Import Question JSON

Current Question (ID: 10794)

Question:

$\text{A pendulum clock runs faster by 5 s per day at } 20^\circ\text{C and goes slow by 10 s per day at } 35^\circ\text{C. It shows the correct time at a temperature of:}$

Options:

1. $27.5^\circ\text{C}$
2. $25^\circ\text{C}$ (Correct)
3. $30^\circ\text{C}$
4. $33^\circ\text{C}$

Solution:

$\text{Let the correct temperature be T.}$ $\text{Using the pendulum thermal expansion formula:}$ $\frac{1}{2}\alpha(35) - T \times 86400 = 10 \quad \ldots(1)$ $\frac{1}{2}\alpha(T -) 20 \times 86400 = 5 \quad \ldots(2)$ $\text{Solving (1) and (2): } T = 25^\circ\text{C}$

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
}