Question

Match List I (Algebraic Codes used in Diameter Formulas) with List II (Geometric Components): 

List I		List II
A.	\(2ka\)	I.	Laghu-vyasaha
B.	\(2a\)	II.	Brihad-vyasaha
C.	\(ka\)	III.	Laghu-vyasardham
D.	\(a\)	IV.	Brihad-vyasardham

• A. A-II, B-I, C-IV, D-III
• B. A-IV, B-III, C-I, D-II
• C. A-III, B-IV, C-II, D-I
• D. A-I, B-II, C-III, D-IV

Hint:

'Vyasardha' = Vyasa (Diameter) + Ardha (Half). So, the terms with '2' must match the full 'Vyasa', and terms without '2' must match 'Vyasardha'.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In the calculation of eclipses and planetary disks, Indian mathematicians used algebraic variables. 'a' often stands for 'Ardh' (half) or a specific radius, and 'ka' stands for a full measure or a specific constant.

Step 2: Matching by Algebraic Proportion:
1. 2 ka (A): Since 'ka' is a radius-like measure, $2 \times ka$ represents the full diameter. Among the options, it corresponds to the Brihad-vyasa (Major Diameter). (A matches II).
2. 2 a (B): $2 \times a$ represents the full diameter of the smaller circle, Laghu-vyasa. (B matches I).
3. ka (C): The single unit 'ka' represents the radius, specifically the Brihad-vyasardha (Major Semi-diameter). (C matches IV).
4. a (D): The single unit 'a' represents the Laghu-vyasardha (Minor Semi-diameter). (D matches III).

Step 3: Verification:
Sequence: A-II, B-I, C-IV, D-III. This corresponds to Option (1).

Step 4: Final Answer:
The codes distinguish between the major and minor axes of the projected elliptical shadow or planetary disk.