Import Question JSON

Current Question (ID: 8885)

Question:

$\text{The displacement of a particle is given by } y = a + bt + ct^2 - dt^4. \text{ The initial velocity and acceleration are, respectively:}$

Options:

1. $b, -4d$
2. $-b, 2c$
3. $b, 2c$
4. $2c, -2d$

Solution:

$\text{Hint: } v = \frac{dy}{dt}$ $\text{Step: Find the initial velocity and acceleration.}$ $y = a + bt + ct^2 - dt^4$ $\therefore v = \frac{dy}{dt} = b + 2ct - 4dt^3 \text{ and } a = \frac{dv}{dt} = 2c - 12dt^2$ $\text{So, at } t = 0, v_{\text{initial}} = b \text{ and } a_{\text{initial}} = 2c.$ $\text{Hence, option (3) is the correct answer.}$

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
}