Import Question JSON

Current Question (ID: 19483)

Question:

$\text{A planet at a distance } r \text{ from the sun takes 200 days to complete one revolution around the sun.}$ $\text{What will be time period for a planet at distance } \frac{r}{4} \text{ from the sun?}$

Options:

1. $50 \text{ days}$
2. $25 \text{ days}$
3. $100 \text{ days}$
4. $12.5 \text{ days}$

Solution:

$\text{Hint: } T^2 \propto R^3$ $\frac{200^2}{T^2} = \frac{r^3}{\left(\frac{r}{4}\right)^3}$ $\frac{200}{T} = (4)^{\frac{3}{2}}$ $\frac{200}{8} = T$ $\Rightarrow T = 25 \text{ days}$

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
}