Import Question JSON

Current Question (ID: 9629)

Question:

$\text{The equation of a projectile is } y = ax - bx^2. \text{ Its horizontal range is?}$

Options:

1. $\frac{a}{b}$
2. $\frac{b}{a}$
3. $a + b$
4. $b - a$

Solution:

\text{Hint: } y = x \tan \theta - \frac{gx^2}{2u^2 \cos^2 \theta} \text{Step: Find the horizontal range of the projectile.} \text{The equation of the trajectory of a projectile motion is:} y = x \tan \theta - \frac{gx^2}{2u^2 \cos^2 \theta} = x \tan \theta \left(1 - \frac{x}{R}\right) \quad (1) y = ax - bx^2 = a \left(x - \frac{b}{a}x^2\right) \quad (2) \text{Comparing equations (1) and (2) we get:} \frac{1}{R} = \frac{b}{a} \Rightarrow R = \frac{a}{b} \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
}