Import Question JSON

Current Question (ID: 10529)

Question:

$\text{Equation of continuity is based on:}$

Options:

1. $\text{Conservation of mass}$
2. $\text{Conservation of energy}$
3. $\text{Conservation of angular momentum}$
4. $\text{None of these}$

Solution:

$\text{The equation of continuity is based on the conservation of mass.}$ $\text{It states that for a steady flow of an incompressible fluid, the mass flow rate must remain constant throughout the fluid system.}$ $\text{Mathematically, this is expressed as } A_1v_1 = A_2v_2\text{, where A is the cross-sectional area and v is the velocity at different points in the flow.}$ $\text{This principle ensures that mass cannot be created or destroyed in the flow, only redistributed.}$

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
}