Import Question JSON

Current Question (ID: 9693)

Question:

$\text{A river is flowing from east to west at a speed of 5 m/min. A man on south bank of river, capable of swimming 10 m/min in still water, wants to swim across the river in shortest time. He should swim:}$

Options:

1. $\text{Due north}$
2. $\text{Due north-east}$
3. $\text{Due north-east with double the speed of the river}$
4. $\text{None of the above}$

Solution:

$\text{From the diagram, we can see the river crossing scenario where:}$ $\text{- Point A is the starting position on the south bank}$ $\text{- Point B is directly across on the north bank}$ $\text{- Point C is where the swimmer actually reaches due to river current}$ $\text{- The angle } \theta \text{ represents the swimming direction}$ $\text{For shortest time to cross the river, the swimmer should swim along AB (due north).}$ $\text{This is because the time to cross depends only on the component of swimming velocity perpendicular to the river flow.}$ $\text{When swimming due north with speed 10 m/min, the perpendicular component is maximum (10 m/min).}$ $\text{The river current will carry him downstream to point C, but the crossing time will be minimum.}$ $\text{Therefore, he should swim due north.}$

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
}