Import Question JSON

Current Question (ID: 20599)

Question:

$\text{Consider the following statements:}$ $\text{Statement 1: An LCR circuit connected to an AC source has maximum average power at resonance.}$ $\text{Statement 2: A resistor only circuit with zero phase difference has maximum average power.}$

Options:

1. $(1) \text{ and } (2) \text{ both are correct}$
2. $(1) \text{ is correct but } (2) \text{ is incorrect}$
3. $(1) \text{ is incorrect but } (2) \text{ is correct}$
4. $\text{Both } (1) \text{ and } (2) \text{ are incorrect}$

Solution:

$\text{Hint: } P_{\text{avg}} = I_{\text{rms}} V_{\text{rms}} \cos \phi$ $\text{For maximum } P_{\text{avg}} \cos \phi = 1$ $\phi = 0$ $\text{or circuit is a resistive circuit or an LCR is at resonance}$

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
}