Import Question JSON

Current Question (ID: 19110)

Question:

$\text{A particle has an initial } (t = 0) \text{ velocity } \vec{u} = 5\hat{i} \text{ and is at its origin at this instant.}$ $\text{Its acceleration is given by } (3\hat{i} + 4\hat{j}).$ $\text{When the particle's } x \text{ co-ordinate is 16 units, then its speed is:}$

Options:

1. $13 \text{ units}$
2. $\sqrt{161} \text{ units}$
3. $12 \text{ units}$
4. $\sqrt{185} \text{ units}$

Solution:

$\text{Hint: } \vec{v} = \vec{u} + \vec{a}t$ $S = ut + \frac{1}{2}at^2$ $\Rightarrow 16 = 5t + \frac{3}{2}t^2$ $\Rightarrow t = 2$ $\Rightarrow \vec{v} = \vec{u} + \vec{a}t = 11\hat{i} + 8\hat{j}$

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
}