Import Question JSON

Current Question (ID: 8803)

Question:

$\text{A car moves with a speed of 60 km/h for 1 hour in the east direction and with the same speed for 30 min in the south direction. The displacement of the car from the initial position is:}$

Options:

1. $60 \text{ km}$
2. $30\sqrt{2} \text{ km}$
3. $30\sqrt{5} \text{ km}$
4. $60\sqrt{2} \text{ km}$

Solution:

\textbf{Hint:} \text{ Distance} = \text{Speed} \times \text{Time} \textbf{Step:} \text{ Find the displacement of the car.} \text{The car travels 60 km east: } AB = 60 \text{ km/h} \times 1 \text{ h} = 60 \text{ km} \text{Then 30 km south: } BC = 60 \text{ km/h} \times 0.5 \text{ h} = 30 \text{ km} \text{This forms a right triangle where displacement AC is the hypotenuse.} \text{Displacement: } AC = \sqrt{(AB)^2 + (BC)^2} = \sqrt{(60)^2 + (30)^2} AC = \sqrt{3600 + 900} = \sqrt{4500} = 30\sqrt{5} \text{ km} \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
}