Import Question JSON

Current Question (ID: 8806)

Question:

$\text{Given below are two statements:}$ $\textbf{Assertion (A):} \text{ Adding a scalar to a vector of the same dimension is a meaningful algebraic operation.}$ $\textbf{Reason (R):} \text{ Displacement can be added to distance.}$

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:

$\textbf{Hint:} \text{ Displacement is a vector quantity, and distance is a scalar quantity.}$ $\textbf{Explanation:} \text{ Adding a scalar to a vector (even of the same dimension) doesn't make sense in vector addition. Vector addition involves adding corresponding components of two vectors, resulting in a new vector. We cannot directly add a scalar (which has no direction) to a vector (which has both magnitude and direction).}$ $\text{Displacement and distance cannot be directly added. Displacement, as mentioned earlier, is a vector with direction, while distance is a scalar representing only the length. Adding them without considering the direction wouldn't provide a meaningful result.}$ $\text{Therefore, Both (A) and (R) are false.}$ $\text{Hence, Option (4) is the correct answer.}$

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
}