Match the following:
Test/Method                    Reagent
(i) Lucas Test                   (a) $$\text{C}_6\text{H}_5\text{SO}_2\text{Cl}$$ / aq. KOH
(ii) Dumas method            (b) $$\text{HNO}_3$$ / $$\text{AgNO}_3$$
(iii) Kjeldahl's method       (c) CuO / $$\text{CO}_3$$
(iv) Hinsberg Test             (d) Conc. HCl and $$\text{ZnCl}_2$$
                                             (e) $$\text{H}_2\text{SO}_4$$

We begin by recalling the characteristic reagents that are classically associated with each of the given organic tests or nitrogen-estimation methods.

For the Lucas Test we know that the reagent is called Lucas reagent. Lucas reagent is a mixture of concentrated hydrochloric acid and anhydrous zinc chloride. The purpose of this reagent is to convert alcohols to their corresponding chlorides so that the relative reactivity of 1°, 2° and 3° alcohols can be judged by the turbidity time. Hence for Lucas Test the correct reagent from the list must be $$\text{Conc. HCl + ZnCl}_2$$, which is option (d).

Next, we think of the Dumas method of nitrogen estimation. In the Dumas method the organic compound is strongly heated with excess cupric oxide to bring about complete combustion. The nitrogen present is converted to molecular nitrogen, while carbon is oxidised to $$\text{CO}_2$$. Thus the reagent invariably mentioned in text books is cupric oxide, written as $$\text{CuO}$$ together with an atmosphere that sweeps away the produced gases (often quoted as $$\text{CO}_2$$). Therefore the pair that best represents the Dumas method is (c) $$\text{CuO / CO}_2$$.

Now we recall Kjeldahl’s method. In Kjeldahl’s digestion the organic compound is heated with concentrated sulphuric acid so that nitrogen is ultimately converted to ammonium sulphate. Hence concentrated $$\text{H}_2\text{SO}_4$$ is the indispensable reagent. Looking at the reagent list, (e) is $$\text{H}_2\text{SO}_4$$, which fits perfectly.

The Hinsberg Test is a classic qualitative test used to distinguish primary, secondary and tertiary amines. The reagent employed is benzene­sulphonyl chloride, written chemically as $$\text{C}_6\text{H}_5\text{SO}_2\text{Cl}$$, used in the presence of aqueous potassium hydroxide. This corresponds exactly to reagent (a).

Collecting all the correct pairings we have

$$\begin{aligned} \text{(i) Lucas Test} &\ \longrightarrow\ (d)\; \text{Conc.\ HCl + ZnCl}_2,\\ \text{(ii) Dumas method} &\ \longrightarrow\ (c)\; \text{CuO / CO}_2,\\ \text{(iii) Kjeldahl's method} &\ \longrightarrow\ (e)\; \text{H}_2\text{SO}_4,\\ \text{(iv) Hinsberg Test} &\ \longrightarrow\ (a)\; \text{C}_6\text{H}_5\text{SO}_2\text{Cl / aq.\ KOH}. \end{aligned}$$

Comparing these matches with the given options, we see that Option C lists the exact same correspondence:

(i)-(d), (ii)-(c), (iii)-(e), (iv)-(a).

Hence, the correct answer is Option C.