Import Question JSON

Current Question (ID: 8810)

Question:

$\text{The figure gives the } (x-t) \text{ plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals } 1, 2 \text{ and } 3, \text{ respectively are:}$

Options:

1. $-, -, +$
2. $+, -, +$
3. $-, +, +$
4. $+, +, -$

Solution:

\text{Hint: } \vec{v}_{\text{average}} = \frac{\vec{x}_2 - \vec{x}_1}{t_2 - t_1} \text{Step: Find the sign of total displacement in each case.} \text{The average velocity} = \frac{\Delta s}{\Delta t} \text{For intervals 1 and 2: } \Delta s > 0 \text{ (displacement is positive)} \text{For interval 3: } \Delta s < 0 \text{ (displacement is negative)} \text{If } \Delta s > 0 \text{, average velocity is positive} \Delta s > 0 \text{ in cases (1) and (2)} \Delta s < 0 \text{ in case (3)} \text{The signs of average velocity are positive, positive, and negative.} \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
}