Import Question JSON

Current Question (ID: 19030)

Question:

$\text{If the velocity-time graph has the shape } AMB, \text{ what would be the shape of the corresponding acceleration-time graph?}$

Options:

1. $\begin{array}{c} \vec{a} \\ \text{(graph 1)} \end{array}$
2. $\begin{array}{c} \vec{a} \\ \text{(graph 2)} \end{array}$
3. $\begin{array}{c} \vec{a} \\ \text{(graph 3)} \end{array}$
4. $\begin{array}{c} \vec{a} \\ \text{(graph 4)} \end{array}$

Solution:

$\text{Hint: The slope of the v-t curve gives acceleration.}$ $\text{Step 1: Compare the slopes in various regions.}$ $\text{In the ADM region: the slope (AM) is negative}$ $\text{In the BCM region: the slope (MB) is positive}$ $\text{The magnitude of the slope (AM and MB) is the same in both cases as shown in the figure.}$ $\text{Step 2: Compare acceleration in various regions.}$ $\text{AM: acceleration is negative and constant.}$ $\text{MB: acceleration is positive and constant}$ $\text{In both cases, acceleration is constant and has the same magnitude.}$ $\text{Therefore, option (2) represents the correct acceleration-time graph.}$ $\text{Hence, option (2) is the correct answer.}$

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
}