The primary task of a teacher is to promote a lively environment.

Explanation:
Teachers play a crucial role in shaping the minds of students and helping them acquire knowledge and skills. While there are different tasks that teachers engage in, the primary task can be considered as promoting a lively environment.

Creating an Engaging Classroom Environment:
- Teachers need to create an environment that is conducive to learning and encourages active student participation. This involves setting up the classroom in a way that promotes student engagement and interaction.
- Teachers can use various strategies such as group work, discussions, hands-on activities, and multimedia resources to make the learning experience more dynamic and interesting.
- By promoting a lively environment, teachers can capture students' attention and maintain their interest throughout the learning process.

Fostering Positive Relationships:
- Teachers are responsible for building positive relationships with their students, which can contribute to a lively environment. When students feel respected and valued, they are more likely to actively participate in class and engage in learning.
- Teachers can establish rapport with their students by showing genuine interest in their lives, listening to their concerns, and providing support when needed.
- By fostering positive relationships, teachers can create a sense of belonging and make the classroom a safe and welcoming space for students to express themselves.

Encouraging Active Learning:
- A lively environment in the classroom promotes active learning, where students are actively involved in the learning process rather than being passive recipients of information.
- Teachers can encourage active learning by incorporating various teaching strategies such as problem-solving activities, hands-on experiments, debates, and group projects.
- By promoting active learning, teachers can stimulate critical thinking, creativity, and collaboration among students, making the learning experience more engaging and meaningful.

In conclusion, while teaching the prescribed curriculum effectively, guiding students in learning, and providing diagnostic and remedial aid are important tasks for teachers, the primary task is to promote a lively environment. This involves creating an engaging classroom environment, fostering positive relationships, and encouraging active learning.