Import Question JSON

Current Question (ID: 20284)

Question:

$\text{An electrical power line, having a total resistance of } 2 \, \Omega, \text{ delivers } 1 \, \text{kW at } 220 \, \text{V. The efficiency of the transmission line is approximately:}$ $1. \, 72\%$ $2. \, 96\%$ $3. \, 91\%$ $4. \, 85\%$

Options:

1. $72\%$
2. $96\%$
3. $91\%$
4. $85\%$

Solution:

$\text{Hint: Power loss } = I^2 R$ $vi = \frac{10^3}{\frac{1000}{220}}$ $i = \frac{1000}{220}$ $\text{loss } = i^2 R = \left(\frac{50}{11}\right)^2 \times 2$ $\text{efficiency } = \frac{1000}{1000 + i^2 R} \times 100 = 96\%$

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
}