Import Question JSON

Current Question (ID: 8727)

Question:

$\text{The position of a body with acceleration } a \text{ is given by } x = Ka^m t^n \text{ (assume } t \text{ to be time). The values of } m \text{ and } n \text{ will be:}$

Options:

1. $m = 1, n = 1$
2. $m = 1, n = 2$
3. $m = 2, n = 1$
4. $m = 2, n = 2$

Solution:

$\text{Hint: Recall the dimensions of quantities.}$ $\text{Step: Find the values of } m \text{ and } n$ $\text{According to dimensions analysis, the dimensions of LHS = Dimensions of RHS.}$ $\Rightarrow x = Ka^m \times t^n$ $[M^0L^1T^0] = [LT^{-2}]^m[T]^n$ $\text{By comparing power on both sides,}$ $m = 1 \text{ and } -2m + n = 0 \Rightarrow n = 2$ $\text{Hence, option (2) is the correct answer.}$

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
}