Import Question JSON

Current Question (ID: 17319)

Question:

$\text{In an } LCR \text{ circuit having } L = 8.0 \text{ H}, C = 0.5 \ \mu\text{F and } R = 100 \ \Omega \text{ in series, what is the resonance frequency?}$ $1. \ 600 \ \text{radian/sec}$ $2. \ 600 \ \text{Hz}$ $3. \ 500 \ \text{radian/sec}$ $4. \ 500 \ \text{Hz}$

Options:

1. $600 \ \text{radian/sec}$
2. $600 \ \text{Hz}$
3. $500 \ \text{radian/sec}$
4. $500 \ \text{Hz}$

Solution:

$\text{Hint: } X_L = X_C$ $\text{Resonance frequency in radian/second is:}$ $\omega = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{8 \times 0.5 \times 10^{-6}}} = 500 \ \text{rad/sec}$

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
}