Import Question JSON

Current Question (ID: 8826)

Question:

$\text{The position of an object moving along the x-axis is given by } x = a + bt^2 \text{ where } a = 10 \text{ m}, b = 2 \text{ ms}^{-2} \text{ and } t \text{ is in seconds. The velocity at } t = 3.0 \text{ s is:}$

Options:

1. $12 \text{ ms}^{-1}$
2. $20 \text{ ms}^{-1}$
3. $36 \text{ ms}^{-1}$
4. $46 \text{ ms}^{-1}$

Solution:

$\text{Hint: } v = \frac{dx}{dt}$ $\text{Step 1: Put the value of a \& b in } x = a + bt^2\text{.}$ $\Rightarrow x = 10 + 2t^2$ $\text{Step 2: The velocity at } t = 3.0 \text{ s.}$ $\Rightarrow x = 10 + 2t^2$ $\Rightarrow \frac{dx}{dt} = 4t$ $\Rightarrow v = 4 \times 3 = 12 \text{ m/s}$ $\text{Hence, Option (1) is the correct answer.}$

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
}