Import Question JSON

Current Question (ID: 18945)

Question:

$\text{If mass, radius of cross-section and height of a cylinder are } (0.4 + 0.01) \text{ g},$ $ (6 + 0.03) \text{ m and height } (8 + 0.04) \text{ m. The maximum}$ $\text{percentage error in the measurement of density of cylinder is:}$ $1. \ 1\%$ $2. \ 4\%$ $3. \ 8\%$ $4. \ 7\%$

Options:

1. $1\%$
2. $4\%$
3. $8\%$
4. $7\%$

Solution:

$\rho = \frac{m}{\pi r^2 h}$ $\frac{\Delta \rho}{\rho} = \pm \left( \frac{\Delta m}{m} + \frac{2 \Delta r}{r} + \frac{\Delta h}{h} \right)$ $= 0.04$

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
}