Import Question JSON

Current Question (ID: 17494)

Question:

$\text{Two slabs } P \text{ and } Q \text{ of transparent materials have a thickness in the ratio } 2 : 5. \text{ If a ray of light takes the same amount of time to move from } A \text{ to } B \text{ and } B \text{ to } C, \text{ then the refractive index of } Q \text{ with respect to } P \text{ will be:}$

Options:

1. $0.4$
2. $2.5$
3. $1.4$
4. $1.85$

Solution:

$\text{Let the thickness of slab } P \text{ be } 2x \text{ and that of } Q \text{ be } 5x. \text{ Since the time taken is the same, we have:}$ $\frac{2x}{v_P} = \frac{5x}{v_Q}$ $\Rightarrow \frac{v_Q}{v_P} = \frac{5}{2}$ $\text{Refractive index } n = \frac{c}{v}$ $\Rightarrow \frac{n_Q}{n_P} = \frac{v_P}{v_Q} = \frac{2}{5}$ $\text{Thus, the refractive index of } Q \text{ with respect to } P \text{ is } 0.4.$

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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
}