Import Question JSON

Current Question (ID: 15999)

Question:

$\text{A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio:}$

Options:

1. $1 : 2$
2. $2 : 3$
3. $3 : 4$
4. $4 : 5$

Solution:

$\text{Hint: } f_c = \frac{v}{4l}$ $\text{Step: Find the ratio of the length of the closed and open pipes.}$ $\text{It is given in the question;}$ $\text{The first overtone of closed pipe = The first overtone of the open pipe}$ $\text{i.e., } 3 \times \frac{v}{4l_1} = 2 \times \frac{v}{2l_2}$ $\text{where } l_1 \text{ and } l_2 \text{ are the lengths of closed and open organ pipes}$ $\Rightarrow \frac{l_1}{l_2} = \frac{3}{4}$ $\text{Therefore, the ratio of the length of the closed and open pipes is } 3 : 4.$ $\text{Hence, option (3) is the correct answer.}$

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
}