Convert Ethanal to But-2-enal
The conversion of Ethanal (Acetaldehyde) to But-2-enal involves an aldol condensation reaction.
The steps are:
1. Aldol condensation: Ethanal undergoes aldol condensation in the presence of a base like NaOH to form But-3-en-2-al (crotonaldehyde). \[ \text{CH}_3\text{CHO} + \text{CH}_3\text{CHO} \xrightarrow{\text{NaOH}} \text{CH}_3\text{CH=CHCHO} \quad (\text{But-3-en-2-al}) \]
2. The final product is But-2-enal, which is the desired compound. \vspace{10pt}
(i) Explain Aldol condensation with example.
(ii) How are the following conversions achieved:
(a) Benzene Benzaldehyde, (b) Ethanoic acid ethanol.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).