Import Question JSON

Current Question (ID: 9687)

Question:

$\text{A car is moving along east at 10 m/s and a bus is moving along north at 10 m/s. The velocity of the car with respect to the bus is along:}$

Options:

1. $\text{North-East}$
2. $\text{South-East}$
3. $\text{North-West}$
4. $\text{South-West}$

Solution:

$\text{Hint: } \vec{v}_{CB} = \vec{v}_C - \vec{v}_B$ $\text{Step 1: Define the coordinate system:}$ $\text{We establish a coordinate system where East is positive x-direction and North is positive y-direction.}$ $\text{Step 2: Write velocity of car & bus}$ $\vec{v}_C = 10\hat{i} \text{ (car moving east)}$ $\vec{v}_B = 10\hat{j} \text{ (bus moving north)}$ $\text{Step 3: Use relative velocity formula}$ $\vec{v}_{C,B} = \vec{v}_C - \vec{v}_B$ $= 10\hat{i} - 10\hat{j}$ $\text{This gives us a vector pointing 10 units east and 10 units south, which makes a 45° angle below the positive x-axis.}$ $\text{Therefore, the direction is South-East.}$

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
}