Import Question JSON

Current Question (ID: 17486)

Question:

$\text{A point object is moving on the principal axis of a concave mirror of focal length } 24 \text{ cm towards the mirror.}$ $\text{When it is at a distance of } 60 \text{ cm from the mirror, its velocity is } 9 \text{ cm/sec.}$ $\text{What is the velocity of the image at that instant?}$

Options:

1. $5 \text{ cm/sec towards the mirror}$
2. $4 \text{ cm/sec towards the mirror}$
3. $4 \text{ cm/sec away from the mirror}$
4. $9 \text{ cm/sec away from the mirror}$

Solution:

$v_i = -\left( \frac{f}{f-u} \right)^2 v_0 = -\left( \frac{-24}{-24-(-60)} \right)^2 \times 9 = -4 \text{ cm/sec.}$

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
}