Import Question JSON

Current Question (ID: 19122)

Question:

$\text{A body of mass 10 kg is projected at an angle of } 45^\circ \text{ with the horizontal.}$ $\text{The trajectory of the body is observed to pass through a point } (20, 10).$ $\text{If } T \text{ is the time of flight, then its momentum vector, at time } t = \frac{T}{\sqrt{2}}, \text{ is }$ $\underline{\phantom{answer}}$ $\text{[Take } g = 10 \text{ m/s}^2]$

Options:

1. $100\hat{i} + (100\sqrt{2} - 200)\hat{j}$
2. $100\sqrt{2}\hat{i} + (100 - 200\sqrt{2})\hat{j}$
3. $100\hat{i} + (100 - 200\sqrt{2})\hat{j}$
4. $100\sqrt{2}\hat{i} + (100\sqrt{2} - 200)\hat{j}$

Solution:

$\text{The correct answer is option 4.}$

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
}