Import Question JSON

Current Question (ID: 18920)

Question:

$\text{The quantities } x = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}, y = \frac{E}{B} \text{ and } z = \frac{L}{CR} \text{ are defined where } C$ $\text{-capacitance, } R\text{-Resistance, } L\text{-length, } E\text{-Electric field, } B\text{-magnetic}$ $\text{field and } \varepsilon_0, \mu_0 \text{ free space permittivity and permeability respectively. Then:}$

Options:

1. $\text{Only } x \text{ and } y \text{ have the same dimension}$
2. $x, y \text{ and } z \text{ have the same dimension}$
3. $\text{Only } x \text{ and } z \text{ have the same dimension}$
4. $\text{Only } y \text{ and } z \text{ have the same dimension}$

Solution:

$\text{Hint: Dimension of speed is } [L^1T^{-1}].$ $x = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = \text{speed} \Rightarrow |x| = [L^1T^{-1}]$ $y = \frac{E}{B} = \text{speed} \Rightarrow [y] = [L^1T^{-1}]$ $z = \frac{l}{RC} = \frac{l}{\tau} \Rightarrow [z] = [L^1T^{-1}]$ $\text{So, } x, y, z \text{ all have the same dimensions.}$

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
}