Import Question JSON

Current Question (ID: 19495)

Question:

$\text{The distance between Sun and Earth is } R. \text{ The duration of the year if the distance between Sun and Earth becomes } 3R \text{ will be:}$

Options:

1. $\sqrt{3} \text{ years}$
2. $3 \text{ years}$
3. $9 \text{ years}$
4. $3\sqrt{3} \text{ years}$

Solution:

$\text{Hint: } T^2 \propto R^3$ $\text{If } T_1^2 \propto R^3 \text{ and } T_2^2 \propto (3R)^3,$ $\text{then } \frac{T_2}{T_1} = \sqrt{3^3} = 3\sqrt{3}$ $\text{Thus, the duration of the year will be } 3\sqrt{3} \text{ years.}$

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
}