Import Question JSON

Current Question (ID: 19971)

Question:

$\text{A progressive wave travelling along the positive } x\text{-direction is represented by } y(x, t) = A \sin(kx - \omega t + \phi).$ $\text{Its snapshot at } t = 0 \text{ is given in the figure.}$

Options:

1. $\frac{\pi}{2}$
2. $\pi$
3. $0$
4. $-\frac{\pi}{2}$

Solution:

$\text{Hint: The equation of given graph is } y = -A \sin(kx)$ $Y = A \sin(kx - \omega t + \phi)$ $\text{At } t = 0$ $Y = A \sin(kx + \phi)$ $-A \sin(kx) = A \sin(kx + \pi)$ $\phi = \pi$

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
}