Import Question JSON

Current Question (ID: 16661)

Question:

$\text{If the voltage across a bulb rated (220 V-100 W) drops by 2.5\% of its rated value, the percentage of the rated value by which the power would decrease is:}$ $1.\ 20\%$ $2.\ 2.5\%$ $3.\ 5\%$ $4.\ 10\%$

Options:

1. $20\%$
2. $2.5\%$
3. $5\%$
4. $10\%$

Solution:

$\text{Given,}$ $\text{Drop in the voltage across 220 V - 100 W bulb = 2.5\% of its rated value}$ $\text{Power, } P = \frac{V^2}{R}$ $\text{For small variation,}$ $\frac{\Delta P}{P} \times 100\% = \frac{2 \times \Delta V}{V} \times 100\%$ $= 2 \times 2.5 = 5\%$ $\text{Therefore, power would decrease by 5\%}$

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
}