Import Question JSON

Current Question (ID: 17284)

Question:

$\text{The rms value of the potential difference } V \text{ shown in the figure is:}$

Options:

1. $\frac{V_0}{\sqrt{3}}$
2. $V_0$
3. $\frac{V_0}{\sqrt{2}}$
4. $\frac{V_0}{2}$

Solution:

$V_{\text{rms}} = \left[ \frac{1}{T} \int_0^{T/2} V_0^2 \text{ dt} \right]^{1/2} = \left[ \frac{V_0^2}{T} \left[ t \right]_0^{T/2} \right]^{1/2}$ $= \left[ \frac{V_0^2}{T} \left( \frac{T}{2} \right) \right]^{1/2} \text{ or } V_{\text{rms}} = \left[ \frac{V_0^2}{2} \right]^{1/2} = \frac{V_0}{\sqrt{2}}$

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
}