Import Question JSON

Current Question (ID: 15935)

Question:

$\text{If a travelling wave pulse is given by } y = \frac{20}{4+(x+4t)^2} \text{ m, then:}$

Options:

1. $\text{the pulse is traveling along the negative } x\text{-axis.}$
2. $\text{the speed of the pulse is } 4 \text{ m/s.}$
3. $\text{the amplitude of the pulse is } 5 \text{ m.}$
4. $\text{all of these.}$

Solution:

$\text{Hint: Compare the given equation with the standard equation.}$ $\text{Step 1: Write the standard equation.}$ $y = \frac{A}{B+(x \pm vt)^2}$ $\text{Given equation is,}$ $y = \frac{20}{4+(x+4t)^2}$ $\text{Step 2: Compare the given equation with the standard equation and find the maximum value of } y.$ $v = 4 \text{ m/s.}$ $\text{For maximum value of } y$ $\text{Its denominator should be the minimum}$ $i.e., (x + 4t)^2 = \text{minimum}$ $\text{At } x = 0 \text{ and } t = 0, y = \text{maximum}$ $\text{Therefore,}$ $A = \frac{20}{4} = 5 \text{ m.}$ $\text{Therefore, all the statements are correct.}$ $\text{Hence, option (4) is the correct answer.}$

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
}