Import Question JSON

Current Question (ID: 18972)

Question:

$\text{The dimensional formula for thermal conductivity is: (here } K \text{ denotes the temperature)}$ $1. \ [MLT^{-2}K]$ $2. \ [MLT^{-3}K]$ $3. \ [MLT^{-3}K^{-1}]$ $4. \ [MLT^{-2}K^{-2}]$

Options:

1. $[MLT^{-2}K]$
2. $[MLT^{-3}K]$
3. $[MLT^{-3}K^{-1}]$
4. $[MLT^{-2}K^{-2}]$

Solution:

$\text{Hint: } \frac{dQ}{dt} = \frac{kA \Delta T}{l}$ $\therefore \frac{d\theta}{dt} = kA \frac{dT}{dx}$ $k = \frac{\left( \frac{d\theta}{dt} \right)}{A \left( \frac{dT}{dx} \right)}$ $[k] = \frac{[ML^2T^{-3}]}{[L^2][KL^{-1}]} = [MLT^{-3}K^{-1}]$

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
}