Import Question JSON

Current Question (ID: 17544)

Question:

$\text{A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is } 1.39 \times 10^9 \text{ m and its mean distance from the earth is } 1.5 \times 10^{11} \text{ m. What is the diameter of the sun's image on the paper?}$

Options:

1. $9.2 \times 10^{-4} \text{ m}$
2. $6.5 \times 10^{-4} \text{ m}$
3. $6.5 \times 10^{-5} \text{ m}$
4. $12.4 \times 10^{-4} \text{ m}$

Solution:

$\text{From the relation}$ $\frac{I}{O} = \frac{v}{u}$ $\text{Here, } O = 1.39 \times 10^9 \text{ m, } v = 0.1 \text{ m,}$ $u = 1.5 \times 10^{11} \text{ m}$ $\therefore I = \frac{0.1}{1.5 \times 10^{11}} \times 1.39 \times 10^9$ $= 9.2 \times 10^{-4} \text{ m}$

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
}