Import Question JSON

Current Question (ID: 20275)

Question:

$\text{In a meter bridge, as shown in the figure. It is given that resistance } Y = 12.5 \, \Omega \text{ and that balance are obtained at a distance } 39.5 \, \text{cm from the end } A \text{ (by Jockey } J). \text{ After interchanging the resistances } X \text{ and } Y, \text{ a new balance point is found at a distance } l_2 \text{ from the end } A. \text{ What are the values of } X \text{ and } l_2?}$

Options:

1. $19.15 \, \Omega \text{ and } 39.5 \, \text{cm}$
2. $8.16 \, \Omega \text{ and } 60.5 \, \text{cm}$
3. $8.16 \, \Omega \text{ and } 39.5 \, \text{cm}$
4. $19.15 \, \Omega \text{ and } 60.5 \, \text{cm}$

Solution:

$\text{Hint: } \frac{P}{Q} = \frac{l}{100 - l}$ $\text{Given: } Y = 12.5 \, \Omega, \ l_1 = 39.5 \, \text{cm}$ $\frac{X}{12.5} = \frac{39.5}{60.5}$ $X = 8.16 \, \Omega$ $\text{After interchange: } \frac{12.5}{8.16} = \frac{l_2}{100 - l_2}$ $12.5 \times (100 - l_2) = 8.16 \times l_2$ $1250 - 12.5l_2 = 8.16l_2$ $1250 = 20.66l_2$ $l_2 = \frac{1250}{20.66} = 60.5 \, \text{cm}$

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
}