Import Question JSON

Current Question (ID: 8878)

Question:

$\text{Starting from rest, a car accelerates uniformly at the rate of } 1 \text{ m/s}^2 \text{ for some time, then decelerates uniformly at the rate of } 2 \text{ m/s}^2 \text{ and finally comes to rest after a journey of } 1 \text{ minute. The maximum possible speed of the car during this journey is:}$

Options:

1. $10 \text{ m/s}$
2. $20 \text{ m/s}$
3. $30 \text{ m/s}$
4. $40 \text{ m/s}$

Solution:

\text{Hint: } v_{max} = (\alpha \beta T)/(\alpha + \beta) \text{Step: Find the maximum speed.} \text{The maximum velocity of the particle is given by:} v_{max} = (\alpha \beta T)/(\alpha + \beta) \text{where:} \text{α = acceleration of the car} \text{β = deceleration of the car} \text{T = total time of the journey} \text{Calculation:} v_{max} = (1 × 2 × 60)/(1 + 2) = 120/3 = 40 \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
}