Import Question JSON

Current Question (ID: 9628)

Question:

$\text{The velocity at the maximum height of a projectile is } \frac{\sqrt{3}}{2} \text{ times its initial velocity of projection } (u). \text{ Its range on the horizontal plane is:}$

Options:

1. $\frac{\sqrt{3}u^2}{2g}$
2. $\frac{3u^2}{2g}$
3. $\frac{3u^2}{g}$
4. $\frac{u^2}{2g}$

Solution:

\text{Hint: } R = \frac{u^2 \sin 2\theta}{g} \text{Step: Find the range of the projectile on a horizontal plane.} \text{Given: } u \cos \theta = \frac{\sqrt{3}u}{2} \Rightarrow \theta = 30° \text{Range, } R = \frac{u^2 \sin 2\theta}{g} = \frac{u^2 \sin 60°}{g} = \frac{\sqrt{3}u^2}{2g} \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
}