Import Question JSON

Current Question (ID: 10438)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): Specific gravity of a fluid is a dimensionless quantity.}$ $\text{Reason (R): It is the ratio of the density of the fluid to the density of water.}$

Options:

1. $\text{Both (A) and (R) are True and (R) is the correct explanation of (A).}$
2. $\text{Both (A) and (R) are True but (R) is not the correct explanation of (A).}$
3. $\text{(A) is True but (R) is False.}$
4. $\text{Both (A) and (R) are False.}$

Solution:

$\text{Based on the statements provided:}$ $\text{Assertion (A): Specific gravity of a fluid is a dimensionless quantity.}$ $\text{This statement is True. Specific gravity is a ratio of densities, so the units of density cancel out, leaving it without dimensions.}$ $\text{Reason (R): It is the ratio of the density of the fluid to the density of water.}$ $\text{This statement is also True. The definition of specific gravity (for liquids and solids) is the ratio of the density of the substance to the density of water (usually at 4°C).}$ $\text{Furthermore, the reason (R) directly explains why the assertion (A) is true. Because specific gravity is a ratio of two quantities with the same units (densities), the resulting value is a pure number without units or dimensions.}$ $\text{Therefore, both the assertion and the reason are true, and the reason is the correct explanation for the assertion.}$ $\text{The correct option is 1.}$

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
}