Import Question JSON

Current Question (ID: 18954)

Question:

$\text{A physical quantity } Q \text{ depends on other physical quantities } a, b \text{ and } c$ $\text{as } Q = \frac{a^4b^3}{c^2}. \text{ If the maximum percentage error in measurement of }$ $a, b \text{ and } c \text{ are } 3\%, 4\% \text{ and } 5\% \text{ respectively, then the maximum}$ $\text{percentage error in measurement of } Q \text{ is:}$

Options:

1. $34\%$
2. $40\%$
3. $32\%$
4. $45\%$

Solution:

$\frac{\Delta Q}{Q} \times 100 = 4 \left( \frac{\Delta a}{a} \times 100 \right) + 3 \left( \frac{\Delta b}{b} \times 100 \right) + 2 \left( \frac{\Delta c}{c} \right)$ $Q = \frac{a^4b^3}{c^2}$ $\frac{\Delta Q}{Q} = 4 \frac{\Delta a}{a} + 3 \frac{\Delta b}{b} + 2 \frac{\Delta c}{c}$ $\frac{\Delta Q}{Q} \times 100 = 4(3) + 3(4) + 2(5)$ $= 12 + 12 + 10$ $\% \text{ error } \frac{\Delta Q}{Q} \% = 34\%$

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
}