Import Question JSON

Current Question (ID: 8785)

Question:

$\text{In certain vernier callipers, 25 divisions on the vernier scale have the same length as 24 divisions on the main scale. One division on the main scale is 1 mm long. The least count of the instrument is:}$

Options:

1. $0.04 \text{ mm}$
2. $0.01 \text{ mm}$
3. $0.02 \text{ mm}$
4. $0.08 \text{ mm}$

Solution:

$\text{Hint: L.C. = 1MSD - 1VSD}$ $\text{Step: Find the least count of the vernier calliper.}$ $\text{L.C.} = 1\text{MSD} - 1\text{VSD}$ $25\text{VSD} = 24\text{MSD}$ $\Rightarrow 1\text{VSD} = \frac{24}{25} \text{MSD}$ $\Rightarrow \text{L.C.} = 1\text{MSD} - \frac{24}{25} \text{MSD}$ $= \frac{1}{25} \text{MSD}$ $= \frac{1}{25} \text{ mm}$ $\Rightarrow \text{L.C.} = 0.04 \text{ mm}$ $\text{Therefore, the least count of vernier calliper is 0.04 mm.}$ $\text{Hence, option (1) is the correct answer.}$

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
}