Import Question JSON

Current Question (ID: 9545)

Question:

$\text{A particle starting from the point (1, 2) moves in a straight line in the XY-plane. Its coordinates at a later time are (2, 3). The path of the particle makes with x-axis an angle of:}$

Options:

1. $30°$
2. $45°$
3. $60°$
4. $\text{data is insufficient}$

Solution:

$\text{Hint: Since the particles move along a straight line. This means that the given coordinates lie on the line on which the particle moves.}$ $\text{Step 1: Draw the line.}$ $\text{Step 2: Calculate the slope of the line}$ $\tan\theta = \frac{H}{B} = \frac{1}{1} = 1$ $\tan 45° = 1$ $\text{Here } \theta = 45°$ $\text{Therefore, the path of the particle makes an angle of } 45° \text{ with the x-axis.}$ $\text{Hence, option (2) is the correct answer.}$

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
}