Import Question JSON

Current Question (ID: 16510)

Question:

$\text{The electric potential in a certain region of space is given by } V = -8x^2 + 4x, \text{ where } V \text{ is in volt and } x \text{ is in metre. In this region, the equipotential surface is:}$

Options:

1. $\text{plane parallel to } yz \text{ plane}$
2. $\text{plane parallel to the } x\text{-axis}$
3. $\text{concentric circle centered at the origin}$
4. $\text{coaxial cylinder with axis parallel to the } y\text{-axis}$

Solution:

$\text{Hint: At equipotential surface, potential does not change}$ $\text{Step 1: Find a region where the potential gradient is 0}$ $V = -8x^2 + 4x$ $\frac{dV}{dx} = -16x + 4 = 0$ $\Rightarrow x = \frac{1}{4}$ $\text{Step 2: Identify the equipotential surface}$

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
}