The creation of pedagogically effective questions is a challenge for teachers and requires significant time and meticulous planning, especially in resource-constrained economies. For example, in India, assessments for social science in high schools are characterized by rote memorization without regard to higher-order skill levels. Automated educational question generation (AEQG) using large language models (LLMs) has the potential to help teachers develop assessments at scale. However, it is important to evaluate the quality and relevance of these questions. In this study, we examine the ability of different LLMs (Falcon 40B, Llama2 70B, Palm 2, GPT 3.5, and GPT 4) to generate relevant and high-quality questions of different cognitive levels, as defined by Bloom’s taxonomy. We prompt each model with the same instructions and different contexts to generate 510 questions in the social science curriculum of a state educational board in India. Two human experts used a nine-item rubric to assess linguistic correctness, pedagogical relevance and quality, and adherence to Bloom’s skill levels. Our results showed that 91.56% of the LLM-generated questions were relevant and of high quality. This suggests that LLMs can generate relevant and high-quality questions at different cognitive levels, making them useful for creating assessments for scaling education in resource-constrained economies.