Import Question JSON

Current Question (ID: 19585)

Question:

$\text{The area of the cross-section of a large tank is } 0.5 \text{ m}^2. \text{ It has a narrow opening near the bottom having an area of cross-section } 1 \text{ cm}^2. \text{ A load of } 25 \text{ kg is applied on the water at the top of the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of the water level in the tank is } 40 \text{ cm above the bottom, will be: [Take } g = 10 \text{ ms}^{-2}]$

Options:

1. $1 \text{ ms}^{-1}$
2. $2 \text{ ms}^{-1}$
3. $3 \text{ ms}^{-1}$
4. $4 \text{ ms}^{-1}$

Solution:

$\text{Hint: } P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}$

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
}