Import Question JSON

Current Question (ID: 8817)

Question:

$\text{A car is moving along a straight line, say OP in the figure. It moves from O to P in 18 s and returns from P to O in 6.0 s. The average velocity and average speed of the car in going from O to P and back to O respectively are:}$

Options:

1. $10 \text{ m/s \& } 10 \text{ m/s}$
2. $20 \text{ m/s \& } 30 \text{ m/s}$
3. $20 \text{ m/s \& } 20 \text{ m/s}$
4. $10 \text{ m/s \& } 20 \text{ m/s}$

Solution:

$\text{Hint:}$ $\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total time taken}}\text{, Average Speed} = \frac{\text{Total Distance}}{\text{Total time taken}}$ $\text{Step 1: Find the average velocity.}$ $\text{Average velocity} = \frac{\text{Total Displacement}}{\text{Total time taken}} = \frac{240}{18 + 6} \Rightarrow 10 \text{ m/s}$ $\text{Step 2: Find the average speed.}$ $\text{Average speed} = \frac{\text{Total Path length}}{\text{Total time taken}} = \frac{OP + PO}{\Delta T} \Rightarrow \frac{360 + 120}{24} = 20 \text{ m/s}$ $\text{Hence, option (4) is the correct answer.}$

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
}