Import Question JSON

Current Question (ID: 9544)

Question:

$\text{The position of a moving particle at time } t \text{ is } \vec{r} = 3\hat{i} + 4t^2\hat{j} - t^3\hat{k}. \text{ Its displacement during the time interval } t = 1\text{s to } t = 3\text{s will be:}$

Options:

1. $\hat{j} - \hat{k}$
2. $3\hat{i} - 4\hat{j} - \hat{k}$
3. $9\hat{i} + 36\hat{j} - 27\hat{k}$
4. $32\hat{j} - 26\hat{k}$

Solution:

$\text{Hint: Displacement} = r_2 - r_1.$ $\text{Step 1: Find the position of t = 1 sec.}$ $\vec{r_1} = 3\hat{i} + 4\hat{j} - \hat{k}$ $\text{Step 2: Find the position at t = 3 sec.}$ $\vec{r_3} = 3\hat{i} + 4(3)^2\hat{j} - (3)^3\hat{k}$ $= 3\hat{i} + 36\hat{j} - 27\hat{k}$ $\text{Step 3: Find the displacement.}$ $\Delta\vec{r} = \vec{r_3} - \vec{r_1}$ $= 32\hat{j} - 26\hat{k}$ $\text{Hence, option (4) is the correct answer.}$

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
}