Import Question JSON

Current Question (ID: 17581)

Question:

$\text{In a compound microscope, the magnification is } 95, \text{ the distance of the object from the objective lens is } \left( \frac{1}{3.8} \right) \text{ cm and the focal length of the objective is } \frac{1}{4} \text{ cm. What is the magnification of the eyepiece when the final image is formed at the least distance of distinct vision?}$ $1. \text{ } 5$ $2. \text{ } 10$ $3. \text{ } 100$ $4. \text{ none of the above}$

Options:

1. $5$
2. $10$
3. $100$
4. $\text{none of the above}$

Solution:

$\text{Hint: } m = m_0 \times m_e$ $\text{Step: Find the magnification of the eye-piece.}$ $\text{The magnification of the compound microscope is given by:}$ $m = m_0 \times m_e$ $m = \left( \frac{f_0}{u + f_0} \right) \times m_e$ $\Rightarrow -95 = \left( \frac{1}{4} \div \left( \frac{-1}{3.8} + \frac{1}{4} \right) \right) m_e$ $\Rightarrow -95 = -19 m_e$ $\Rightarrow m_e = \frac{95}{19} = 5$ $\text{Therefore, the magnification of the eye-piece is } 5.$ $\text{Hence, option (1) is the correct answer.}$

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
}