Import Question JSON

Current Question (ID: 8807)

Question:

$\text{A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. There is a pit on the road 13 m away from the starting point. The drunkard will fall into the pit after:}$

Options:

1. $37 \text{ s}$
2. $31 \text{ s}$
3. $29 \text{ s}$
4. $33 \text{ s}$

Solution:

$\text{Hint: The displacement is defined as the shortest path length between the initial and final positions.}$ $\text{Step 1: Find the displacement of the drunkard in one cycle.}$ $\text{Displacement in 1 cycle = steps in forward direction + steps in backward direction}$ $= 2 \text{ steps in } 8 \text{ sec}$ $\text{Step 2: Find the displacement of the drunkard in 4 cycles.}$ $\text{So in 4 cycles, displacement = 8 m, time = 32 sec}$ $\text{Step 3: Find the total time taken by the drunkard.}$ $\text{For 5}^{\text{th}} \text{ cycle, the man reaches the pit \& falls.}$ $\text{So the total time = 32 + 5}$ $= 37 \text{ sec}$ $\text{Hence, option (1) is the correct answer.}$

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
}