Import Question JSON

Current Question (ID: 10463)

Question:

A tank is filled with water up to a height $H$. The water is allowed to come out of a hole $P$ in one of the walls at a depth $D$ below the surface of the water. The horizontal distance $x$ in terms of $H$ and $D$ is:

Options:

1. $x = \sqrt{D(H - D)}$
2. $x = \sqrt{\frac{D(H - D)}{2}}$
3. $x = 2\sqrt{D(H - D)}$
4. $x = 4\sqrt{D(H - D)}$

Solution:

\text{Time taken by water to reach the bottom is given by } t = \sqrt{\frac{2(H - D)}{g}} \text{and velocity of water coming out of the hole is } v = \sqrt{2gD} \text{Therefore, the horizontal distance covered is } x = v \times t x = \sqrt{\frac{2(H - D)}{g}} \times \sqrt{2gD} = 2\sqrt{D(H - D)}

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
}