Import Question JSON

Current Question (ID: 9633)

Question:

$\text{A body is thrown vertically so as to reach its maximum height in } t \text{ second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is:}$

Options:

1. $\sqrt{2}t$
2. $\left(1 + \frac{1}{\sqrt{2}}\right)t$
3. $\frac{3t}{2}$
4. $\frac{t}{\sqrt{2}}$

Solution:

$\text{Hint: } H = ut + \frac{1}{2}at^2$ $\text{Step: Find the total time from the time of projection.}$ $\text{Let time to reach P from A be } t$ $H = \frac{1}{2}gt^2$ $t = \sqrt{\frac{2H}{g}}$ $\text{Time to reach C from P be } t'$ $\frac{H}{2} = \frac{1}{2}g(t')^2$ $t' = \sqrt{\frac{H}{g}} = \sqrt{\frac{2H}{2g}} = \frac{t}{\sqrt{2}}$ $\text{So total time to go from A to C}$ $t + t' = t + \frac{t}{\sqrt{2}}$ $= t\left[1 + \frac{1}{\sqrt{2}}\right]$ $\text{Hence, option (2) is the correct answer.}$

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
}