Import Question JSON

Current Question (ID: 19995)

Question:

$\text{Which, of the following equation represents a travelling wave?}$ $1.\ y = A \sin(15x - 2t)$ $2.\ y = Ae^{-x^2}(vt + \theta)$ $3.\ y = Ae^x \cos(\omega t - \theta)$ $4.\ y = A \sin x \cos \omega t$

Options:

1. $y = A \sin(15x - 2t)$
2. $y = Ae^{-x^2}(vt + \theta)$
3. $y = Ae^x \cos(\omega t - \theta)$
4. $y = A \sin x \cos \omega t$

Solution:

$\text{Hint: General form of wave is given by: } y = f\left(t - \frac{x}{v}\right)$ $\text{Step: Identify the equation representing a travelling wave.}$ $y = A \sin(15x - 2t)$ $\Rightarrow y = A \sin\left(15\left(x - \frac{t}{\frac{15}{2}}\right)\right)$ $\therefore y = f\left(x - \frac{t}{v}\right)$ $\text{Therefore, the equation } y = A \sin(15x - 2t), \text{ represents a travelling wave.}$ $\text{Hence, option (1) is the correct answer.}$

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
}