What is meant by the following terms? Give an example of the reaction in each case.
\((i)\)\(Cyanohydrin\)
\((ii)Acetal \)
\((iii)Semicarbazone \)
\((iv)Aldol \)
\((v)Hemiacetal \)
\((vi)Oxime \)
\((vii)Ketal \)
\((vii)Imine \)
\((ix)\)\(2,4-DNP-derivative \)
\((x)Schiff's base\)
(i) Cyanohydrin:
Cyanohydrins are organic compounds having the formula\( RR“²C(OH)CN,\) where R and \(R“²\) can be alkyl or aryl groups.
Aldehydes and ketones react with hydrogen cyanide (HCN) in the presence of excess sodium cyanide (NaCN) as a catalyst to field cyanohydrin. These reactions are known as cyanohydrin reactions.
Cyanohydrins are useful synthetic intermediates.
(ii) Acetal:
Acetals are gem - dialkoxy alkanes in which two alkoxy groups are present on the terminal carbon atom. One bond is connected to an alkyl group while the other is connected to a hydrogen atom.
When aldehydes are treated with two equivalents of a monohydric alcohol in the presence of dry HCl gas, hemiacetals are produced that further react with one more molecule of alcohol to yield acetal.
(iii) Semicarbarbazone:
Semicarbazones are derivatives of aldehydes and ketones produced by the condensation reaction between a ketone or aldehyde and semicarbazide.
Semicarbazones are useful for identification and characterization of aldehydes and ketones.
(iv) Aldol: A β-hydroxy aldehyde or ketone is known as an aldol. It is produced by the condensation reaction of two molecules of the same or one molecule each of two different aldehydes or ketones in the presence of a base. 
(v) Hemiacetal:
Hemiacetals are α - alkoxyalcohols
General structure of a hemiacetal Aldehyde reacts with one molecule of a monohydric alcohol in the presence of dry HCl gas.
(vi) Oxime:
Oximes are a class of organic compounds having the general formula \(RR“²CNOH\), where R is an organic side chain and \(R“² \) is either hydrogen or an organic side chain. If R“² is H, then it is known as aldoxime and if R“² is an organic side chain, it is known as ketoxime.
On treatment with hydroxylamine in a weakly acidic medium, aldehydes or ketones form oximes.
(vii) Ketal:
Ketals are gem - dialkoxyalkanes in which two alkoxy groups are present on the same carbon atom within the chain. The other two bonds of the carbon atom are connected to two alkyl groups.
Ketones react with ethylene glycol in the presence of dry HCl gas to give a cyclic product known as ethylene glycol ketals.
(viii) Imine:
Imines are chemical compounds containing a carbon nitrogen double bond.
Imines are produced when aldehydes and ketones react with ammonia and its derivatives.
(ix) 2, 4 - DNP - derivative:
2, 4 - dinitrophenylhydragones are 2, 4 - DNP - derivatives, which are produced when aldehydes or ketones react with 2, 4 - dinitrophenylhydrazine in a weakly acidic medium
To identify and characterize aldehydes and ketones, 2, 4 - DNP derivatives are used.
(x) Schiff's base:
Schiff's base (or azomethine) is a chemical compound containing a carbon-nitrogen double bond with the nitrogen atom connected to an aryl or alkyl group-but not hydrogen. They have the general formula \(R1R2C = NR3\). Hence, it is an imine.
It is named after a scientist, Hugo Schiff. 
(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 \(P,O,Q\).