Import Question JSON

Current Question (ID: 9547)

Question:

\text{A particle starting from the origin } (0, 0) \text{ moves in a straight line in the } (x, y) \text{ plane.} \text{Its coordinates at a later time are } (\sqrt{3}, 3). \text{The path of the particle makes an angle of _______ with the } x\text{-axis.}

Options:

1. $30^\circ$
2. $45^\circ$
3. $60^\circ$
4. $0$

Solution:

$\text{Hint: The angle required can be measured by the slope of the path of the particle.}$ $\text{Step 1: Find the slope of the line.}$ $\tan \theta = \text{slope of line } OA = \frac{AB}{OB} = \frac{3}{\sqrt{3}} = \sqrt{3}$ $\text{Step 2: Find the angle required.}$ $\Rightarrow \tan \theta = \tan 60^\circ$ $\theta = 60^\circ$ $\text{Hence, option (3) is the correct answer.}$

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
}