Import Question JSON

Current Question (ID: 19020)

Question:

$\text{The four graphs below are intended to represent the same motion.}$ $\text{However, one of them is incorrect. Identify the graph that does not}$ $\text{accurately depict the motion.}$

Options:

1. $\text{Velocity vs. Position}$
2. $\text{Distance vs. Time}$
3. $\text{Position vs. Time}$
4. $\text{Velocity vs. Time}$

Solution:

$\text{Hint: The graph represents uniformly accelerated motion.}$ $\text{Step: Identify the incorrect graph.}$ $\text{In the first option, a velocity vs. position graph represents motion}$ $\text{reversing direction, possibly a type of oscillatory motion. So, this}$ $\text{graph is true for periodic motions.}$ $\text{In the second option, a distance vs. time graph initially rises and}$ $\text{then declines, which is incorrect because distance is always}$ $\text{positive and non-decreasing.}$ $\text{In the third option, a position vs. time graph follows a smooth}$ $\text{oscillatory pattern that correctly matches with periodic motion or}$ $\text{oscillations.}$ $\text{In the fourth option, a velocity vs. time graph decreases steadily,}$ $\text{possibly representing deceleration, which is true for motion under}$ $\text{gravity.}$ $\text{Therefore, the incorrect graph is shown in the figure below;}$ $\text{Distance vs. Time}$ $\text{Hence, option (2) is the correct answer.}$

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
}