Import Question JSON

Current Question (ID: 19033)

Question:

$\text{A scooter accelerates from rest for time } t_1 \text{ at constant rate } a_1 \text{ and then retards at constant rate } a_2 \text{ for time } t_2 \text{ and comes to rest. The correct value of } \frac{t_1}{t_2} \text{ will be:}$

Options:

1. $\frac{a_1 + a_2}{a_2}$
2. $\frac{a_2}{a_1}$
3. $\frac{a_1}{a_1 + a_2}$
4. $\frac{a_2}{a_1 + a_2}$

Solution:

$\text{Hint: Draw v-t curve.}$ $\tan \theta_1 = a_1 = \frac{v_{\text{max}}}{t_1}$ $\& \tan \theta_2 = a_2 = \frac{v_{\text{max}}}{t_2}$ $\div \text{ above}$ $\frac{t_1}{t_2} = \frac{a_2}{a_1}$

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
}