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Current Question (ID: 20169)

Question:

$\text{The electric field in a region is given by } \vec{E} = (Ax + B)\hat{i}, \text{ where } E \text{ is in NC}^{-1} \text{ and } x \text{ is in meters.}$ $\text{The value of constants are } A = 20 \text{ SI unit and } B = 10 \text{ SI unit.}$ $\text{If the potential at } x = 1 \text{ is } V_1 \text{ and that at } x = -5 \text{ is } V_2, \text{ then } V_1 - V_2 \text{ is:}$

Options:

1. $-520 \text{ V}$
2. $180 \text{ V}$
3. $-48 \text{ V}$
4. $320 \text{ V}$

Solution:

$\text{Hint: } \Delta V = \int \vec{E} \cdot d\vec{r}$ $\Delta V = \frac{A}{2} \left[ x^2 \right]_{1}^{-5} + B \left[ x \right]_{1}^{-5}$ $= 10(24) - 60$ $= 180$

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
}