Summary: Let \(G\) be a connected graph of ordern. Let \(\operatorname{Diag}(\mathrm{Tr})\) be the diagonal matrix of vertex transmissions and let \(\mathcal{D}(G)\) be the distance matrix of \(G\). The distance signless Laplacian matrix of \(G\) is defined as \(\mathcal{D}^{\mathcal{Q}}(G) =\operatorname{Diag}(\mathrm{Tr}) + \mathcal{D}(G)\) and the eigenvalues of \(\mathcal{D}^{\mathcal{Q}}(G)\) are called the distance signless Laplacian eigenvalues of \(G\). Let \(\partial^{\mathcal{Q}}_1(G) \geq \partial^{\mathcal{Q}}_2(G) \geq \cdots \geq \partial^{\mathcal{Q}}_n(G)\) be the distance signless Laplacian eigenvalues of \(G\). The largest eigenvalue \(\partial^{\mathcal{Q}}_1(G)\) is called the distance signless Laplacian spectral radius. We obtain a lower bound for \(\partial^{\mathcal{Q}}_1(G)\) in terms of the diameter and order of \(G\). With a given interval \(I\), denote by \(m_{\mathcal{D}^{\mathcal{Q}}(G)}I\) the number of distance signless Laplacian eigenvalues of \(G\) which lie in\(I\). For a given interval \(I\), we also obtain several bounds on \(m_{\mathcal{D}^{\mathcal{Q}}(G)}I\) in terms of various structural parameters of the graph \(G\), including diameter and clique number.