Question

Find the area bounded by the curve \( y^2 = 4x \) and its latus rectum.

• A. \( \frac{4}{3} \) sq units
• B. \( \frac{8}{3} \) sq units
• C. \( \frac{16}{3} \) sq units
• D. \( \frac{2}{3} \) sq units

Hint:

For the parabola \(y^2 = 4ax\), the latus rectum is \(x=a\). When finding the area bounded by the parabola and its latus rectum, use symmetry about the \(x\)-axis and integrate the positive branch of the curve.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to distinguish between addition polymers (formed by simply linking monomers) and condensation polymers (formed with the loss of small molecules).
Step 2: Key Formula or Approach:
Condensation polymerization typically involves bifunctional or trifunctional monomers and results in the elimination of a byproduct like \( H_2O \), \( NH_3 \), or \( HCl \).
Step 3: Detailed Explanation:
1. Polyethylene, PVC, and Polystyrene: These are addition polymers formed from alkenes (ethene, vinyl chloride, and styrene respectively) without any loss of molecules.
2. Nylon 6,6: It is prepared by the condensation of hexamethylenediamine and adipic acid.
\[ n H_2N(CH_2)_6NH_2 + n HOOC(CH_2)_4COOH \rightarrow \dots \] In this process, water (\( H_2O \)) molecules are eliminated as the amide bonds form. This makes it a condensation polymer.
Step 4: Final Answer:
Nylon 6,6 is the correct example of a condensation polymer.