In this article, we consider colorable variations of the Unit Disk Cover (UDC) problem as follows.k-Colorable Discrete Unit Disk Cover (k-CDUDC): Given a set P of n points, and a set D of m unit disks (of radius=1), both lying in the plane, and a parameter k, the objective is to compute a set D ′ ⊆ D such that every point in P is covered by at least one disk in D ′ and there exists a function χ : D ′ → C that assigns colors to disks in D ′ such that for any d and, where C denotes a set containing k distinct colors.For the k-CDUDC problem, our proposed algorithms approximate the number of colors used in the coloring if there exists a k-colorable cover. We first propose a 4-approximation algorithm in O(m 7k n log k) time for this problem and then show that the running time can be improved by a multiplicative factor of m k , where a positive integer k denotes the cardinality of a color-set. The previous best known result for the problem when k = 3 is due to the recent work of Biedl et al., (2021)[3], who proposed a 2-approximation algorithm in O(m 25 n) time. For k = 3, our algorithm runs in O(m 18 n) time, faster than the previous best algorithm, but gives a 4-approximate result. We then generalize our approach to yield a family of ρ-approximation algorithms in O(m αk n log k) time, where (ρ, α) ∈ {(4, 7), (6, 5), (7, 5), (9, 4)}. We further generalize this to exhibit a O( 1 τ )-approximation algorithm in O(m αk n log k) time for a given 1 ≤ τ ≤ 2, where α = O(τ 2

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