Import Question JSON

Current Question (ID: 20001)

Question:

$\text{A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of the last fork is:}$ $1.\ 152\ \text{Hz}$ $2.\ 234\ \text{Hz}$ $3.\ 134\ \text{Hz}$ $4.\ 144\ \text{Hz}$

Options:

1. $152\ \text{Hz}$
2. $234\ \text{Hz}$
3. $134\ \text{Hz}$
4. $144\ \text{Hz}$

Solution:

$\text{Hint: } t_n = a + (n-1)d$ $\text{Step: Find the frequency of the last fork.}$ $\Rightarrow f_1 = f$ $f_2 = f + 4$ $\Rightarrow f_3 = f + 2 \times 4$ $f_4 = f + 3 \times 4$ $\Rightarrow f_{20} = f + 19 \times 4$ $f + (19 \times 4) = 2 \times f$ $\Rightarrow f = 76\ \text{Hz}.$ $\text{Frequency of last tuning forks } f_L = 2f$ $\Rightarrow f_L = 152\ \text{Hz}$ $\text{Hence, option (1) is the correct answer.}$

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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
}