Import Question JSON

Current Question (ID: 16668)

Question:

$\text{Six similar bulbs are connected as shown in the figure with a DC source of emf } E \text{ and zero internal resistance.}$ $\text{The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section } A \text{ and one from section } B \text{ are glowing, will be:}$

Options:

1. $2 : 1$
2. $4 : 9$
3. $9 : 4$
4. $1 : 2$

Solution:

$\text{For all bulbs glowing:}$ $P_1 = \frac{E^2}{2R/3} = \frac{3E^2}{2R}$ $\text{For two bulbs from section A and one from section B glowing:}$ $P_2 = \frac{E^2}{3R/2} = \frac{2E^2}{3R}$ $\frac{P_1}{P_2} = \frac{3E^2}{2R} \times \frac{3R}{2E^2} = \frac{9}{4}$

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
}