Import Question JSON

Current Question (ID: 16035)

Question:

$\text{Eleven tuning forks are arranged in increasing order of frequency in such a way that any two consecutive tuning forks produce 4 beats per second. The highest frequency is twice that of the lowest. The highest and the lowest frequencies (in Hz) are, respectively:}$

Options:

1. $100 \text{ and } 50$
2. $44 \text{ and } 22$
3. $80 \text{ and } 40$
4. $72 \text{ and } 30$

Solution:

$\text{Hint: Beat frequency per second} = |f_1 - f_2|$ $\text{Step: Find the highest and lowest frequencies of the tuning fork.}$ $\text{Let the lowest frequency} = f$ $\text{Then, highest frequency} = f + (11 - 1) \times 4 = f + 40$ $\text{Now, } f + 40 = 2f \Rightarrow f = 40$ $\text{Therefore, the highest frequency of the tuning fork is 80 Hz and the lowest frequency of the tuning fork is 40 Hz.}$ $\text{Hence, option 3 is the correct answer.}$

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
}