Import Question JSON

Current Question (ID: 8895)

Question:

$\text{The displacement time graph of a moving particle is shown in the figure below. The instantaneous velocity of the particle is negative at the point:}$ $\text{The graph shows a curved line with labeled points C, D, E, and F, where the curve rises to a maximum at D, then decreases through E, and rises again toward F.}$

Options:

1. $D$
2. $F$
3. $C$
4. $E$

Solution:

\text{Hint: } v = \frac{dx}{dt} \text{Explanation: The slope of the displacement-time graph is equal to the instantaneous velocity.} \text{The slope of the graph is negative at E.} \text{At point E, the curve is decreasing, which means the slope } \frac{dx}{dt} \text{ is negative.} \text{Since velocity equals the slope of the displacement-time graph, the instantaneous velocity is negative at point E.} \text{Hence, option (4) 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
}