Import Question JSON

Current Question (ID: 19052)

Question:

$\text{A particle is moving along a straight line, and its displacement at time } t \text{ seconds is given by:}$ $S = (2t^2 + 5) \text{ (in metres)}$ $\text{What is the velocity of the particle at } t = 1 \text{ s?}$

Options:

1. $4 \text{ m/s}$
2. $2 \text{ m/s}$
3. $6 \text{ m/s}$
4. $7 \text{ m/s}$

Solution:

$\text{Hint: } v = \frac{dS}{dt}$ $\text{Step 1: Find the expression for velocity.}$ $v = \frac{dS}{dt}$ $\Rightarrow v = 4t$ $\text{Step 2: Find the velocity of the particle at } t = 1 \text{ s.}$ $v = 4t$ $\Rightarrow v_{t=1} = 4 \times 1$ $\Rightarrow v_{t=1} = 4 \text{ m/s}$ $\text{Hence, option (1) is the correct answer.}$

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
}