Import Question JSON

Current Question (ID: 19101)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): The range of a horizontal projectile is maximum when}$ \text{the angle of projection is } \theta = 45^\circ.$ $\text{Reason (R): The range is maximum when } \sin(2\theta) = 1.$

Options:

1. $\text{Both (A) and (R) are True and (R) is the correct explanation of (A).}$
2. $\text{Both (A) and (R) are True but (R) is not the correct explanation of (A).}$
3. $\text{(A) is True but (R) is False.}$
4. $\text{Both (A) and (R) are False.}$

Solution:

$\text{Hint: } R = \frac{u^2 \sin 2\theta}{g}$ $\text{Explanation: The range of a horizontal projectile is maximum when}$ $\text{the angle of projection is } \theta = 45^\circ \text{ as shown below;} \ R = \frac{u^2 \sin(2\theta)}{g}$ $\text{For, } R_{\text{max}} \Rightarrow \sin(2\theta) = 1$ $\Rightarrow 2\theta = 90^\circ \Rightarrow \theta = 45^\circ$ $\text{The range of the projectile is maximum when } \sin(2\theta) = 1.$ $\text{Therefore, both (A) and (R) are True and (R) is the correct}$ $\text{explanation of (A).}$ $\text{Hence, option (1) is the correct answer.}$

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
}