Import Question JSON

Current Question (ID: 9554)

Question:

$\text{A man starts from point } P \text{ and goes 20 m due East, then 5 m due North, then 35 m due West, and finally 25 m due South. His displacement from point } P \text{ is:}$

Options:

1. $25 \text{ m at } \tan^{-1}\left(\frac{4}{3}\right) \text{ west of south.}$
2. $85 \text{ m in south-west.}$
3. $25 \text{ m at } \tan^{-1}\left(\frac{3}{4}\right) \text{ west of south.}$
4. $15 \text{ m at } \tan^{-1}\left(\frac{3}{4}\right) \text{ west of south}$

Solution:

\text{Hint: Find the final and initial position} \text{Step 1: Set coordinate axes} \text{Step 2: Draw a vector diagram} \text{Step 3: Find the displacement vector} \text{Vector r = 20i + 5j - 35i - 25j} \text{Vector r = -15i - 20j} \text{Magnitude: r = sqrt(225 + 400) = 25 m} \text{Step 4: Find the angle of the displacement vector} \text{The angle θ makes with south direction (negative y-axis)} \text{Using tangent function: tan θ = 15/20 = 3/4} \text{Therefore: θ = tan⁻¹(3/4)} \text{Displacement: 25 m at θ = tan⁻¹(3/4) west of south} \text{Hence, option (3) 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
}