Import Question JSON

Current Question (ID: 9556)

Question:

$\text{A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio of } \frac{|displacement|}{distance} \text{ will be:}$

Options:

1. $0$
2. $\frac{1}{7}$
3. $\frac{2}{7}$
4. $\frac{1}{11}$

Solution:

\text{Hint: Displacement = 2r} \text{Step: Find the ratio of } \frac{|\text{displacement}|}{distance} \text{displacement} = 2r \text{distance} = 3 \times 2\pi r + \pi r = 7\pi r \text{Now,} \frac{|\text{displacement}|}{distance} = \frac{2r}{7\pi r} = \frac{2}{7\pi} = \frac{2}{7 \times \frac{22}{7}} = \frac{1}{11} \text{Hence, option (4) 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
}