Import Question JSON

Current Question (ID: 10787)

Question:

\text{A certain quantity of water cools from 70°C to 60°C in the first 5 minutes and to 54°C in the next 5 minutes. The temperature of the surroundings will be:}

Options:

1. $45°\text{C}$ (Correct)
2. $20°\text{C}$
3. $42°\text{C}$
4. $10°\text{C}$

Solution:

\text{Let the temperature of the surrounding be } t\text{°C} \text{For first case: } \frac{70-60}{5} = K(65 - t) \text{(65°C is average of 70°C and 60°C)} \frac{10}{5} = K(65 - t) \text{ ...(i)} \text{For second case: } \frac{60-54}{5} = K(57 - t) \text{ ...(ii)} \text{(57°C is average of 60°C and 54°C)} \text{From equations (i) and (ii): } \frac{10}{6} = \frac{65-t}{57-t} \text{Solving, we get } t = 45\text{°C}

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
}