Import Question JSON

Current Question (ID: 17532)

Question:

$\text{A biconvex lens is cut into two halves along (i) } XOX' \text{ and (ii) } YOY' \text{ as shown in the figure. Let } f, f', f'' \text{ be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively.}$

Options:

1. $f' = f, f'' = 2f$
2. $f' = 2f, f'' = f$
3. $f' = f, f'' = f$
4. $f' = 2f, f'' = 2f$

Solution:

$f \text{ (complete lens)}$ $f' = f \text{ (half along } XOX')$ $f'' = 2f \text{ (half along } YOY')$

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
}