Import Question JSON

Current Question (ID: 9660)

Question:

$\text{A deer wants to save her life from a lion. The lion follows a path whose equation is } x^2 + y^2 = 16. \text{ For saving her life, the deer needs to move on a path whose equation will be:}$

Options:

1. $x^2 + y^2 = 4$
2. $x^2 + y^2 = 16$
3. $x^2 + y^2 - 64 = 0$
4. $\text{Both (1) and (3) are correct.}$

Solution:

$\text{Hint: Deer must not follow the path which the lion follows.}$ $\text{Step: Find the equations of the path of lion and deer.}$ $\text{The equation of lion path,}$ $x^2 + y^2 = 16$ $\text{Compared with circle equation,}$ $x^2 + y^2 = a^2$ $\Rightarrow a^2 = 16$ $\Rightarrow a = 4$ $\text{So, deer must be on another path to save itself}$ $\text{i.e., } x^2 + y^2 > 16$ $\text{or, } x^2 + y^2 < 16$ $\text{Thus, option (4) is correct.}$

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
}