Import Question JSON

Current Question (ID: 5)

Question:

\text{In an experiment the initial number of radioactive nuclei is 3000, It is found that } 1000 \pm 40 \text{ nuclei decayed in the first } 1.0 \text{ s. For } |x| \ll 1, \ln(1 + x) = x \text{ up to first power in } x. \text{ The error } \Delta\lambda, \text{ in the determination of the decay constant } \lambda, \text{ in } s^{-1}, \text{ is}

Options:

1. 0.04
2. 0.03
3. 0.02
4. 0.01

Solution:

\text{The relation between } [\varepsilon_0] \text{ and } [\mu_0] \text{ is}

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
}