Import Question JSON

Current Question (ID: 17527)

Question:

$\text{A plane convex lens } (\mu = 1.5) \text{ has a radius of curvature } 10 \text{ cm.}$ $\text{It is silvered on its plane surface.}$ $\text{The focal length of the lens after silvering is:}$

Options:

1. $10 \text{ cm}$
2. $20 \text{ cm}$
3. $15 \text{ cm}$
4. $25 \text{ cm}$

Solution:

$\text{Equivalent power of combination:}$ $P_{eq} = 2P_L + P_M$ $= 2\left(\mu - 1\right)\left(\frac{1}{R}\right) + 0$ $\text{The required focal length:}$ $f = \frac{1}{P_{eq}} = -\frac{R}{2(\mu-1)} = -\frac{10}{2(1.5-1)} = -10 \text{ cm}$

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
}