Import Question JSON

Current Question (ID: 17534)

Question:

$\text{A lens forms an image of a point object placed at distance } 20 \text{ cm from it. The image is formed just in front of the object at a distance } 4 \text{ cm from the object (and towards the lens). The power of the lens is:}$

Options:

1. $-2.25 \text{ D}$
2. $1.75 \text{ D}$
3. $-1.25 \text{ D}$
4. $1.4 \text{ D}$

Solution:

$\text{Hint: } \frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ $\text{Step: Find the power of the lens.}$ $\text{Using the lens formula we get:}$ $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ $\frac{1}{f} = \frac{1}{-16} - \frac{1}{-20}$ $\frac{1}{f} = \frac{-5+4}{80} \Rightarrow \frac{-1}{80}$ $\Rightarrow f = -80 \text{ cm} = -0.8 \text{ m}$ $\text{The power is given by:}$ $P = \frac{1}{f(\text{m})} = \frac{1}{-0.8}$ $P = -1.25 \text{ D}$ $\text{Hence, option (3) is the correct answer.}$

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
}