Import Question JSON

Current Question (ID: 18921)

Question:

$\text{A screw gauge has } 50 \text{ divisions on its circular scale. The circular scale is } 4 \text{ units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of } 0.5 \text{ mm is noticed on the pitch scale. The nature of the zero error involved and the last count of the screw gauge are respectively:}$

Options:

1. $\text{Positive, } 10 \, \mu \text{m}$
2. $\text{Negative, } 2 \, \mu \text{m}$
3. $\text{Positive, } 0.1 \, \mu \text{m}$
4. $\text{Positive, } 0.1 \, \mu \text{m}$

Solution:

$\text{Least count of screw gauge} = \frac{\text{Pitch}}{\text{Number of division on circular scale}}$ $= \frac{0.5}{50} \, \text{mm} = 1 \times 10^{-5} \, \text{m}$ $= 10 \, \mu \text{m}$ $\text{Zero error in positive}$

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
}