}$ $\frac{dI}{dt} = \frac{d}{dt}(3t^2 + 2t) = 6t + 2$ $\varepsilon = -10 \times 10^{-3} \times (6 \times 2 + 2)$ $= -10 \times 10^{-3} \times 14$ $= -0.14 \text{ V}$

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
}