Step 1: Understanding the Concept:
This question checks basic concepts of crop breeding and botany regarding the staple crop, rice.
Step 2: Detailed Explanation:
Let us examine the statements individually:
- Statement 1: "Dee-Geo-Woo-gen" (DGWG) is a famous dwarfing gene in rice that led to the Green Revolution varieties like IR8. This statement is correct.
- Statement 2: The fruit of the grass family (Poaceae), including rice, is a dry, one-seeded fruit called a caryopsis, where the pericarp is fused with the seed coat. This statement is also correct.
Since both statements are correct, the appropriate option is both Statement 1 and 2 are true.
Step 3: Final Answer
The correct option is (D).