Let us analyze each option:
1. Lecture Method (a):
- The lecture method is a teacher-centered approach where the teacher delivers information to students. It focuses on verbal instruction and direct delivery of content.
- This matches with (II) Teacher-centered, focuses on delivery.
2. Demonstration Method (b):
- The demonstration method involves the teacher showing or illustrating concepts through practical examples or experiments. It helps students understand abstract ideas by observing real-world applications.
- This matches with (III) Students explore real-life problems.
3. Project Method (c):
- The project method encourages students to engage in hands-on activities and solve problems through exploration and experimentation. It promotes active learning and creativity.
- This matches with (IV) Learning through discovery.
4. Heuristic Method (d):
- The heuristic method involves problem-solving and critical thinking, where students are guided to discover Solution on their own. It emphasizes learning by doing and applying knowledge to solve problems.
- This matches with (I) Learning by doing.
- Based on this analysis, the correct matching is:
- (a) Lecture Method → (II) Teacher-centered, focuses on delivery
- (b) Demonstration Method → (III) Students explore real-life problems
- (c) Project Method → (IV) Learning through discovery
- (d) Heuristic Method → (I) Learning by doing
- Therefore, the correct answer is:
\[
\text{(A) a-II, b-III, c-IV, d-I}
\]