An organic compound(A)(molecular formula\( C_8H_{16}O_2\))was hydrolysed with dilute sulphuric acid to give a carboxylic acid(B)and an alcohol(C).Oxidation of(C)with chromic acid produced (B).(C)on dehydration gives \(but-1-ene\).Write equations for the reactions involved.
An organic compound A with molecular formula \(C_8H_{16}O_2\) gives a carboxylic acid(B)and an alcohol(C)on hydrolysis with dilute sulphuric acid.Thus,compound A must be an ester.Further, alcohol C gives acid B on oxidation with chromic acid.Thus,B and C must contain equal number of carbon atoms.
Since compound A contains a total of 8 carbon atoms,each of B and C contain 4 carbon atoms.
Again,on dehydration,alcohol C gives \(but-1-ene\).Therefore,C is of straight chain and hence,it is \(butan-1-ol\).
On oxidation,\(Butan-1-ol\) gives butanoic acid.
Hence, acid B is butanoic acid.Hence,the ester with molecular formula \(C_8H_{16}O_2\)2 is butylbutanoate.

All the given reactions can be explained by the following equations.

(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 \(P,O,Q\).






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