Import Question JSON

Current Question (ID: 10812)

Question:

$\text{If the temperature of the body is increased from } -73°\text{C to } 327°\text{C, then the ratio of energy emitted per second in both cases is:}$

Options:

1. $1 : 3$
2. $1 : 81$ (Correct)
3. $1 : 27$
4. $1 : 9$

Solution:

\text{Energy per second } P = \frac{Q}{t} \propto T^4, \quad \frac{P_1}{P_2} = \left(\frac{T_1}{T_2}\right)^4 = \left(\frac{273+73}{273+327}\right)^4 = \left(\frac{346}{600}\right)^4

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
}