Import Question JSON

Current Question (ID: 20008)

Question:

$\text{In the wave equation, } y = 0.5 \sin \frac{2\pi}{\lambda} (400t - x) \text{ m, the velocity of the wave will be:}$

Options:

1. $200 \text{ m/s}$
2. $200\sqrt{2} \text{ m/s}$
3. $400 \text{ m/s}$
4. $400\sqrt{2} \text{ m/s}$

Solution:

$\text{Hint: } v = \frac{\omega}{k}.$ $\text{Step: Find the velocity of the wave.}$ $\Rightarrow v = \frac{\omega}{K} = \frac{400}{1}$ $\Rightarrow v = 400 \text{ m/s}$ $\text{Therefore, the velocity of wave is } 400 \text{ m/s.}$ $\text{Hence, option (3) is the correct answer.}$

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
}