Import Question JSON

Current Question (ID: 9615)

Question:

$\text{A body is projected with a velocity of } (3\hat{i} + 4\hat{j}) \text{ m/s. The maximum height attained by the projectile is: } (g = 10 \text{ ms}^{-2})$

Options:

1. $0.8 \text{ m}$
2. $8 \text{ m}$
3. $4 \text{ m}$
4. $0.4 \text{ m}$

Solution:

\text{Hint: The maximum height of the projectile is given by } H = \frac{u_y^2}{2g} \text{Step 1: Find the vertical component of velocity.} \text{The projectile is projected with a velocity } (3\hat{i} + 4\hat{j}) \text{ m/s} u_x = 3 \text{ m/s} u_y = 4 \text{ m/s} \text{Step 2: Calculate the maximum height} H = \frac{4^2}{2 \times 10} = \frac{16}{20} = 0.8 \text{ m} \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
}