Import Question JSON

Current Question (ID: 17280)

Question:

$\text{The peak value of an alternating emf;} \ E = E_0 \sin \omega t \ \text{is} \ 10 \ \text{V and its frequency is} \ 50 \ \text{Hz. At a time} \ t = \frac{1}{600} \ \text{s, the instantaneous value of the emf will be:}$ $1. \ 1 \ \text{V}$ $2. \ 5\sqrt{3} \ \text{V}$ $3. \ 5 \ \text{V}$ $4. \ 10 \ \text{V}$

Options:

1. $1 \ \text{V}$
2. $5\sqrt{3} \ \text{V}$
3. $5 \ \text{V}$
4. $10 \ \text{V}$

Solution:

$\text{Hint:} \ \omega = 2\pi f$ $\text{Step: Find the instantaneous value of the emf.}$ $\text{The angular frequency is given by;} \ \omega = 2\pi f$ $\text{Substitute the given values we get;} \ \Rightarrow \omega = 100\pi$ $\text{Using the equation at the given time we get;} \ E = E_0 \sin 100\pi \times \frac{1}{600}$ $E = 10 \times \sin \left( \frac{\pi}{6} \right)$ $\Rightarrow E = 5 \ \text{V}$ $\text{Hence, option (3) is the correct answer.}$

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
}