Import Question JSON

Current Question (ID: 18985)

Question:

$\text{The Vernier constant of Vernier callipers is } 0.1 \text{ mm and it has zero error of } (-0.05) \text{ cm.}$ $\text{While measuring the diameter of a sphere, the main scale reading is } 1.7 \text{ cm and the coinciding Vernier division is } 5.$ $\text{The corrected diameter will be:}$

Options:

1. $1.75 \times 10^{-2} \text{ cm}$
2. $1.80 \times 10^{-2} \text{ cm}$
3. $1.75 \times 10^{-2} \text{ cm}$
4. $17.5 \text{ cm}$

Solution:

$\text{Corrected diameter} = \text{Main scale reading} + (\text{Coinciding Vernier division} \times \text{Vernier constant}) + \text{Zero error}$ $= 1.7 + (5 \times 0.01) - 0.05$ $= 1.7 + 0.05 - 0.05$ $= 1.7 \text{ cm}$

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
}