Import Question JSON

Current Question (ID: 17476)

Question:

$\text{The diagram represents a concave mirror, where } F \text{ is the principal focus and } f \text{ is the focal length. The mirror is used to produce an image of an object.}$ $\text{Which of the following statements are correct? (assume the mirror is parabolic)}$

Options:

1. $(A) \text{ Incident rays traveling parallel to the principal axis always pass through } F \text{ after reflection.}$
2. $(B) \text{ Incident rays passing through } F \text{ always travel parallel to the principal axis after reflection.}$
3. $(C) \text{ The image formed is always inverted.}$
4. $(D) \text{ The image formed is always real.}$

Solution:

$\text{Hint: The nature of the image depends on the position of the object.}$ $\text{Explanation: Incident rays travelling parallel to the principal axis always pass through } F \text{ after reflection.}$ $\text{Incident rays passing through } F \text{ always travel parallel to the principal axis after reflection.}$ $\text{The image can be real or virtual, erect or inverted, and large or small depending on the position of the object.}$ $\text{Therefore, the correct statements are (A) and (B) only.}$ $\text{Hence, option (4) is the correct answer.}$

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
}