Import Question JSON

Current Question (ID: 17479)

Question:

$\text{A } 4.5 \text{ cm needle is placed } 12 \text{ cm away from a convex mirror of focal length } 15 \text{ cm. What is the magnification?}$ $1.\ 0.5$ $2.\ 0.56$ $3.\ 0.45$ $4.\ 0.15$

Options:

1. $0.5$
2. $0.56$
3. $0.45$
4. $0.15$

Solution:

$\text{Hint: magnification, } m = \frac{-v}{u}$ $\text{Step: Find the magnification.}$ $\text{Using the mirror formula, the distance of the image is given by:}$ $\Rightarrow \frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ $\text{Substituting the known values, we get:}$ $\Rightarrow \frac{1}{v} = \frac{+1}{15} - \frac{1}{12} = \frac{4+5}{60} = \frac{9}{60}$ $\Rightarrow v = \frac{60}{9} = \frac{20}{3} \text{ cm}$ $\text{The magnification of the object due to the mirror is given by:}$ $\Rightarrow m = \frac{-v}{u} = \frac{-20}{-3 \times 12}$ $\Rightarrow m = \frac{5}{9} = 0.56$ $\text{Hence, option (2) is the correct answer.}$

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
}