Import Question JSON

Current Question (ID: 18970)

Question:

$\text{Using a screw gauge with pitch } 0.1 \text{ cm and } 50 \text{ divisions on its circular scale, the thickness of an object is measured. It should be accurately recorded as:}$ $1.\ 2.124\ \text{cm}$ $2.\ 2.121\ \text{cm}$ $3.\ 2.125\ \text{cm}$ $4.\ 2.123\ \text{cm}$

Options:

1. $2.124\ \text{cm}$
2. $2.121\ \text{cm}$
3. $2.125\ \text{cm}$
4. $2.123\ \text{cm}$

Solution:

$\text{Hint: Measurement should be an integral multiple of least count.}$ $\text{Step: Find the value of the measurement.}$ $\text{The least count of the screw gauge is given by:}$ $LC = \frac{\text{pitch}}{\text{CSD}}$ $\Rightarrow LC = \frac{0.1\ \text{cm}}{50} = 0.002\ \text{cm}$ $\text{So, the measurement will be an integral multiple of } LC \text{ i.e.,}$ $2.124 = 0.002 \times 1070$ $\text{Therefore, the correct measurement is } 2.124\ \text{cm.}$ $\text{Hence, option (1) is the correct answer.}$

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
}