Import Question JSON

Current Question (ID: 19104)

Question:

$\text{If a projectile is launched at an angle of } 15^\circ \text{ with the horizontal and achieves a range of } 50 \text{ m, what will be the range when it is launched at an angle of } 45^\circ \text{ with the horizontal?}$

Options:

1. $50 \text{ m}$
2. $100 \text{ m}$
3. $80 \text{ m}$
4. $120 \text{ m}$

Solution:

$\text{Hint: } R = \frac{u^2 \sin 2\theta}{g}$ $\text{Step: Find the range of the given projectile.}$ $R = \frac{u^2 \sin 2\theta}{g}$ $\Rightarrow 50 = \frac{u^2 \sin 30^\circ}{g}$ $\Rightarrow 100 = \frac{u^2}{g}$ $\text{and } R' = \frac{u^2 \sin 90^\circ}{g} = \frac{u^2}{g}$ $\Rightarrow R' = 100 \text{ m}$ $\text{Hence, option (2) is the correct answer.}$

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
}