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Current Question (ID: 17549)

Question:

$\text{A point object } O \text{ is placed at a distance } 20 \text{ cm from a biconvex lens of the radius of curvature } 20 \text{ cm and } \mu = 1.5. \text{ The final image produced by lens and mirror combination will be at:}$

Options:

1. $10 \text{ cm from the mirror}$
2. $20 \text{ cm from the lens}$
3. $-20 \text{ cm from the lens}$
4. $-15 \text{ cm from the mirror}$

Solution:

$\text{Hint: The object is at the focus of the lens}$ $\text{Step 1:}$ $\text{Find the focal length of the lens}$ $\frac{1}{f} = (\mu - 1) \left[ \frac{1}{R_1} - \frac{1}{R_2} \right]$ $= (1.5 - 1) \left[ \frac{1}{20} - \left( -\frac{1}{20} \right) \right]$ $f = 20 \text{ cm}$ $\text{Step 2:}$ $\text{Draw ray diagram:}$ $\text{So, the final image produced at } -20 \text{ cm.}$

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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
}