Import Question JSON

Current Question (ID: 9842)

Question:

$\text{The relationship between the force F and the position x of a body is as shown in the figure. The work done in displacing the body from x = 1 m to x = 5 m will be:}$

Options:

1. $\text{30 J}$
2. $\text{15 J}$
3. $\text{25 J}$
4. $\text{20 J}$

Solution:

$\text{Work done = area under F-x graph.}$ $\text{The work done in displacing the body from x = 1 m to x = 5 m i.e.,}$ $W = \text{Area of ABNM} + \text{Area of CDEN} - \text{Area of EHGF} + \text{Area of HIJ}$ $= (2 - 1) \times (10 - 0) + (3 - 2)(5 - 0) + (4 - 3)(-5 - 0) + \frac{1}{2}(5 - 4)(10 - 0)$ $= 15 \text{ J}$ $\text{Note: Do not include the area from x = 0 to x = 1 m while finding the work done from x = 1 m to x = 5 m.}$

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
}