Import Question JSON

Current Question (ID: 20263)

Question:

$\text{Select increasing order of power consumption.}$

Options:

1. $P_1 < P_2 < P_4 < P_3$
2. $P_3 < P_4 < P_1 < P_2$
3. $P_4 < P_3 < P_1 < P_2$
4. $P_2 < P_1 < P_4 < P_3$

Solution:

$\text{Hint: } P = \frac{V^2}{R_{\text{eq}}}$ $\text{Suppose battery of emf } \varepsilon \text{ is applied across each circuit}$ $\therefore P_1 = \frac{\varepsilon^2}{R_{\text{eq}}} = \frac{\varepsilon^2}{\frac{3R}{2}} = 0.67 \frac{\varepsilon^2}{R}$ $P_2 = \frac{\varepsilon^2}{R_{\text{eq}}} = \frac{\varepsilon^2}{3R} = 0.33 \frac{\varepsilon^2}{R}$ $P_3 = \frac{\varepsilon^2}{R_{\text{eq}}} = \frac{\varepsilon^2}{\frac{R}{3}} = 3 \frac{\varepsilon^2}{R}$ $P_4 = \frac{\varepsilon^2}{R_{\text{eq}}} = \frac{\varepsilon^2}{\frac{2R}{3}} = 1.5 \frac{\varepsilon^2}{R}$ $\text{Increasing order is - } P_2 < P_1 < P_4 < P_3$

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
}