Import Question JSON

Current Question (ID: 15988)

Question:

$\text{The length of the string of a musical instrument is } 90 \text{ cm and has a fundamental frequency of } 120 \text{ Hz. Where should it be pressed to produce a fundamental frequency of } 180 \text{ Hz?}$

Options:

1. $75 \text{ cm}$
2. $60 \text{ cm}$
3. $45 \text{ cm}$
4. $80 \text{ cm}$

Solution:

$\text{Hint: The velocity of the wave in the string remains the same.}$ $\text{Step 1: Find the velocity of the wave.}$ $f = 120 \text{ Hz} = \frac{v}{2l}$ $\Rightarrow 120 = \frac{v}{2 \times 0.9} \Rightarrow v = 120 \times 2 \times 0.9 \text{ m/s}$ $\text{Step 2: Find the length of the new string.}$ $f = 180 \text{ Hz} = \frac{v}{2l}$ $\Rightarrow 180 = \frac{120 \times 0.9}{l}$ $l = 60 \text{ cm}$ $\text{Hence, option (2) is the correct answer.}$

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
}