Import Question JSON

Current Question (ID: 16666)

Question:

$\text{When a } 100 \text{ W, } 240 \text{ V bulb is operated at } 200 \text{ volt, the current in it is:}$ $1.\ 0.35\ \text{A}$ $2.\ 0.42\ \text{A}$ $3.\ 0.50\ \text{A}$ $4.\ 0.58\ \text{A}$

Options:

1. $0.35\ \text{A}$
2. $0.42\ \text{A}$
3. $0.50\ \text{A}$
4. $0.58\ \text{A}$

Solution:

$\text{Hint: } P = \frac{V^2}{R}$ $\text{Step 1: Find resistance of the bulb.}$ $\text{Using, } \Rightarrow P = \frac{V^2}{R} \Rightarrow R = \frac{V^2}{P}$ $\Rightarrow R = \frac{(204)^2}{100}$ $\text{Step 2: Find the current.}$ $\text{The resistance will remain constant, thus;}$ $\Rightarrow V = IR \Rightarrow I = \frac{V}{R}$ $\text{Substituting the value of } R \text{ in the equation, we get;}$ $\Rightarrow I = \frac{V}{R} \Rightarrow I = \frac{200 \times 100}{(240)^2} \Rightarrow I = 0.35\ \text{A}$ $\text{Hence, option (1) is the correct answer.}$

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
}