Import Question JSON

Current Question (ID: 16488)

Question:

$\text{The increasing order of the electrostatic potential energies for the given system of charges is given by:}$ $\text{Q} \quad -\text{Q} \quad -\text{Q} \quad -\text{Q} \quad 2\text{Q} \quad \text{Q} \quad 2\text{Q}$ $\text{r} \quad \text{r} \quad \text{r} \quad 2\text{Q} \quad 2\text{r}$

Options:

1. $\text{a = d < b < c}$
2. $\text{b = d < c < a}$
3. $\text{b = c < a < d}$
4. $\text{c < a < b < d}$

Solution:

$\text{The potential energy of a system is given by,}$ $U = \frac{k q_1 q_2}{r}$ $U_a = -\frac{kQ^2}{r}$ $U_b = \frac{kQ^2}{r}$ $U_c = \frac{2kQ^2}{r}$ $U_d = -\frac{kQ^2}{r}$ $\text{a = d < b < c}$

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
}