Import Question JSON

Current Question (ID: 19061)

Question:

$\text{Two balls A and B are placed at the top of a 180 m tall tower. Ball A is released from the top at } t = 0 \text{ s. Ball B is thrown vertically down with an initial velocity 'u' at } t = 2 \text{ s.}$ $\text{After a certain time, both balls meet 100 m above the ground.}$ $\text{The value of 'u' in ms}^{-1} \text{ is: [use } g = 10 \text{ ms}^{-2}] :$

Options:

1. $10$
2. $15$
3. $20$
4. $30$

Solution:

$\text{Let the time taken for ball A to reach 100 m above the ground be } t \text{ seconds.}$ $\text{For ball A:}$ $s = ut + \frac{1}{2}gt^2 \Rightarrow 80 = 0 + \frac{1}{2} \times 10 \times t^2 \Rightarrow t^2 = 16 \Rightarrow t = 4 \text{ s}$ $\text{For ball B:}$ $\text{Time taken to reach 100 m above the ground is } (t - 2) \text{ seconds.}$ $\text{Using } s = ut + \frac{1}{2}gt^2:$ $80 = u \times 2 + \frac{1}{2} \times 10 \times 4$ $80 = 2u + 20 \Rightarrow 2u = 60 \Rightarrow u = 30 \text{ ms}^{-1}$

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
}