Import Question JSON

Current Question (ID: 19963)

Question:

$\text{A pipe length of } 85 \text{ cm is closed from one end. Find the number of possible natural oscillations of the air column in the pipe whose frequencies lie below } 1250 \text{ Hz. The velocity of sound in air is } 340 \text{ m/s:}$

Options:

1. $8$
2. $6$
3. $4$
4. $12$

Solution:

$\text{Hint: } f = \frac{(2n+1)v}{4\ell}$ $\ell = 85 \text{ cm}$ $\text{Velocity of sound } = 340 \text{ m/s}$ $f = \frac{(2n+1)v}{4\ell}$ $n = 0, 1, \ldots$ $2n + 1 = \frac{4f \times \ell}{v} = \frac{4 \times 1250 \times 0.85}{340 \times 100} = 12.5$ $2n = 11.5$ $n = \frac{11.5}{2} = 5.7$ $\text{Hence the maximum value of } n = 5$ $\text{hence total no. of oscillation } = 6$

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
}