Import Question JSON

Current Question (ID: 17278)

Question:

$\text{A generator produces a voltage that is given by } V = 240 \sin(120t), \text{ where } t \text{ is in seconds. The frequency and rms voltage are:}$

Options:

1. $60 \text{ Hz and } 240 \text{ V}$
2. $19 \text{ Hz and } 120 \text{ V}$
3. $19 \text{ Hz and } 170 \text{ V}$
4. $754 \text{ Hz and } 70 \text{ V}$

Solution:

$(3) \ \nu = \frac{\omega}{2\pi} = \frac{120 \times 7}{2 \times 22} = 19 \ \text{Hz}$ $V_{\text{r.m.s.}} = \frac{240}{\sqrt{2}} = 120 \sqrt{2} \approx 170 \ \text{V}$

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
}