Import Question JSON

Current Question (ID: 17014)

Question:

$\text{Calculate the self-inductance of a solenoid having 1000 turns and length 1 m.}$ $\text{(The area of cross-section is } 7 \text{ cm}^2 \text{ and } \mu_r = 1000).$

Options:

1. $888 \text{ H}$
2. $0.88 \text{ H}$
3. $0.088 \text{ H}$
4. $88.8 \text{ H}$

Solution:

$\text{Hint: Use the formula of self-inductance of the solenoid.}$ $\text{Step 1: Calculate the self-inductance by using the formula given below.}$ $L = \mu_0 \mu_r n^2 A l$ $= 4 \pi \times 10^{-7} \times 1000 \times (1000)^2 \times 7 \times 10^{-4} \times 1$ $= 0.88 \text{ H}$

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
}