Hydroxyacetic acid (HOCH \(_{2}\) COOH ) is obtained by (a) the reduction of acetic acid by LiAlH (b) the hydrolysis of ethylene chlorohydrin, by aqueous alkali (c) the reaction of \(\mathrm{CH}_{3} \mathrm{CHO}\) with HCN followed by acid hydrolysis (d) Cannizzaro reaction of glyoxal.

LiAlH (lithium aluminium hydride) is a reducing agent commonly used to reduce carboxylic acids to primary alcohols. However, in the case of acetic acid (CH\(_{3}\)COOH), the reduction would result in ethanol (CH\(_{3}\)CH\(_{2}\)OH), not Hydroxyacetic acid (HOCH\(_{2}\)COOH). So, option (a) is not the correct answer.

Ethylene chlorohydrin is a chlorinated derivative of ethylene glycol (ClCH\(_{2}\)CH\(_{2}\)OH). Upon hydrolysis with aqueous alkali, the chlorine atom is replaced with a hydroxyl group, resulting in ethylene glycol (HOCH\(_{2}\)CH\(_{2}\)OH). So, option (b) is also not the correct answer.

Acetaldehyde (CH\(_{3}\)CHO) reaction with HCN (hydrogen cyanide) yields an addition product, which is CH\(_{3}\)CHOH \(\mathrm{CN}\). Acid hydrolysis of the cyanide group yields corresponding carboxylic acid. The product formed will be Hydroxyacetic acid (HOCH\(_{2}\)COOH). Thus, option (c) is the correct answer.

The Cannizzaro reaction is a disproportionation reaction where an aldehyde without an alpha-hydrogen atom is treated with a strong base. The aldehyde is both oxidized to a carboxylic acid and reduced to an alcohol. In the case of glyoxal (OCH \(_{2}\) CHO), the resulting products would be glycolic acid (HOCH\(_{2}\)COOH) and ethylene glycol (HOCH\(_{2}\)CH\(_{2}\)OH). Although one product is the desired Hydroxyacetic acid (HOCH\(_{2}\)COOH), the mechanism of the reaction does not match with the correct answer. So, option (d) is not the correct answer. In conclusion, Hydroxyacetic acid (HOCH\(_{2}\)COOH) can be obtained by the reaction of \(\mathrm{CH}_{3} \mathrm{CHO}\) with HCN followed by acid hydrolysis, which corresponds to option (c).