Import Question JSON

Current Question (ID: 17536)

Question:

$\text{Two similar plano-convex lenses are combined together in three different ways as shown in the adjoining figure. The ratio of the focal lengths in three cases will be:}$

Options:

1. $1 : 2 : 2$
2. $1 : 1 : 1$
3. $1 : 2 : 2$
4. $2 : 1 : 1$

Solution:

$\text{When two plano-convex lenses are combined, the focal length of the combination depends on the arrangement.}$ $\text{In the first case, the lenses are combined with their curved surfaces facing each other, resulting in a focal length of } f_1.$ $\text{In the second case, the lenses are combined with their plane surfaces facing each other, resulting in a focal length of } f_2.$ $\text{In the third case, the lenses are combined with one curved and one plane surface facing each other, resulting in a focal length of } f_3.$ $\text{The ratio of the focal lengths is } 1 : 1 : 1.$

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
}