Import Question JSON

Current Question (ID: 9605)

Question:

$\text{At the top of the trajectory of a projectile, the directions of its velocity and acceleration are:}$

Options:

1. $\text{perpendicular to each other.}$
2. $\text{parallel to each other.}$
3. $\text{inclined to each other at an angle of } 45°\text{.}$
4. $\text{antiparallel to each other.}$

Solution:

\text{Hint: At the highest point, } v_x = v\cos\theta\text{.} \text{Explanation: The direction of velocity is always tangent to the path so, at the top of the trajectory, it is in a horizontal direction, and acceleration due to gravity is always in the vertically downward direction. It means angles between } \vec{v} \text{ and } \vec{g} \text{ are perpendicular to each other.} \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
}