Import Question JSON

Current Question (ID: 9920)

Question:

A water pump rated 400 W has an efficiency of 75%. If it is employed to raise water to a height of 40 m, then the volume of water drawn in 10 min is:

Options:

1. $10.9 \text{ m}^3$
2. $0.45 \text{ m}^3$
3. $1.8 \text{ m}^3$
4. $0.25 \text{ m}^3$

Solution:

$\text{The useful power output of the pump is } 400 \text{ W} \times 0.75 = 300 \text{ W}.$ $\text{In 10 minutes (600 seconds), the useful work done is } 300 \text{ W} \times 600 \text{ s} = 180000 \text{ J}.$ $\text{This work is used to increase the potential energy of the water, } W = mgh.$ $\text{So, } 180000 \text{ J} = m \times 9.81 \text{ m/s}^2 \times 40 \text{ m}.$ $\text{Solving for mass } m: m \approx 458.7 \text{ kg}.$ $\text{Since the density of water is approximately } 1000 \text{ kg/m}^3, \text{ the volume } V = \frac{m}{\rho} = \frac{458.7 \text{ kg}}{1000 \text{ kg/m}^3} \approx 0.4587 \text{ m}^3.$ $\text{The closest option is 2. } 0.45 \text{ m}^3.$

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
}