Import Question JSON

Current Question (ID: 20317)

Question:

$\text{If the length of a conductor is increased by 20 percent and cross-sectional area is decreased by 4 percent, then calculate the percentage change in resistance of a conductor.}$

Options:

1. $27\%$
2. $25\%$
3. $20\%$
4. $16\%$

Solution:

$\text{Hint: } R = \frac{\rho l}{A}$ $R = \left( \frac{\rho l}{A} \right)$ $R' = \frac{\rho l'}{A'}; \Rightarrow l' = 1.2l$ $A' = 0.96A$ $R' = \frac{\rho \times 1.2l}{0.96A} = \frac{10}{8} \left( \frac{\rho l}{A} \right)$ $\frac{R' - R}{R} = \left( \frac{1}{4} \right)$ $\Rightarrow 25\%$

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
}