Import Question JSON

Current Question (ID: 18989)

Question:

$\text{A screw gauge of pitch } 0.5 \text{ mm is used to measure the diameter of uniform wire of length } 6.8 \text{ cm, the main scale reading is } 1.5 \text{ mm and circular scale reading is } 7. \text{ The calculated curved surface area of wire to the appropriate significant figures is:}$ $[\text{Screw gauge has } 50 \text{ divisions on the circular scale}]$

Options:

1. $6.8 \text{ cm}^2$
2. $3.4 \text{ cm}^2$
3. $3.9 \text{ cm}^2$
4. $2.4 \text{ cm}^2$

Solution:

$\text{The least count of the screw gauge is } \frac{0.5}{50} = 0.01 \text{ mm.}$ $\text{Total reading} = 1.5 + 7 \times 0.01 = 1.57 \text{ mm} = 0.157 \text{ cm.}$ $\text{Curved surface area} = \pi \times \text{diameter} \times \text{length} = \pi \times 0.157 \times 6.8 = 3.36 \text{ cm}^2.$ $\text{To appropriate significant figures, the answer is } 3.4 \text{ cm}^2.$

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
}