Import Question JSON

Current Question (ID: 20327)

Question:

$\text{If electric current passing through a conductor varies with time as } I = I_0 + \beta t \text{ where } I_0 = 20 \text{ A}, \beta = 3 \text{ A/s}, \text{ then the charge flows through the conductor in the first 10 sec is:}$

Options:

1. $400 \text{ C}$
2. $500 \text{ C}$
3. $200 \text{ C}$
4. $350 \text{ C}$

Solution:

$\text{Hint: } Q = \int I \cdot dt$ $\Rightarrow Q = \int I \cdot dt = \int_0^{10} (20 + 3t) dt$ $= (20t)_0^{10} + 3 \left( \frac{t^2}{2} \right)_0^{10} = 350 \text{ C}$

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
}