Import Question JSON

Current Question (ID: 17530)

Question:

$\text{The focal length of a convex lens is } 40 \text{ cm and the size of the inverted image formed is half of the object. The distance of the object is:}$

Options:

1. $60 \text{ cm}$
2. $120 \text{ cm}$
3. $30 \text{ cm}$
4. $180 \text{ cm}$

Solution:

$\text{Hint: } \frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ $\text{Step: Find the distance of the object.}$ $\text{Given; } f = +40 \text{ cm}, m = -\frac{1}{2}$ $\text{Magnification is given by;}$ $m = \frac{v}{u} \Rightarrow -\frac{1}{2} = \frac{v}{u} \Rightarrow v = -\frac{u}{2}$ $\text{Substituting the value of } u \text{ in lens formula;}$ $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \Rightarrow \frac{1}{40} = \frac{-u}{2} - \frac{1}{u} \Rightarrow \frac{1}{40} = \frac{-3}{u}$ $\Rightarrow u = -120 \text{ cm}$ $\text{Hence, option (2) is the correct answer.}$

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
}