Import Question JSON

Current Question (ID: 18907)

Question:

$\text{A student measured the length of a rod and wrote its as } 3.50 \text{ cm.}$ $\text{Which instrument did he use to measure it?}$

Options:

1. $\text{A vernier calliper where the 10 divisions in the vernier scale match with 9 divisions in the main scale and main scale has 10 divisions in } 1 \text{ cm.}$
2. $\text{A screw gauge having 100 divisions in the circular scale and pitch as } 1 \text{ mm.}$
3. $\text{A screw gauge having 50 divisions in the circular scale and pitch as } 1 \text{ mm.}$
4. $\text{A meter-scale.}$

Solution:

$\text{Hint: The least count of the instrument used must be } 0.01 \text{ cm.}$ $\text{Vernier caliper}$ $10 \text{ divisions is vernier scale}$ $= 9 \text{ divisions in main scale}$ $\Rightarrow 10V = 9S$ $\Rightarrow V = \frac{9}{10}S$ $\Rightarrow \text{Least count} = S - V = \left( \frac{1}{10} \right)(S)$ $\Rightarrow \text{Least count} = \left( \frac{1}{10} \right)(0.1 \text{ cm}) = 0.01 \text{ cm}$

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
}