Import Question JSON

Current Question (ID: 19076)

Question:

$\text{Ship } A \text{ is sailing towards north-east with velocity } \vec{v} = 30\hat{i} + 50\hat{j} + 50\hat{k} \text{ km/hr where } \hat{i} \text{ and } \hat{j} \text{ north.}$ $\text{Ship } B \text{ is at a distance of } 80 \text{ km east and } 150 \text{ km north of Ship } A \text{ and is sailing towards west at } 10 \text{ km/hr.}$ $A \text{ will be at minimum distance from } B \text{ in:}$

Options:

1. $4.2 \text{ hrs}$
2. $2.2 \text{ hrs}$
3. $2.6 \text{ hrs}$
4. $3.2 \text{ hrs}$

Solution:

$\text{Hint: } V_{AB} = V_B - V_A$ $\vec{V}_{AB} = 40\hat{i} + 50\hat{j}$ $\vec{r}_{AB} = 150\hat{j}$ $t_{\text{min}} = \frac{\vec{V}_{AB} \cdot \vec{r}_{AB}}{|\vec{V}_{AB}|^2} = 2.6 \text{ hrs}$

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
}