Summary: For a connected graph \(G\) of order \(n\), let \(\mathcal{D}(G)\) be the distance matrix and \(Tr(G)\) be the diagonal matrix of vertex transmissions of \(G\). The distance signless Laplacian (dsL, for short) matrix of \(G\) is defined as \(\mathcal{D}^Q(G)=Tr(G)+\mathcal{D}(G)\), and the corresponding eigenvalues are the dsL eigenvalues of \(G\). For an interval \(I\), let \(m_{\mathcal{D}^Q(G) } I\) denote the number of dsL eigenvalues of \(G\) lying in the interval \(I\). In this paper, for some prescribed interval \(I\), we obtain bounds for \(m_{\mathcal{D}^Q(G)}I\) in terms of the independence number \(\alpha\) and the chromatic number \(\chi\) of \(G\). Furthermore, we provide lower bounds of \(\partial_1^Q(G)\), the dsL spectral radius, for certain families of graphs in terms of the order \(n\) and the independence number \(\alpha \), or the chromatic number \(\chi \).