Import Question JSON

Current Question (ID: 38)

Question:

Let $\vec{a},\vec{b},\vec{c}$be three vectors such that $\vec{a}\bullet (\vec{b}+\vec{c})+\vec{b}\bullet (\vec{c}+\vec{a})+\vec{c}\bullet (\vec{a}+\vec{b})=0$and $\left| {\vec{a}} \right|=1,\,\left| {\vec{b}} \right|=4,\left| {\vec{c}} \right|=8,$then $\left| \vec{a}+\vec{b}+\vec{c} \right|$equals

Options:

1. 13
2. 81
3. 9
4. 5

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
}