Import Question JSON

Current Question (ID: 9553)

Question:

$\text{A vector } \vec{a} \text{ is turned without a change in its length through a small angle } d\theta. \text{ The value of } |\Delta \vec{a}| \text{ and } \Delta a \text{ are, respectively:}$

Options:

1. $0, ad\theta$
2. $ad\theta, 0$
3. $0, 0$
4. $\text{None of these}$

Solution:

\text{Hint: Angle = arc/radius} \text{Step: Find the value of |Δa| and Δa} \text{From the figure:} \text{|OA| = a and |OB| = a} \text{From triangle rule: OB - OA = AB = Δa} \text{Therefore: |Δa| = AB} \text{Using angle = arc/radius} \text{AB = a × dθ} \text{So |Δa| = a × dθ} \text{Δa means change in magnitude of vector:} \text{|OB| - |OA| = a - a = 0} \text{So Δa = 0} \text{Therefore: |Δa| = a dθ and Δa = 0} \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
}