Import Question JSON

Current Question (ID: 8788)

Question:

$\text{A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm.}$ $\text{The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level.}$ $\text{If the screw gauge has a zero error of } -0.004 \text{ cm, the correct diameter of the ball is:}$

Options:

1. $0.521 \text{ cm}$
2. $0.525 \text{ cm}$
3. $0.053 \text{ cm}$
4. $0.529 \text{ cm}$

Solution:

$\text{The reading of the screw gauge is given by;}$ $= \text{MSR} + \text{CSR} - \text{Zero Error}$ $= 0.5 \text{ cm} + 0.001 \times 25 \text{ cm} - (-0.004 \text{ cm})$ $= 0.529 \text{ cm}$ $\text{Therefore, the correct diameter of the ball is 0.529 cm.}$ $\text{Hence, option (4) is the correct answer.}$

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
}