Import Question JSON

Current Question (ID: 20429)

Question:

$\text{An electron with energy } 0.1 \text{ keV moves at right angle to the earth's magnetic field of } 1 \times 10^{-4} \text{ Wbm}^{-2}. \text{ The frequency of revolution of the electron will be}$ $\text{(Take mass of electron } = 9.0 \times 10^{-31} \text{ kg)}$

Options:

1. $1.6 \times 10^5 \text{ Hz}$
2. $5.6 \times 10^5 \text{ Hz}$
3. $2.8 \times 10^6 \text{ Hz}$
4. $1.8 \times 10^6 \text{ Hz}$

Solution:

$\text{The frequency of revolution is given by } f = \frac{qB}{2\pi m}$ $\text{where } q = 1.6 \times 10^{-19} \text{ C, } B = 1 \times 10^{-4} \text{ Wb/m}^2, \text{ and } m = 9.0 \times 10^{-31} \text{ kg}$ $f = \frac{1.6 \times 10^{-19} \times 1 \times 10^{-4}}{2\pi \times 9.0 \times 10^{-31}} = 2.8 \times 10^6 \text{ Hz}$

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
}