Import Question JSON

Current Question (ID: 17531)

Question:

$\text{A concave lens of focal length } 25 \text{ cm produces an image } \frac{1}{10} \text{th of the size of the object. The distance of the object from the lens is:}$

Options:

1. $225 \text{ cm}$
2. $250 \text{ cm}$
3. $150 \text{ cm}$
4. $175 \text{ cm}$

Solution:

$\text{Hint: } \frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ $\text{Step: Find the distance of the object from the lens.}$ $m = \frac{v}{u} = \frac{1}{10} \Rightarrow v = \frac{u}{10}$ $\text{Using the lens formula we get;} \Rightarrow \frac{1}{v} = \frac{1}{u} - \frac{1}{f} \Rightarrow \frac{10}{u} - \frac{1}{u} = \frac{1}{-25}$ $\Rightarrow u = -225 \text{ cm}$ $\text{Hence, option (1) is the correct answer.}$

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
}