Import Question JSON

Current Question (ID: 19304)

Question:

$\text{A ball was dropped from } 20 \text{ m height from the ground. The height up to which it rises after the collision is: (Use } e = \frac{1}{2}, g = 10 \text{ m/s}^2)$ $\text{1. } 3 \text{ m}$ $\text{2. } 5 \text{ m}$ $\text{3. } 10 \text{ m}$ $\text{4. } 6 \text{ m}$

Options:

1. $3 \text{ m}$
2. $5 \text{ m}$
3. $10 \text{ m}$
4. $6 \text{ m}$

Solution:

$h = \frac{v^2}{2g}$ $v' = ev$ $h' = \frac{(v')^2}{2g} = \frac{e^2v^2}{2g} = e^2h = 0.5^2 \times 20 = \frac{20}{4} = 5 \text{ m}$ $h' = 5 \text{ m}$

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
}