Import Question JSON

Current Question (ID: 8847)

Question:

$\text{The velocity } v \text{ of an object varies with its position } x \text{ on a straight line as } v = 3\sqrt{x}\text{. Its acceleration versus time } (a-t) \text{ graph is best represented by:}$

Options:

1. $\text{Decreasing linear graph}$
2. $\text{Increasing linear graph}$
3. $\text{Horizontal line (constant acceleration)}$
4. $\text{Increasing curved graph}$

Solution:

$\text{Hint: The acceleration of the particle is given by } a = v\frac{dv}{dx}$ $\text{Step: Find the acceleration of the given body.}$ $\text{As } a = v\frac{dv}{dx}$ $\text{or, } a = 3\sqrt{x} \times \frac{d}{dx}(3\sqrt{x})$ $= 3\sqrt{x} \times 3 \times \frac{1}{2\sqrt{x}}$ $\text{or, } a = \frac{9}{2} \text{ (constant)}$ $\text{Hence, option (3) is the correct answer.}$

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
}