Import Question JSON

Current Question (ID: 17017)

Question:

$\text{Work done in increasing the current through a solenoid from 0 to 2 A is 20 J.}$ $\text{Work done in increasing the current from 4 A to 6 A is:}$

Options:

1. $100 \text{ J}$
2. $60 \text{ J}$
3. $80 \text{ J}$
4. $120 \text{ J}$

Solution:

$\text{Step 1: Find formula for work done}$ $U = \frac{1}{2} L i^2$ $W = \frac{1}{2} L [i_2^2 - i_1^2]$ $\text{Step 2: Find work done in both cases}$ $W_1 = \frac{1}{2} L [2^2 - 0^2] = 2L = 20 I$ $W_2 = \frac{1}{2} L [6^2 - 4^2] = 10 L$ $W_2 = 5W_1 = 100 J$ $\text{NCERT Reference: Class XII, part 1, pg. 223.}$ $\text{Hint: Work is done to increase magnetic energy of inductor.}$

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
}