Import Question JSON

Current Question (ID: 9622)

Question:

$\text{The horizontal range of a projectile is } 4\sqrt{3} \text{ times its maximum height. Its angle of projection will be:}$

Options:

1. $45°$
2. $60°$
3. $90°$
4. $30°$

Solution:

\text{Hint: } H = \frac{u^2 \sin^2 \theta}{2g} \text{Step: Find the angle of the projectile.} \text{Given: The horizontal range of a projectile is } 4\sqrt{3} \text{ times its maximum height i.e., } R = 4\sqrt{3}H R = 4H \cot \theta 4\sqrt{3}H = 4H \cot \theta \Rightarrow \cot \theta = \sqrt{3} \theta = \cot^{-1}(\sqrt{3}) \Rightarrow \theta = 30° \text{Hence, option (4) 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
}