This paper tackles the intricate challenge of video question-answering (VideoQA). Despite notable progress, current methods fall short of effectively integrating questions with video frames and semantic object-level abstractions to create question-aware video representations. We introduce Local-Global Question Aware Video Embedding (LGQAVE), which incorporates three major innovations to integrate multi-modal knowledge better and emphasize semantic visual concepts relevant to specific questions. LGQAVE moves beyond traditional ad-hoc frame sampling by utilizing a cross-attention mechanism that precisely identifies the most relevant frames concerning the questions. It captures the dynamics of objects within these frames using distinct graphs, grounding them in question semantics with the miniGPT model. These graphs are processed by a question-aware dynamic graph transformer (Q-DGT), which refines the outputs to develop nuanced global and local video representations. An additional cross-attention module integrates these local and global embeddings to generate the final video embeddings, which a language model uses to generate answers. Extensive evaluations across multiple benchmarks demonstrate that LGQAVE significantly outperforms existing models in delivering accurate multi-choice and open-ended answers.