Import Question JSON

Current Question (ID: 16605)

Question:

$\text{The current in a wire varies with time according to the relation } i = (3 + 2t) \text{ A.}$ $\text{The amount of charge passing a cross section of the wire in the time interval } t = 0 \text{ to } t = 4.0 \text{ s would be: (where } t \text{ is time in seconds)}$

Options:

1. $28 \text{ C}$
2. $30.5 \text{ C}$
3. $8 \text{ C}$
4. $82 \text{ C}$

Solution:

$i = (3 + 2t)$ $\frac{dq}{dt} = 3 + 2t$ $\int_{0}^{q} dq = \int_{0}^{4} (3 + 2t) dt$ $q = (3t + t^2)\bigg|_{0}^{4}$ $q = 12 + 16 = 28 \text{ C}$

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
}