Import Question JSON

Current Question (ID: 16005)

Question:

$\text{Stationary waves are formed on a stretched string. If the wavelength is } \lambda, \text{ then the distance between two points having the maximum displacement can be:}$

Options:

1. $\frac{3\lambda}{2}$
2. $4\lambda$
3. $\frac{5\lambda}{2}$
4. $\text{All of these}$

Solution:

$\text{Hint: Distance between 2 consecutive nodes or antinodes } = \frac{\lambda}{2}$ $\text{Step: Find the distance between two antinodes.}$ $\text{So, the distance between two points having maximum displacement } = n \times \frac{\lambda}{2}$ $\text{distance between 2 consecutive antinodes } = \frac{n\lambda}{2}$ $\text{Hence, option (4) is the correct answer.}$

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
}