Import Question JSON

Current Question (ID: 15941)

Question:

$\text{Three progressive waves } A, B \text{ and } C \text{ are shown below. With respect to wave } A:$

Options:

1. $\text{Wave } C \text{ lags behind in phase by } \pi/2 \text{ and wave } B \text{ leads by } \pi/2.$
2. $\text{Wave } C \text{ leads in phase by } \pi \text{ and wave } B \text{ lags behind by } \pi.$
3. $\text{Wave } C \text{ lags behind in phase by } \pi/2 \text{ and wave } B \text{ leads by } \pi.$
4. $\text{Wave } C \text{ lags behind in phase by } \pi \text{ and wave } B \text{ leads by } \pi.$

Solution:

$\text{Hint: Compare the phase angle of given waves.}$ $\text{Step: Identify the equations of given waves.}$ $Y_A = A \sin \omega t$ $Y_B = A \sin (\omega t + \pi/2)$ $Y_C = A \sin (\omega t - \pi/2)$ $\text{So, from above, it is clear that the wave } C \text{ lags behind in phase by } \pi/2 \text{ and } B \text{ leads by } \pi/2.$ $\text{Hence, option (1) is the correct answer.}$

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
}