Import Question JSON

Current Question (ID: 17521)

Question:

$\text{A spherical fishbowl of radius } 15 \text{ cm is filled with water of refractive index } \frac{4}{3}. \text{ A cat standing outside in the air at a distance of } 30 \text{ cm from the centre of the fishbowl is looking at the fish. At what distance from the centre would the cat appear to the fish situated at the centre?}$

Options:

1. $45 \text{ cm}$
2. $30 \text{ cm}$
3. $15 \text{ cm}$
4. $25 \text{ cm}$

Solution:

$\text{Using formula:}$ $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{(\mu_2 - \mu_1)}{R}$ $\Rightarrow \frac{4/3}{v} - \frac{1}{-15} = \frac{(4/3 - 1)}{15}$ $\Rightarrow \frac{4}{3v} + \frac{1}{15} = \frac{1}{45}$ $v = -30 \text{ cm}$ $\text{Distance from fish} = 15 + 30 = 45 \text{ cm}$

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
}