Import Question JSON

Current Question (ID: 17899)

Question:

$\text{The unit cell dimensions of a cubic lattice (edges } a, b, c \text{ and the angles between them, } \alpha, \beta, \gamma \text{) are:}$

Options:

1. $a = b = c, \alpha = \beta = \gamma = 90^\circ$
2. $a = b \neq c, \alpha = \beta = \gamma = 90^\circ$
3. $a = b = c, \alpha = \gamma = 90^\circ, \beta \neq 90^\circ$
4. $a \neq b \neq c, \alpha = \beta = 90^\circ, \gamma \neq 90^\circ$

Solution:

$\text{For Cubic lattice, all sides and all angles are equal.}$ $\text{It is based on the definition of the cubic lattice. The cubic lattice is the most symmetrical.}$ $\text{In cubic lattice all sides are equal and all angles are } 90^\circ \text{ i.e. } a = b = c, \alpha = \beta = \gamma = 90^\circ.$ $\text{Hence, option 1 is the correct answer.}$

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
}