Import Question JSON

Current Question (ID: 19035)

Question:

$\text{A car travels a distance } AB \text{ in three equal segments: the first third at a velocity of } v_1 \text{ m/s, the second third at } v_2 \text{ m/s, and the final third at } v_3 \text{ m/s.}$ $\text{Given that } v_3 = 3v_1, \ v_2 = 2v_1 \text{ and } v_1 = 11 \text{ m/s, the average velocity of the car is:}$

Options:

1. $12 \text{ m/s}$
2. $18 \text{ m/s}$
3. $16 \text{ m/s}$
4. $11 \text{ m/s}$

Solution:

$\text{The average velocity of an object is the ratio of the displacement and the corresponding time interval.}$ $\text{The average velocity of the car is given by:}$ $\frac{n}{v_{\text{avg}}} = \frac{1}{v_1} + \frac{1}{v_2} + \frac{1}{v_3}$ $\Rightarrow \frac{3}{v_{\text{avg}}} = \frac{1}{11} + \frac{1}{2 \times 11} + \frac{1}{3 \times 11}$ $\Rightarrow \frac{3}{v_{\text{avg}}} = \frac{6 + 3 + 2}{66} = \frac{11}{66}$ $\Rightarrow \frac{3}{v_{\text{avg}}} = \frac{1}{6}$ $\Rightarrow v_{\text{avg}} = 18 \text{ m/s}$ $\text{Hence, option (2) is the correct answer.}$

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
}