Import Question JSON

Current Question (ID: 17491)

Question:

$\text{In the figure shown the angle made by the light ray with the normal in the medium of refractive index } \sqrt{2} \text{ is:}$ $n_1 = 1$ $n_2 = \sqrt{3}$ $n_3 = \sqrt{2}$ $n_4 = 2$ $n_5 = 1.6$

Options:

1. $30^\circ$
2. $60^\circ$
3. $90^\circ$
4. $\text{None of these}$

Solution:

$n_1 \sin 45^\circ = n_3 \sin \theta$ $\Rightarrow \left(1\right) \left(\frac{1}{\sqrt{2}}\right) = \sqrt{2} \sin \theta$ $\Rightarrow \sin \theta = \frac{1}{2} \Rightarrow \theta = 30^\circ$

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
}