Import Question JSON

Current Question (ID: 8760)

Question:

$\text{The thickness of a pencil measured by using a screw gauge (least count 0.001 cm) comes out to be 0.802 cm. The percentage error in the measurement is:}$

Options:

1. $0.125\%$
2. $2.43\%$
3. $4.12\%$
4. $2.14\%$

Solution:

$\text{Hint: Absolute error is the same as the least count of the instrument.}$ $\text{Step 1: Find the absolute error of the instrument.}$ $\Delta t = \text{Least count} = 0.001 \text{ cm}$ $\text{Step 2: Find the percentage error in the measurement.}$ $\Rightarrow \left( \frac{\Delta t}{t} \times 100 \right) = \left( \frac{0.001}{0.802} \times 100 \right) = 0.125\%$ $\text{Hence, option (1) is the correct answer.}$

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
}