Import Question JSON

Current Question (ID: 19073)

Question:

$\text{A particle moving in a straight line covers half the distance with speed } 6 \text{ m/s.}$ $\text{The other half is covered in two equal time intervals with speeds } 9 \text{ m/s and } 15 \text{ m/s respectively.}$ $\text{The average speed of the particle during the motion is:}$

Options:

1. $8.8 \text{ m/s}$
2. $8 \text{ m/s}$
3. $9.2 \text{ m/s}$
4. $10 \text{ m/s}$

Solution:

$\text{Let the total distance be } 2d. \text{ Half the distance is } d. \text{ Time taken for first half: } t_1 = \frac{d}{6}.$ $\text{For the second half, let the time intervals be } t_2 \text{ and } t_3.$ $t_2 = t_3, \text{ so } \frac{d/2}{9} = \frac{d/2}{15}.$ $\text{Average speed } = \frac{\text{Total distance}}{\text{Total time}} = \frac{2d}{t_1 + t_2 + t_3}.$ $= \frac{2d}{\frac{d}{6} + \frac{d/2}{9} + \frac{d/2}{15}} = 8 \text{ m/s}$

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
}