Import Question JSON

Current Question (ID: 17487)

Question:

$\text{A concave mirror of focal length } f \text{ produces an image } n \text{ times the size of the object. If the image is real, then the distance of the object from the mirror is:}$

Options:

1. $(n - 1)f$
2. $\frac{(n - 1)}{n}f$
3. $\frac{(n + 1)}{n}f$
4. $(n + 1)f$

Solution:

$\text{Since the image formed is real, it must be inverted \& the magnification ratio must be negative. So,}$ $\text{magnification} = \frac{-v}{u}$ $-n = \frac{-v}{d}, \ u = -d$ $v = -nd$ $\text{From mirror formula:}$ $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ $\frac{1}{-f} = \frac{1}{-nd} + \frac{1}{-d}$ $d = \frac{f(n+1)}{n}$

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
}