Import Question JSON

Current Question (ID: 17519)

Question:

$\text{A glass sphere } \left( \mu = \frac{3}{2} \right) \text{ of radius } 12 \text{ cm has a small mark at a distance of } 3 \text{ cm from its centre. Where will this mark appear when it is viewed from the side nearest to the mark along the line joining the centre and the mark?}$

Options:

1. $8 \text{ cm inside the sphere}$
2. $12 \text{ cm inside the sphere}$
3. $4 \text{ cm inside the sphere}$
4. $3 \text{ cm inside the sphere}$

Solution:

$\text{Taking } u, v \text{ according to the sign convention}$ $u = -9 \text{ cm}, R = -12 \text{ cm}, \text{ and } \mu_1 = \frac{3}{2}, \mu_2 = 1,$ $\text{Applying refraction at the curved surface for:}$ $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$ $\frac{1}{v} - \frac{3/2}{-9} = \frac{1 - (3/2)}{-12}$ $\Rightarrow v = -8 \text{ cm}$ $\text{Hence, option (1) is the correct answer.}$

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
}