The GATE Grind

GATE Engineering Mathematics: Calculus: Line, surface and volume integrals, theorems of Stokes, Gauss and Green – Previous Year Questions

3 GATE previous year questions on Calculus: Line, surface and volume integrals, theorems of Stokes, Gauss and Green (Engineering Mathematics, Aerospace Engineering) with answers and explanations, from every paper.

  1. GATE 2022 AE Q48 (2 marks, Numerical answer) – For v=x3 i+y3 j+z3 k, the outward flux over the unit sphere centered at the origin (one decimal place) is .
  2. GATE 2026 AE Q11 (1 mark, Multiple choice) – Consider the contour C shown in the figure below. For the vector F = (x + 2y) e x + (2x + 4y) e y, the integral C F d l = . Here d l represents an…
  3. GATE 2025 AE Q45 (2 marks, Numerical answer) – i and j denote unit vectors in the x and y directions, respectively. The outward flux of the two-dimensional vector field v = x i + y j over the unit…