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Current Question (ID: 17548)

Question:

$\text{A luminous object is placed at a distance of } 30 \text{ cm from the convex lens with a focal length of } 20 \text{ cm.}$ $\text{On the other side of the lens, at what distance from the lens, a convex mirror with a radius of curvature of } 10 \text{ cm be placed in order to have an upright image of the object coincident with it?}$

Options:

1. $12 \text{ cm}$
2. $30 \text{ cm}$
3. $50 \text{ cm}$
4. $60 \text{ cm}$

Solution:

$\text{For lens, } u = -30 \text{ cm}, f = 20 \text{ cm},$ $\text{Hence, by using } \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \Rightarrow \frac{1}{+20} = \frac{1}{v} - \frac{1}{-30} \Rightarrow v = 60 \text{ cm}$ $\text{The final image will coincide with the object if the light ray falls normally on the convex mirror as shown.}$ $\text{From the figure, it is seen clearly that the separation between lens and mirror is } 60 - 10 = 50 \text{ cm.}$

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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
}