Import Question JSON

Current Question (ID: 20662)

Question:

$\text{Nearly } 10\% \text{ of the power of a } 110 \text{ W light bulb is converted to visible radiation.}$ $\text{The change in average intensities of visible radiation, at a distance of } 1 \text{ m from the bulb to a distance of } 5 \text{ m is } a \times 10^{-2} \text{ W/m}^2.$ $\text{The value of } a \text{ will be:}$

Options:

1. 100
2. 58
3. 84
4. 112

Solution:

$\text{Hint: } I = \frac{P}{4 \pi r^2}$ $P = \frac{10}{100} \times 110 = 11 \text{ W}$ $I_1 - I_2 = a \times 10^{-2}$ $\frac{11}{4 \pi (1)^2} - \frac{11}{4 \pi (5)^2} = a \times 10^{-2}$

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
}