Import Question JSON

Current Question (ID: 18979)

Question:

$\text{The dimension of mutual inductance is:}$

Options:

1. $[\text{ML}^2\text{T}^{-2}\text{A}^{-1}]$
2. $[\text{ML}^2\text{T}^{-3}\text{A}^{-1}]$
3. $[\text{ML}^2\text{T}^{-2}\text{A}^{-2}]$
4. $[\text{ML}^2\text{T}^{-3}\text{A}^{-2}]$

Solution:

$\text{The dimension of mutual inductance is derived from the formula:}$ $\text{Mutual Inductance (M) = } \frac{\text{Voltage (V)}}{\text{Rate of change of current (dI/dt)}}$ $\text{Dimension of Voltage (V) is } [\text{ML}^2\text{T}^{-3}\text{A}^{-1}]$ $\text{Dimension of Rate of change of current (dI/dt) is } [\text{T}^{-1}\text{A}]$ $\text{Therefore, dimension of M is } [\text{ML}^2\text{T}^{-2}\text{A}^{-2}]$

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
}