Step 1: Understanding the Concept:
Crop yield is typically measured in quintals per hectare ($\text{q/ha}$, where $1\text{ q} = 100\text{ kg}$).
Yields vary widely depending on the crop's genetic potential, photosynthetic efficiency ($C_{3}$ vs $C_{4}$ pathway), water requirement, and duration.
Step 2: Detailed Explanation:
Let us compare the average national yields of these four crops in India:
- (B) Pigeon pea (Arhar):
Being a long-duration rainfed legume susceptible to wilt and insect pests, its national average yield is relatively low, typically around 8 to 10 q/ha.
- (A) Chickpea (Gram):
A Rabi legume with a shorter growth duration, its national average yield is slightly higher, typically around 10 to 12 q/ha.
- (C) Wheat:
An irrigated Rabi cereal crop with a high harvest index, its national average yield is around 33 to 35 q/ha (ranging up to 50 q/ha in progressive regions).
- (D) Sugarcane:
A heavy-biomass, long-duration $C_{4}$ perennial grass, sugarcane yields are measured in tonnes. The national average yield is around 70 to 80 tonnes per hectare, which corresponds to 700 to 800 q/ha.
Arranging these yields in ascending order (lowest to highest):
\[ \text{Pigeon pea (B)} < \text{Chickpea (A)} < \text{Wheat (C)} < \text{Sugarcane (D)} \]
This corresponds to the sequence: (B), (A), (C), (D).
Step 3: Final Answer:
Therefore, the correct ascending order is (B), (A), (C), (D).