Import Question JSON

Current Question (ID: 17481)

Question:

$\text{A convex mirror of focal length } f \text{ forms an image which is } \frac{1}{n} \text{ times the length of the object. The distance of the object from the mirror is:}$

Options:

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

Solution:

$\text{Hint: } m = \frac{f}{f - u}$ $\text{Step 1: Find the magnification.}$ $m = \frac{h_i}{h_0}$ $= \frac{1}{n}$ $\text{Step 2: Use magnification formula}$ $m = \frac{f}{f - u}$ $\frac{1}{n} = \frac{f}{f - u}$ $nf = f - u$ $u = f(1 - n)$ $\text{Step 3: Find the distance of the object from the mirror.}$ $d = f(n - 1)$

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
}