Import Question JSON

Current Question (ID: 16439)

Question:

$\text{The net dipole moment of the system is of the magnitude:}$

Options:

1. $q \times 2a$
2. $2q \times 2a$
3. $q \times a$
4. $2 \times (2q \times 2a)$

Solution:

$p_1 = q \times 2a$ $p_2 = q \times 2a$ $p_{\text{net}} = \sqrt{p_1^2 + p_2^2 + 2p_1p_2 \cos 120^\circ}$ $= \sqrt{p^2 + p^2 + 2p^2 \left(-\frac{1}{2}\right)} \quad [p_1 = p_2 = p]$ $p_{\text{net}} = \sqrt{p^2} = p = q \times 2a$

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
}