Import Question JSON

Current Question (ID: 10201)

Question:

$\text{If a body is moving in a circular path with decreasing speed, then (symbols have their usual meanings):}$

Options:

1. $\vec{r} \cdot \vec{\omega} = 0$
2. $\vec{\tau} \cdot \vec{v} = 0$
3. $\vec{a} \cdot \vec{v} < 0$
4. $\text{All of these}$

Solution:

\text{1. } \vec{r} \cdot \vec{\omega} = 0 \text{: True} \text{Reason: } \vec{r} \text{ is in plane, } \vec{\omega} \text{ is perpendicular to plane} \text{2. } \vec{\tau} \cdot \vec{v} = 0 \text{: True} \text{Reason: } \vec{\tau} \text{ perpendicular to plane, } \vec{v} \text{ in plane} \text{3. } \vec{a} \cdot \vec{v} < 0 \text{: True} \text{Reason: Speed decreasing, so } \vec{a} \text{ opposes } \vec{v} \text{Answer: 4. All of these}

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
}