Import Question JSON

Current Question (ID: 8782)

Question:

$\text{If } x = 10.0 \pm 0.1 \text{ and } y = 10 \pm 0.1, \text{ then } 2x - 2y \text{ with consideration of significant figures is equal to:}$

Options:

1. $\text{zero}$
2. $0.0 \pm 0.1$
3. $0.0 \pm 0.2$
4. $0.0 \pm 0.4$

Solution:

\text{Hint: For finding absolute error, we will find the maximum error.} \text{Step 1: Consider two new quantities, a and b.} \text{Thus, } a = 2x \text{ where } \Delta a = 2\Delta x = 0.2 b = 2y \text{ where } \Delta b = 2\Delta y = 0.2 c = a - b \text{Mean value of } c = 0 \text{Step 2: Find the reporting value of the given quantity.} \text{For maximum error,} \Delta a + \Delta b = 0.4 \text{Therefore, the reporting value is } 0.0 \pm 0.4 \text{Hence, option (4) is the correct answer.}

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
}