Import Question JSON

Current Question (ID: 20588)

Question:

$\text{To light, a } 50 \text{ W, } 100 \text{ V lamp is connected in series with a capacitor of capacitance } \frac{50}{\pi \sqrt{x}} \mu\text{F}, \text{ with } 200 \text{ V, } 50 \text{ Hz AC source. The value of } x \text{ will be:}$

Options:

1. $3$
2. $6$
3. $9$
4. $1$

Solution:

$\text{Hint: } P = \frac{V^2}{R}$ $\text{Z} = \sqrt{X_C^2 + R^2}$ $\text{Z} = \sqrt{X_C^2 + (200)^2}$ $\text{(200)}^2 = (400)^2$ $400^2 - 200^2$ $400 \times (400 - 200)$

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
}