Import Question JSON

Current Question (ID: 17480)

Question:

$\text{A concave mirror gives an image three times as large as the object placed at a distance of } 20 \text{ cm from it. For the image to be real, the focal length should be:}$

Options:

1. $10 \text{ cm}$
2. $15 \text{ cm}$
3. $20 \text{ cm}$
4. $30 \text{ cm}$

Solution:

$\text{Hint: The magnification } m = \frac{f}{f-u}$ $\text{Step: Find the focal length for the image.}$ $\text{Write } 'u' \text{ and } 'm' \text{ according to the sign convention}$ $m = -3$ $u = -20 \text{ cm}$ $\text{The formula for magnification for the mirror is given by:}$ $m = \frac{f}{f-u}$ $-3 = \frac{f}{f+20}$ $-60 = 4f$ $\Rightarrow f = -15 \text{ cm}$ $\text{Hence, option (2) is the correct answer.}$

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
}