Import Question JSON

Current Question (ID: 18942)

Question:

$\text{If } R, X_L \text{ and, } X_C \text{ denote resistance, inductive reactance, and}$ $\text{capacitive reactance respectively. Then which of the following}$ $\text{options shows the 'dimensionless' physical quantity?}$

Options:

1. $\frac{X_L X_C}{R}$
2. $\frac{R}{\sqrt{X_L X_C}}$
3. $\frac{R}{X_L X_C}$
4. $\frac{R}{(X_L X_C)^2}$

Solution:

$\text{Hint: } [R] = [X_L] = [X_C]$ $\text{Step: Identify the correct option.}$ $\text{As } [R] = [X_L] = [X_C]$ $\text{so, } \frac{R}{\sqrt{X_L X_C}} \text{ is a dimensionless quantity.}$

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
}