Import Question JSON

Current Question (ID: 9631)

Question:

$\text{A body is thrown horizontally with a velocity } \sqrt{2gh} \text{ from the top of a tower of height } h. \text{ It strikes the level ground through the foot of the tower at a distance } x \text{ from the tower. The value of } x \text{ is:}$

Options:

1. $h$
2. $\frac{h}{2}$
3. $2h$
4. $\frac{2h}{3}$

Solution:

$\text{Hint: } x = u_x t + \frac{1}{2}a_x t^2$ $\text{Step: Find the horizontal range i.e., } x.$ $\text{The horizontal range of the body is given by;}$ $x = u_x \sqrt{\frac{2h}{g}} = \sqrt{2gh} \times \sqrt{\frac{2h}{g}}$ $\Rightarrow x = 2h$ $\text{Hence, option (3) is the correct answer.}$

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
}