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Current Question (ID: 8758)

Question:

$\text{A physical quantity } A \text{ is related to four observable quantities } a, b, c \text{ and } d \text{ as follows, } A = \frac{a^2 b^3}{c\sqrt{d}}, \text{ the percentage errors of measurement in } a, b, c \text{ and } d \text{ are } 1\%, 3\%, 2\% \text{ and } 2\% \text{ respectively. The percentage error in quantity } A \text{ will be:}$

Options:

1. $12\%$
2. $7\%$
3. $5\%$
4. $14\%$

Solution:

$\text{Hint: Recall the percentage error.}$ $\text{Step: Find the percentage error in quantity } A.$ $\text{The physical quantity } A \text{ is given as; } A = \frac{a^2 b^3}{c\sqrt{d}}$ $\text{The percentage error in quantity } A \text{ is given by;}$ $\Rightarrow \left( \frac{\Delta A}{A} \times 100 \right) = 2 \times \left( \frac{\Delta a}{a} \times 100 \right) + 3 \times \left( \frac{\Delta b}{b} \times 100 \right) + 1 \times \left( \frac{\Delta c}{c} \times 100 \right) + \frac{1}{2} \times \left( \frac{\Delta d}{d} \times 100 \right)$ $\Rightarrow \left( \frac{\Delta A}{A} \times 100 \right) = (2 \times 1 + 3 \times 3 + 1 \times 2 + \frac{1}{2} \times 2)\% = 14\%$ $\text{Hence, option (4) is the correct answer.}$

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
}