Import Question JSON

Current Question (ID: 17566)

Question:

$\text{The Refractive index of material of an equilateral prism is } \sqrt{2}. \text{ Angle of incidence for minimum deviation is:}$ $1.\ 60^\circ$ $2.\ 45^\circ$ $3.\ 30^\circ$ $4.\ 15^\circ$

Options:

1. $60^\circ$
2. $45^\circ$
3. $30^\circ$
4. $15^\circ$

Solution:

$\text{for minimum deviation}$ $r_1 = r_2$ $\Rightarrow r_1 + r_2 = 60^\circ \Rightarrow 2r_1 = 60^\circ \Rightarrow r_1 = 30^\circ$ $\text{then, } \sin i = \mu \sin r_1$ $\Rightarrow \sin i = \sqrt{2} \sin 30^\circ$ $\Rightarrow \frac{1}{\sqrt{2}} = \sin i$ $\Rightarrow \angle i = 45^\circ$

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
}