Import Question JSON

Current Question (ID: 19608)

Question:

$\text{A liquid of density } 750 \text{ kgm}^{-3} \text{ flows smoothly through a horizontal pipe that tapers in cross-sectional area from } A_1 = 1.2 \times 10^{-2} \text{ m}^2 \text{ to } A_2 = \frac{A_1}{2} . \text{ The pressure difference between the wide and narrow sections of the pipe is } 4500 \text{ Pa. The rate of flow of liquid is:}$

Options:

1. $20 \times 10^{-3} \text{ m}^{-3}\text{s}^{-1}$
2. $30 \times 10^{-3} \text{ m}^{-3}\text{s}^{-1}$
3. $28 \times 10^{-3} \text{ m}^{-3}\text{s}^{-1}$
4. $24 \times 10^{-3} \text{ m}^{-3}\text{s}^{-1}$

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
}