Import Question JSON

Current Question (ID: 9680)

Question:

$\text{When a man walks on a horizontal road with velocity 1 km/h, the rain appears to him coming vertically at a speed of 2 km/h. The actual speed of the rain with respect to ground is:}$

Options:

1. $\sqrt{3} \text{ km/h}$
2. $\sqrt{5} \text{ km/h}$
3. $1 \text{ km/h}$
4. $3 \text{ km/h}$

Solution:

\text{Given, } \vec{v}_m = 1\hat{i} \text{ km/h}, \vec{v}_{rm} = -2\hat{j} \text{ km/h} \text{As we know, } \vec{v}_{r,m} = \vec{v}_r - \vec{v}_m \Rightarrow \vec{v}_r = \vec{v}_{r,m} + \vec{v}_m \vec{v}_r = (-2\hat{j} + 1\hat{i}) \text{ km/h} |\vec{v}_r| = \sqrt{2^2 + 1^2} = \sqrt{5} \text{ km/h} \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
}