Import Question JSON

Current Question (ID: 19423)

Question:

$\text{The torque of a force } 5\hat{i} + 3\hat{j} - 7\hat{k} \text{ about the origin is } \tau. \text{ If the force acts on a particle whose position vector is } 2\hat{i} + 2\hat{j} + \hat{k}, \text{ then the value of } \tau \text{ will be:}$

Options:

1. $11\hat{i} + 19\hat{j} - 4\hat{k}$
2. $-11\hat{i} + 9\hat{j} - 16\hat{k}$
3. $-17\hat{i} + 19\hat{j} - 4\hat{k}$
4. $17\hat{i} + 9\hat{j} + 16\hat{k}$

Solution:

$\text{Hint: } \vec{\tau} = \vec{r} \times \vec{F}$

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
}