Import Question JSON

Current Question (ID: 9549)

Question:

$\text{Coordinates of a particle as a function of time } t \text{ are } x = 2t, y = 4t. \text{ It can be inferred that the path of the particle will be:}$

Options:

1. $\text{Straight line}$
2. $\text{Ellipse}$
3. $\text{Parabola}$
4. $\text{Hyperbola}$

Solution:

$\text{Hint: Relate the } x \text{ and } y \text{ component of the particle.}$ $\text{Step: Find the path traced by the particle.}$ $\text{Given: } x = 2t, \quad y = 4t$ $\Rightarrow y = 2x$ $\text{This is an equation of a straight line.}$ $\text{Therefore, the path traced by the particle is a straight line.}$ $\text{Hence, option (1) is the correct answer.}$

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
}