Import Question JSON

Current Question (ID: 17585)

Question:

$\text{In normal adjustment, the angular magnification of an astronomical telescope is } 39. \text{ If length of the tube is } 2 \text{ m, then focal length of the objective and eyepiece are respectively:}$

Options:

1. $195 \text{ cm, } 5 \text{ cm}$
2. $190 \text{ cm, } 10 \text{ cm}$
3. $20 \text{ cm, } 180 \text{ cm}$
4. $10 \text{ cm, } 190 \text{ cm}$

Solution:

$\text{For normal adjustment, } L = f_o + f_e = 2 \text{ m} = 200 \text{ cm}$ $\text{Angular magnification } M = \frac{f_o}{f_e} = 39$ $\text{Solving these equations: } f_o = 195 \text{ cm, } f_e = 5 \text{ cm}$

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
}