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GATE 2025 Chemical Engineering, Q36 · Mathematics

The correct answer is A, a − b = 0.

Question

Consider a Cartesian coordinate system with orthogonal unit basis vectors î, ĵ defined over a domain: x, y ∈ [0,1]. Choose the condition for which the divergence of the vector field u = ax î − by ĵ is zero.

  • A. a − b = 0
  • B. a < b
  • C. a > b
  • D. a + b = 0

Official answer: a − b = 0

Why

GATE 2025 official key: (A). ∇⋅u=∂(ax)/∂x+∂(−by)/∂y=\nabla \cdot u = \partial (ax)/\partial x + \partial (−by)/\partial y = a − b. This vanishes only when a = b, i.e., a − b = 0.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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