Import Question JSON

Current Question (ID: 19071)

Question:

$\text{A train starting from rest first accelerates uniformly up to a speed of } 80 \text{ km/h for time } t, \text{ then it moves with a constant speed for time } 3t. \text{ The average speed of the train for this duration of the journey will be (in km/h):}$

Options:

1. $30$
2. $80$
3. $40$
4. $70$

Solution:

$\text{The train accelerates to } 80 \text{ km/h in time } t. \text{ It then travels at this speed for time } 3t. \text{ Total distance } = \frac{1}{2} \times 80 \times t + 80 \times 3t = 40t + 240t = 280t. \text{ Total time } = t + 3t = 4t. \text{ Average speed } = \frac{\text{Total distance}}{\text{Total time}} = \frac{280t}{4t} = 70 \text{ km/h.}$

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
}