Import Question JSON

Current Question (ID: 8900)

Question:

$\text{The position (x) of a particle in a straight line motion is given by } x = 2 + 10t - 5t^2 \text{ m. Its velocity (v) is best represented by?}$

Options:

1. $\text{Linear graph starting at 10 m/s at t=0, decreasing to 0 m/s at t=1s}$
2. $\text{Linear graph starting at 20 m/s, decreasing to 5 m/s at t=1s}$
3. $\text{Curved graph starting at 10 m/s, decreasing to 0 m/s at t=1s}$
4. $\text{Curved graph starting at 20 m/s, decreasing to 0 m/s at t=2s}$

Solution:

$\text{Hint: The velocity of the particle is the derivative of x with respect to time.}$ $\text{Step 1: Find the velocity of the particle.}$ $v = \frac{dx}{dt}$ $v = 10 - 10t$ $\text{Step 2: Plot the velocity of the particle as a function of time.}$ $\text{Equation of a straight line}$ $y = mx + c$ $m = -10$ $c = 10$ $0 = 10 - 10t$ $t = 1s$ $\text{Hence, option (1) is the correct answer.}$

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
}