Import Question JSON

Current Question (ID: 19054)

Question:

$\text{An object is dropped from rest at point } P. \text{ It crosses two points } A \text{ and } B \text{ in a time interval of } 2 \text{ s, where the distance } AB = 80 \text{ m. If } g = 10 \text{ m/s}^2, \text{ then what is the distance } AP \text{ in metres?}$

Options:

1. $70$
2. $45$
3. $60$
4. $55$

Solution:

$\text{Hint: } S = ut + \frac{1}{2} at^2$ $\text{Step 1: Draw the diagram.}$ $\text{Step 2: Find the time taken by the object from point } P \text{ to } A.$ $PB - PA = \frac{1}{2} g(t+2)^2 - \frac{1}{2} gt^2$ $\Rightarrow AB = \frac{1}{2} \times 10(t+2)^2 - \frac{1}{2} \times 10t^2$ $\Rightarrow 80 = 5(t+2)^2 - 5t^2$ $\Rightarrow t = 3 \text{ s}$ $\text{Step 3: Find the distance } AP.$ $AP = \frac{1}{2} gt^2$ $\Rightarrow AP = \frac{1}{2} \times 10 \times 3^2$ $\Rightarrow AP = 45 \text{ m}$ $\text{Hence, option (2) is the correct answer.}$

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
}