Import Question JSON

Current Question (ID: 15968)

Question:

$\text{Given below are two statements:}$ $\text{Statement I: The speed of sound waves in a medium depends on the elastic modulus and the density of the medium.}$ $\text{Statement II: The speed of sound in a gas is independent of its temperature.}$

Options:

1. $\text{Statement I is incorrect and Statement II is correct.}$
2. $\text{Both Statement I and Statement II are correct.}$
3. $\text{Both Statement I and Statement II are incorrect.}$
4. $\text{Statement I is correct and Statement II is incorrect.}$

Solution:

$\text{Hint: } v = \sqrt{\frac{\gamma RT}{M}}$ $\text{Step: Find the speed of the sound in a medium.}$ $\text{The velocity of sound in terms of elastic modulus and density is given as:}$ $v = \sqrt{\frac{B}{\rho}}$ $\text{Speed of sound, } v = \sqrt{\frac{\gamma P}{\rho}}$ $v = \sqrt{\frac{\gamma PV}{nM}}$ $\Rightarrow v = \sqrt{\frac{\gamma nRT}{nM}} \quad [PV = nRT]$ $\Rightarrow v = \sqrt{\frac{\gamma RT}{M}}$ $\text{So, the speed of the sound depends on the temperature of the medium.}$ $\text{Therefore, Statement I is correct and Statement II is incorrect.}$ $\text{Hence, option (4) is the correct answer.}$

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
}