To solve this problem, we need to determine why the greater part of secondary xylem in old trees is dark brown and resistant to insect attack. Let's analyze each option:$\newline \bullet$(a) Secretion of secondary metabolites and their deposition in the lumen of vessels:$\newline$ - Secondary metabolites such as lignin, tannins, and other phenolic compounds are often deposited in the xylem.$\newline$ - These compounds can make the wood more resistant to decay and insect attack.$\newline$ - This option is relevant to the question.$\newline \bullet$(b) Deposition of organic compounds like tannins and resins in the central layers of stem:$\newline$ - Tannins and resins are known to be deposited in the heartwood, which is the central part of the stem.$\newline$ - These compounds contribute to the dark color and resistance to pests.$\newline$ - This option is also relevant to the question.$\newline \bullet$(c) Deposition of suberin and aromatic substances in the outer layer of stem:$\newline$ - Suberin is typically found in the bark and not in the xylem.$\newline$ - This option does not directly relate to the darkening and resistance of the xylem.$\newline \bullet$(d) Deposition of tannins, gum, resin, and aromatic substances in the peripheral layers of stem:$\newline$ - While these substances can be found in the stem, the option specifies peripheral layers, which are not the main focus for xylem properties.$\newline$ - This option is less relevant to the question.$\newline \bullet$(e) Presence of parenchyma cells, functionally active xylem elements and essential oils:$\newline$ - Parenchyma cells and essential oils do not contribute to the darkening and resistance of the xylem.$\newline$ - This option is not relevant to the question.$\newline$Based on the analysis, the correct options are (a) and (b), which correspond to Option 1.