An alkene A with molecular formula C\(_6\)H\(_{10}\) on ozonolysis gives a mixture of two compounds B and C. Compound B gives a positive Fehling's test and also reacts with iodine and NaOH solution. Compound C does not give Fehling's test but forms iodoform. Identify the compounds A, B, and C.
The molecular formula of the alkene is \( C_6H_{10} \). The ozonolysis of this alkene breaks it into two carbonyl compounds. After ozonolysis, the two products formed are acetaldehyde (B) and butan-2-one (C).
The alkene with the formula \( C_6H_{10} \) and a structure that undergoes ozonolysis to give acetaldehyde and butan-2-one is likely 1,5-hexadiene. The structure of 1,5-hexadiene is: \[ \text{CH}_2\text{=CH-CH}_2\text{CH}_2\text{CH}_3 \]
Ozonolysis of 1,5-hexadiene results in the following products:
- Alkene A is 1,5-hexadiene. - Compound B is acetaldehyde (\( \text{CH}_3\text{CHO} \)). - Compound C is butan-2-one (\( \text{CH}_3\text{COCH}_2\text{CH}_3 \)).
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 \(P,O,Q\).