Import Question JSON

Current Question (ID: 17546)

Question:

$\text{When an object is placed at } 10 \text{ cm and } 30 \text{ cm from a convex lens, images obtained are of the same magnitude of magnification. The focal length of the lens may be:}$

Options:

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

Solution:

$\text{Hint: In one case, real image is formed. In other case, inverted image.}$ $\text{Step 1: Recall magnification formula}$ $m = \frac{f}{f+u}$ $\text{Step 2: Find magnification in both cases}$ $m_1 = \frac{f}{f-10}$ $m_2 = \frac{f}{f-30}$ $\text{Step 3: Apply given conditions on } m_1 \text{ and } m_2$ $m_1 = -m_2$ $\frac{f}{f-10} = \frac{-f}{f-30}$ $\Rightarrow f = 20 \text{ cm}$

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
}