Import Question JSON

Current Question (ID: 18981)

Question:

$\text{A silver wire has a mass } (0.6 \pm 0.006) \text{ g, radius } (0.5 \pm 0.005) \text{ mm}$ $\text{and length } (4 \pm 0.04) \text{ cm. The maximum percentage error in the}$ $\text{measurement of its density will be:}$

Options:

1. $4\%$
2. $3\%$
3. $6\%$
4. $7\%$

Solution:

$\text{The formula for density } \rho = \frac{m}{V} = \frac{m}{\pi r^2 l}$ $\text{Percentage error in } \rho = \left( \frac{\Delta m}{m} + 2 \frac{\Delta r}{r} + \frac{\Delta l}{l} \right) \times 100$ $= \left( \frac{0.006}{0.6} + 2 \times \frac{0.005}{0.5} + \frac{0.04}{4} \right) \times 100 = 4\%$

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
}