Import Question JSON

Current Question (ID: 17541)

Question:

$\text{A concave lens forms the image of an object such that the distance between the object and image is 10 cm.}$ $\text{If magnification of the image is } \frac{1}{4}, \text{ the focal length of the lens is:}$

Options:

1. $-\frac{20}{3} \text{ cm}$
2. $\frac{20}{3} \text{ cm}$
3. $\frac{40}{9} \text{ cm}$
4. $-\frac{40}{9} \text{ cm}$

Solution:

$\text{Hint: } u-v = 10 \text{ cm}$ $\text{Step 1:}$ $\text{Obtain relation between } v \text{ and } u$ $v-u=10 \quad \cdots (1)$ $m = \frac{v}{u} = \frac{1}{4} \quad \cdots (2)$ $\frac{u}{4} = -u = 10$ $u = -\frac{40}{3} \text{ cm}$ $\text{Step 2:}$ $\text{Use lens formula}$ $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ $\frac{-3}{10} - \left(-\frac{3}{40}\right) = \frac{1}{f}$ $-3 \left[\frac{3}{40}\right] = \frac{1}{f}$ $f = -\frac{40}{9} \text{ cm}$

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
}