Import Question JSON

Current Question (ID: 19661)

Question:

$\text{An object cools down from } 80^\circ\text{C to } 60^\circ\text{C in } 5 \text{ min in a surrounding of temperature } 20^\circ\text{C.}$ $\text{The time taken to cool from } 60^\circ\text{C to } 40^\circ\text{C will be:}$ $\text{(Assume Newton's law of cooling to be valid.)}$

Options:

1. $\frac{25}{3} \text{ min}$
2. $5 \text{ min}$
3. $\frac{25}{4} \text{ min}$
4. $9 \text{ min}$

Solution:

$\text{Hint: Apply Newton's law of cooling.}$ $\text{Step 1: Use Newton's law of cooling for given situations.}$ $\frac{20}{5} = K(70 - 20) \quad \ldots (1)$ $\text{also}$ $\frac{20}{t} = K(50 - 20) \quad \ldots (2)$ $\text{Step 2: Find the time taken to cool from } 60^\circ\text{C to } 40^\circ\text{C.}$ $\text{After solving equation (1) \& (2), we get;}$ $\Rightarrow t = \frac{25}{3} \text{ min}$ $\text{Hence, option (1) is the correct answer.}$

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
}