Import Question JSON

Current Question (ID: 19181)

Question:

$\text{A given object takes } n \text{ times more time to slide down a } 45^\circ \text{ rough}$ $\text{inclined plane as it takes to slide down a perfectly smooth } 45^\circ \text{ incline.}$ $\text{The coefficient of kinetic friction between the object and the incline is:}$

Options:

1. $\sqrt{1 - \frac{1}{n^2}}$
2. $1 - \frac{1}{n^2}$
3. $\frac{1}{2 - n^2}$
4. $\sqrt{\frac{1}{1 - n^2}}$

Solution:

$\text{Hint: } t = \sqrt{\frac{2S}{a}}$

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
}