Import Question JSON

Current Question (ID: 9582)

Question:

$\text{If the position of a particle varies according to the equations } x = 3t^2, y = 2t, \text{ and } z = 4t + 4, \text{ then which of the following is incorrect?}$

Options:

1. $\text{Velocities in } y \text{ and } z \text{ directions are constant}$
2. $\text{Acceleration in the } x \text{ direction is non-uniform}$
3. $\text{Acceleration in the } x \text{ direction is uniform}$
4. $\text{Motion is not in a straight line}$

Solution:

\text{Hint: } v_x = \frac{dx}{dt} \text{Step: Find the incorrect statement.} \text{Given:} x = 3t^2 \Rightarrow v_x = \frac{dx}{dt} = 6t \text{ and } a_x = \frac{dv_x}{dt} = 6 y = 2t \Rightarrow v_y = \frac{dy}{dt} = 2 \text{ and } a_y = \frac{dv_y}{dt} = 0 z = 4t + 4 \Rightarrow v_z = \frac{dz}{dt} = 4 \text{ and } a_z = \frac{dv_z}{dt} = 0 \text{So, the acceleration is uniform along x-axis.} \text{Therefore, the incorrect statement is acceleration in the x-direction is non-uniform.} \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
}