Import Question JSON

Current Question (ID: 10790)

Question:

$\text{A body cools down from } 80^\circ\text{C to } 70^\circ\text{C in 5 minutes. The temperature of the same body will fall from } 70^\circ\text{C to } 60^\circ\text{C in:}$

Options:

1. $\text{less than 5 minutes.}$
2. $\text{equal to 5 minutes.}$
3. $\text{more than 5 minutes.}$ (Correct)
4. $\text{can't say anything as the temperature of the surroundings is not known.}$

Solution:

$T_S = T$ $\text{Applying Newton's law of cooling,}$ $\text{For the 1st case:}$ $\frac{10}{5} = -bA(75 - T) \ldots\ldots(1)$ $\text{For the 2nd case:}$ $\frac{10}{t} = -bA(65 - T) \ldots\ldots(2)$ $\text{From (1) and (2): we can say that t>5 min.}$

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
}