Import Question JSON

Current Question (ID: 17533)

Question:

$\text{The power of an equi-convex lens is } P. \text{ After cutting it in different ways, the combination of lenses is listed in Column I, along with their effective powers in Column II. Match the items in the two columns.}$ $\text{Column I}$ $\text{(A)}$ $\text{(B)}$ $\text{(C)}$ $\text{(D)}$ $\text{Column II}$ $\text{(P) zero}$ $\text{(Q) } P$ $\text{(R) } 2P$ $\text{(S) } \frac{P}{2}$

Options:

1. $\text{A} \rightarrow \text{Q}, \text{B} \rightarrow \text{P}, \text{C} \rightarrow \text{S}, \text{D} \rightarrow \text{R}$
2. $\text{A} \rightarrow \text{S}, \text{B} \rightarrow \text{R}, \text{C} \rightarrow \text{Q}, \text{D} \rightarrow \text{P}$
3. $\text{A} \rightarrow \text{Q}, \text{B} \rightarrow \text{S}, \text{C} \rightarrow \text{Q}, \text{D} \rightarrow \text{R}$
4. $\text{A} \rightarrow \text{S}, \text{B} \rightarrow \text{R}, \text{C} \rightarrow \text{Q}, \text{D} \rightarrow \text{Q}$

Solution:

$\text{Hint: } P = \frac{1}{f}$ $\text{Step: Find the power of the combination of lenses.}$ $\text{Lens A is a single part of the original equi-convex lens that resembles a single convex lens shape. This is effectively half of the lens horizontally, not vertically split. So its power remains as } P. \text{ So, A} \rightarrow \text{Q.}$ $\text{Lens B appears to be a plano-convex lens that is half of the original equi-convex lens. When an equi-convex lens of power } P \text{ is cut along the diameter, each half has half the power, so its power should be } \frac{P}{2}. \text{ So, B} \rightarrow \text{S.}$ $\text{Lens C appears to be two plano-convex lenses opposite to each other symmetrically, the net power of the combination is } \frac{P}{2}. \text{ So, C} \rightarrow \text{Q.}$ $\text{Lens D resembles a combination of two equi-convex lenses placed together, which would double the effective power i.e., } 2P. \text{ So, D} \rightarrow \text{R.}$ $\text{Therefore, the correct match is A} \rightarrow \text{Q, B} \rightarrow \text{S, C} \rightarrow \text{Q, D} \rightarrow \text{R.}$ $\text{Hence, option (3) is the correct answer.}$

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
}