An organic compound with the molecular formula \( C_9H_{10}\)O forms \(2,4-DNP\) derivative,reduces Tollens’ reagent and undergoes Cannizzaro reaction.On vigorous oxidation,it gives \(1,2-benzenedicarboxylic\) acid.Identify the compound.
It is given that the compound(with molecular formula \(C_9H_{10}O\))forms 2,4-DNP derivative and reduces Tollen's reagent.Therefore,the given compound must be an aldehyde.
Again,the compound undergoes cannizzaro reaction and on oxidation gives \(1,2-benzenedicarboxylic\) acid.Therefore,the\( -CHO\) group is directly attached to a benzene ring and this benzaldehyde is ortho-substituted.Hence,the compound is \(2-ethylbenzaldehyde.\)

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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