Import Question JSON

Current Question (ID: 17516)

Question:

$\text{The following diagram shows a glass sphere of radius } 10 \text{ cm with a paraxial incident ray.}$ $\text{The refractive index of the material of the glass is:}$

Options:

1. $2$
2. $1.5$
3. $1.75$
4. $1.3$

Solution:

$\text{Hint: Use Snell's law.}$ $\text{Step 1: Find } u, v \text{ and } R \text{ according to sign convention.}$ $u = -\infty$ $v = 20 \text{ cm}$ $R = 10 \text{ cm}$ $\text{Step 2: Apply the formula for refraction at the curved surface.}$ $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$ $\frac{\mu_2}{20} - \frac{1}{-\infty} = \frac{\mu_2 - 1}{10}$ $\Rightarrow \mu_2 = 2$

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
}