Import Question JSON

Current Question (ID: 15937)

Question:

$\text{A wave traveling in the } +ve \ x\text{-direction having maximum displacement along } y\text{-direction as } 1 \ \text{m, wavelength } 2\pi \ \text{m and frequency of } \frac{1}{\pi} \ \text{Hz, is represented by:}$

Options:

1. $y = \sin(2\pi x - 2\pi t)$
2. $y = \sin(10\pi x - 20\pi t)$
3. $y = \sin(2\pi x + 2\pi t)$
4. $y = \sin(x - 2t)$

Solution:

$\text{Hint: } y = a \sin(\omega t - kx)$ $\text{Step: Find the equation of the wave.}$ $\text{The equation of the wave is given by; } y = a \sin(\omega t - kx)$ $\text{here, } k = \frac{2\pi}{\lambda} = \frac{2\pi}{2\pi} = 1$ $\omega = 2\pi f = 2\pi \times \frac{1}{\pi} = 2$ $a = 1$ $\text{Therefore, the equation of the wave is } y = \sin(x - 2t)$ $\text{Hence, option (4) is the correct answer.}$

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
}