Import Question JSON

Current Question (ID: 8897)

Question:

$\text{In the following graph, the distance travelled by the body in metres is:}$ $\text{The velocity-time graph shows:}$ $\text{- From } t = 0 \text{ to } t = 10\text{s: velocity increases linearly from 0 to 10 m/s}$ $\text{- From } t = 10 \text{ to } t = 20\text{s: velocity remains constant at 10 m/s}$ $\text{- From } t = 20 \text{ to } t = 30\text{s: velocity decreases linearly from 10 to 0 m/s}$

Options:

1. $200$
2. $250$
3. $300$
4. $400$

Solution:

\text{Hint: Distance = area under the v-t graph.} \text{Step: Find the distance travelled by the body.} \text{distance = area covered under velocity-time graph} s = \frac{1}{2}(30 + 10) \times 10 = 200 \text{ meter} \text{Alternatively, we can calculate by breaking into three parts:} \text{Area}_{1} = \frac{1}{2} \times 10 \times 10 = 50 \text{ m (triangle from 0-10s)} \text{Area}_{2} = 10 \times 10 = 100 \text{ m (rectangle from 10-20s)} \text{Area}_{3} = \frac{1}{2} \times 10 \times 10 = 50 \text{ m (triangle from 20-30s)} \text{Total distance} = 50 + 100 + 50 = 200 \text{ m} \text{Hence, option (1) 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
}