Import Question JSON

Current Question (ID: 17274)

Question:

$\text{In the diagram, two sinusoidal voltages of the same frequency are shown.}$ $\text{What is the frequency and the phase relationship between the voltages?}$

Options:

1. $0.4 \quad -\pi/4$
2. $2.5 \quad -\pi/2$
3. $2.5 \quad +\pi/2$
4. $2.5 \quad -\pi/4$

Solution:

$\text{From the graph shown below. It is clear that phase lead of } N \text{ over } M \text{ is } -\frac{\pi}{2}. $ $\text{Since time period (i.e. taken to complete one cycle) } = 0.4 \text{ sec.}$ $\text{Hence frequency } \nu = \frac{1}{T} = 2.5 \text{ Hz}$

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
}