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Current Question (ID: 17474)

Question:

$\text{An object is placed } 20 \text{ cm in front of a concave mirror of a radius of curvature } 10 \text{ cm.}$ $\text{The position of the image from the pole of the mirror is:}$

Options:

1. $7.67 \text{ cm}$
2. $6.67 \text{ cm}$
3. $8.67 \text{ cm}$
4. $9.67 \text{ cm}$

Solution:

$\text{Hint: } \frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ $\text{Step 1: Find the focal length of the mirror.}$ $\text{The focal length of the mirror is given by:}$ $f = \frac{R}{2} = -5 \text{ cm}$ $\text{Step 2: Find the position of the image from the pole of the mirror.}$ $\text{Use the mirror formula}$ $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ $\Rightarrow \frac{1}{v} + \frac{1}{20} = \frac{-1}{5} \Rightarrow v = \frac{-20}{3} = -6.67 \text{ cm}$ $\text{Hence, option (2) is the correct answer.}$

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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
}