Import Question JSON

Current Question (ID: 19043)

Question:

$\text{A stone is thrown vertically up with speed } v_0 \text{ from a cliff of height } H. \text{ What would be the average speed of the ball till the moment it reaches ground?}$ $\text{(Given, } H = 100 \text{ m, } v_0 = 10 \text{ m/s, } g = 10 \text{ m/s}^2.)$

Options:

1. $\frac{64}{1+\sqrt{21}} \text{ m/s}$
2. $55 \text{ m/s}$
3. $110 \left(1 + \sqrt{21}\right) \text{ m/s}$
4. $\frac{110}{1+\sqrt{21}} \text{ m/s}$

Solution:

$\text{Total distance} = \frac{v_0^2}{2g} \times 2 + 100 = 110 \text{ m}$ $\text{Total time} = t_0$ $S = ut_0 + \frac{1}{2} a t_0^2$ $\Rightarrow -100 = 10t_0 - \frac{1}{2} \times 10 \times t_0^2$ $\Rightarrow t_0 = 1 + \sqrt{21} \text{ s}$ $\Rightarrow \text{Average speed} = \frac{110}{1+\sqrt{21}} \text{ m/s}$

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
}