Import Question JSON

Current Question (ID: 8827)

Question:

$\text{The position-time } (x-t) \text{ graphs for two children } A \text{ and } B \text{ returning from their school } O \text{ to their homes } P \text{ and } Q \text{ respectively are shown in the graph. Choose the incorrect statement.}$

Options:

1. $B \text{ reaches home faster than } A\text{.}$
2. $B \text{ overtakes } A \text{ on the road twice.}$
3. $B \text{ walks faster than } A\text{.}$
4. $A \text{ lives closer to the school than } B\text{.}$

Solution:

$\text{Hint: The position is given by the x-coordinate of the graph and the velocity is given by the slope of the graph.}$ $\text{Step 1: Find the x-coordinate of the graphs.}$ $A \text{ reaches home in time } t_2\text{.}$ $B \text{ reaches home in time } t_1\text{.}$ $\text{As } t_2 > t_1\text{, } B \text{ reaches home first.}$ $\text{Step 2: Find the slope of the graphs.}$ $B \text{ walks faster than } A \text{ \& } B \text{ overtakes } A \text{ only once.}$ $\text{Hence, Option (2) is the correct answer.}$

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
}