Question

Match List - I with List - II

List - I (Function/Property)	List - II (Definition/Explanation)
A. Singular point	III. A point at which function is not differentiable.
B. Holomorphic function	IV. Other name of analytic function.
C. Entire function	II. Any function which is analytic everywhere.
D. Harmonic function	I. Any function which satisfies the Laplace's equation.

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

Hint:

Remember: Entire = Everywhere analytic. Harmonic = Laplace's equation. Holomorphic = Analytic.

Answer 1

The Correct Option is A

Concept: Complex analysis relies on specific terminology for the behavior of functions. Analytic (or holomorphic) functions are those differentiable in a neighborhood of every point in their domain.

Step 1: Define Function Types.
- Singular Point (A): A point where a function fails to be analytic (often where it is not differentiable or defined). Match: A-III. - Holomorphic Function (B): This is the standard term used in complex analysis as a synonym for an analytic function. Match: B-IV.

Step 2: Define Domain and Equation Properties.
- Entire Function (C): A complex-valued function that is analytic at all points in the entire complex plane. Match: C-II. - Harmonic Function (D): A twice-differentiable real-valued function that satisfies Laplace's equation ($\nabla^2 f = 0$). Match: D-I.

Step 3: Final Mapping.
Combining these matches: A-III, B-IV, C-II, D-I. This corresponds to Option (1).