Import Question JSON

Current Question (ID: 8926)

Question:

$\text{Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time } t_1\text{. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time } t_2\text{. The time taken by her to walk upon the moving escalator will be:}$

Options:

1. $\frac{t_1 t_2}{t_2 - t_1}$
2. $\frac{t_1 t_2}{t_2 + t_1}$
3. $t_1 - t_2$
4. $\frac{t_1 + t_2}{2}$

Solution:

$\text{Hint: Velocity} = \frac{\text{displacement}}{\text{time}}$ $\text{Step: Find the time taken by Preeti to walk upon the moving escalator.}$ $\text{The velocity of Preeti with respect to the elevator, } v = \frac{d}{t_1}$ $\text{The velocity of the elevator with respect to the ground, } v = \frac{d}{t_2}$ $\text{Then the velocity of Preeti with respect to the ground is given by;}$ $v = v_1 + v_2$ $\Rightarrow \frac{d}{t} = \frac{d}{t_1} + \frac{d}{t_2}$ $\Rightarrow t = \frac{t_1 t_2}{t_1 + t_2}$ $\text{Here, } t \text{ is the time taken by Preeti to walk upon the moving escalator.}$ $\text{Hence, option (2) is the correct answer.}$

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
}