Import Question JSON

Current Question (ID: 8850)

Question:

$\text{A point moves in a straight line so that its displacement is } x \text{ m at time } t \text{ sec, given by } x^2 = t^2 + 1\text{. Its acceleration in m/s}^2 \text{ at time 1 sec is:}$

Options:

1. $\frac{1}{x}$
2. $\frac{1}{x} - \frac{1}{x^3}$
3. $\frac{2}{x}$
4. $-\frac{t^2}{x^3}$

Solution:

$\text{Hint: The acceleration of the particle is given by } a = \frac{dv}{dt}$ $\text{Step: Find the acceleration of the point at the given time.}$ $x^2 = t^2 + 1$ $2x\left(\frac{dx}{dt}\right) = 2t$ $v = \frac{t}{x}$ $a = \frac{x - vt}{x^2} = \frac{1}{x} - \frac{t^2}{x^3}$ $\text{At } t = 1 \text{ sec}$ $a = \frac{1}{x} - \frac{1}{x^3}$ $\text{Hence, option (2) is the correct answer.}$

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
}