Import Question JSON

Current Question (ID: 19067)

Question:

$\text{A car travels } 4 \text{ km distance with a speed of } 3 \text{ km/hr and next } 4 \text{ km with a speed of } 5 \text{ km/hr. What is the average speed of the car?}$

Options:

1. $\frac{15}{2} \text{ km/hr}$
2. $\frac{15}{4} \text{ km/hr}$
3. $15 \text{ km/hr}$
4. $10 \text{ km/hr}$

Solution:

$\text{Hint: } v_{\text{avg}} = \frac{2v_1v_2}{v_1+v_2}$ $\text{Step: Find the average speed of the car.}$ $\text{The average speed of the car is given by:}$ $\text{Average velocity} = \frac{\text{Total Distance}}{\text{Total time}}$ $\Rightarrow v = \frac{4+4}{\frac{4}{3} + \frac{4}{5}} \text{ km/hr}$ $\Rightarrow v = \frac{15}{4} \text{ km/hr}$ $\text{Hence, option (2) is the correct answer.}$

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
}