Import Question JSON

Current Question (ID: 19965)

Question:

$\text{A pipe open at both ends has a fundamental frequency } f \text{ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:}$

Options:

1. $\frac{f}{2}$
2. $\frac{3f}{4}$
3. $2f$
4. $f$

Solution:

$\text{Hint: } f = \frac{v}{\lambda}$ $\ell = \frac{\lambda}{4} + \frac{\lambda}{4} = \frac{\lambda}{2}$ $\lambda = 2\ell$ $f = \frac{v}{\lambda} = \frac{v}{2\ell}$ $\frac{\ell}{2} = \frac{\lambda}{4} \Rightarrow \lambda = 2\ell$ $\therefore f' = \frac{v}{\lambda} = \frac{v}{2\ell} = f$

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
}