Import Question JSON

Current Question (ID: 9543)

Question:

$\text{Three girls skating on a circular ice ground of radius 200 m start from a point } P \text{ on the edge of the ground and reach a point } Q \text{ diametrically opposite to } P \text{ following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:}$

Options:

1. $A > B > C$
2. $C > A > B$
3. $B > A > C$
4. $A = B = C$

Solution:

$\text{Hint: Displacement depends only on the initial and final position.}$ $\text{Step 1: Find the initial and final positions in each case.}$ $\text{The initial and final positions in each case are the same.}$ $\text{Step 2: Find the displacement in each case.}$ $\text{Hence, the magnitudes of displacements are the same for the three girls.}$ $\text{Hence, option (4) is the correct answer.}$

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
}