Import Question JSON

Current Question (ID: 19595)

Question:

$\text{An air bubble having volume } 1 \ \text{cm}^3 \text{ at depth } 40 \ \text{m inside water comes to surface.}$ $\text{What will be the volume of the bubble at the surface?}$

Options:

1. $5 \ \text{cm}^3$
2. $2 \ \text{cm}^3$
3. $4 \ \text{cm}^3$
4. $3 \ \text{cm}^3$

Solution:

$\text{Hint: } PV = \text{constant}$ $\text{Initial pressure } = P_0 + \rho gh$ $= 10^5 + 1000 \times 10 \times 40$ $= 5 \times 10^5$ $\text{Final pressure } = 10^5$ $PV = \text{constant}$ $\Rightarrow 5 \times 10^5 \times V_i = 10^5 \times V_f$ $\Rightarrow V_f = 5 \ \text{cm}^3$

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
}