Import Question JSON

Current Question (ID: 19008)

Question:

$\text{In finding out refractive index of glass slab the following observations were made through travelling microscope } 50 \text{ vernier scale division} = 49 \text{ MSD} ; 20 \text{ divisions on main scale in each cm}$ $\text{For mark on paper: } MSR = 8.45 \text{ cm}, VC = 26$ $\text{For mark on paper seen through slab: } MSR = 7.12 \text{ cm}, VC = 41$ $\text{For powder particle on the top surface of the glass slab: } MSR = 4.05 \text{ cm}, VC = 1$ $(MSR = \text{Main Scale Reading}, VC = \text{Vernier Coincidence})$ $\text{Refractive index of the glass slab is:}$

Options:

1. 1.24
2. 1.35
3. 1.42
4. 1.52

Solution:

$\text{Refractive index } n = \frac{\text{Real thickness}}{\text{Apparent thickness}}$ $\text{Real thickness} = (MSR + \frac{VC}{50}) \text{ for top surface}$ $= 4.05 + \frac{1}{50} = 4.07 \text{ cm}$ $\text{Apparent thickness} = (MSR + \frac{VC}{50}) \text{ for mark seen through slab}$ $= 7.12 + \frac{41}{50} = 7.94 \text{ cm}$ $\text{Refractive index } n = \frac{4.07}{7.94} = 1.42$

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
}