Import Question JSON

Current Question (ID: 15980)

Question:

$\text{A point source emits sound equally in all directions in a non-absorbing medium. Two points, } P \text{ and } Q, \text{ are at distances of } 2 \text{ m and } 3 \text{ m, respectively, from the source. The ratio of the intensities of the waves at } P \text{ and } Q \text{ is:}$ $1.\ 3 : 2$ $2.\ 2 : 3$ $3.\ 9 : 4$ $4.\ 4 : 9$

Options:

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

Solution:

$\text{Hint: } I \propto \frac{1}{r^2}$ $\text{Step: Find the ratio of intensities at points } P \text{ and } Q.$ $\text{The intensity of the waves is given by; } I \propto \frac{1}{r^2}$ $\text{The ratio of intensities at points } P \text{ and } Q \text{ is } \frac{I_P}{I_Q} = \left(\frac{r_Q}{r_P}\right)^2$ $\text{Given: } r_P = 2 \text{ m, } r_Q = 3 \text{ m}$ $\Rightarrow \frac{I_P}{I_Q} = \left(\frac{3}{2}\right)^2 = \frac{9}{4}$ $\text{Hence, option (3) is the correct answer.}$

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
}