Import Question JSON

Current Question (ID: 17539)

Question:

$\text{A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point } 15 \text{ cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move } 5 \text{ cm closer to the lens. The focal length of the lens is:}$

Options:

1. $-10 \text{ cm}$
2. $20 \text{ cm}$
3. $-30 \text{ cm}$
4. $5 \text{ cm}$

Solution:

$\text{Given } u = 10 \text{ cm}, v = 15 \text{ cm.}$ $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ $\frac{1}{f} = \frac{1}{15} - \frac{1}{10}$ $\frac{1}{f} = \frac{10 - 15}{150}$ $\frac{1}{f} = \frac{-5}{150}$ $f = -30 \text{ cm}$

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
}