Import Question JSON

Current Question (ID: 20200)

Question:

$\text{In a large building, there are 15 bulbs of } 40 \text{ W, 5 bulbs of } 100 \text{ W, 5 fans of } 80 \text{ W and 1 heater of } 1 \text{ kW. The voltage of the electric mains is } 220 \text{ V. The minimum capacity of the main fuse of the building will be:}$ $1. \ 10 \text{ A}$ $2. \ 12 \text{ A}$ $3. \ 14 \text{ A}$ $4. \ 8 \text{ A}$

Options:

1. $10 \text{ A}$
2. $12 \text{ A}$
3. $14 \text{ A}$
4. $8 \text{ A}$

Solution:

$\text{Hint: } P = iV = \frac{V^2}{R} = i^2R$ $\text{Using } i = \frac{P}{V}$ $\text{Total current passing through mains}$ $i = \frac{40}{220} \times 15 + \frac{100}{220} \times 5 + \frac{80}{220} \times 5 + \frac{1000}{220} \times 1$ $= \frac{600 + 500 + 400 + 1000}{220}$ $= \frac{2500}{220}$ $= 11.36 \text{ A}$ $\therefore \text{ min current capacity of fuse } = 12 \text{ A}$

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
}