Import Question JSON

Current Question (ID: 20216)

Question:

$\text{In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line.}$ $\ln R(T)$ $\frac{1}{T^2}$ $\text{One may conclude that:}$

Options:

1. $R(T) = R_0 e^{T^2/T_0^2}$
2. $R(T) = \frac{R_0}{T^2}$
3. $R(T) = R_0 e^{-T^2/T_0^2}$
4. $R(T) = R_0 e^{-T_0^2/T^2}$

Solution:

$\text{Find the slope-intercept form of the given line.}$ $y = -mx + c$ $\ln(R) = \frac{-m}{T^2} + c$ $\text{If } R = R_0 e^{-T_0^2/T^2}$ $\ln R = \frac{-T_0^2}{T^2} + \ln(R_0)$ $\text{satisfies the equation}$

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
}