Import Question JSON

Current Question (ID: 16624)

Question:

$\text{The current-voltage graph for a given metallic conductor at two different temperatures } T_1 \text{ and } T_2 \text{ is as shown in the figure. Then:}$ $1. \ T_1 = T_2$ $2. \ T_2 > T_1$ $3. \ T_1 > T_2$ $4. \ \text{Insufficient information to conclude.}$

Options:

1. $T_1 = T_2$
2. $T_2 > T_1$
3. $T_1 > T_2$
4. $\text{Insufficient information to conclude.}$

Solution:

$\text{Hint: } R = \frac{1}{\text{slope of } (I-V) \text{ graph}}$ $\text{Step: Find the correct relation for temperatures.}$ $\text{The slope of } I-V \text{ graph is given by the reciprocal of resistance i.e., } \frac{1}{R}$ $\text{The resistance of the metallic conductor is directly proportional to temperature i.e., } R \propto T$ $\text{So, Slope } \propto \frac{1}{T}$ $\text{The slope of } T_1 \text{ curve is more than the } T_2$ $\text{Therefore, } T_1 < T_2$ $\text{Hence, option (2) is the correct answer.}$

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
}