Import Question JSON

Current Question (ID: 8937)

Question:

$\text{A particle moving in unidirectional motion travels half of the total distance with a constant speed of 15 m/s.}$ $\text{Now the first half of the remaining journey time, it travels at 10 m/s, and the second half of the remaining journey time, it travels at 5 m/s.}$ $\text{The average speed of the particle is:}$

Options:

1. $12 \text{ m/s}$
2. $10 \text{ m/s}$
3. $7 \text{ m/s}$
4. $15 \text{ m/s}$

Solution:

$\text{Hint: } v_{avg} = \frac{2v_1v_2}{v_1+v_2}$ $\text{Step: Find the average velocity of the given particle.}$ $v_{avg} = \frac{2v_1v_2}{v_1+v_2}$ $\text{Here, } v_2 = \frac{v_3+v_4}{2} = \frac{10+5}{2} = 7.5$ $v_{avg} = \frac{2 \times 15 \times 7.5}{15+7.5} = \frac{225}{22.5}$ $v_{avg} = 10 \text{ m/s}$ $\text{Hence, Option (2) is the correct answer.}$

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
}