The GATE Grind

GATE Mathematical Physics: Linear vector spaces: basis, orthogonality and completeness – Previous Year Questions

8 GATE previous year questions on Linear vector spaces: basis, orthogonality and completeness (Mathematical Physics, Physics) with answers and explanations, from every paper.

  1. GATE 2023 PH Q32 (1 mark, Multiple select) – Which of the following options represent(s) linearly independent pair(s) of functions of a real variable x ?
  2. GATE 2026 PH Q14 (1 mark, Multiple choice) – For a scalar field ( r) and a vector field A( r), ( A) is equivalent to the expression
  3. GATE 2026 PH Q21 (1 mark, Multiple choice) – Given v 1=12pmatrix1\pmatrix, v 2=12pmatrix1\\-ipmatrix, the tensor product v 1 v 2 is
  4. GATE 2026 PH Q22 (1 mark, Multiple choice) – Sketch of a two-dimensional vector field V⃗ is shown below. Here, length and arrow head of the arrows denote magnitude and direction of the vector…
  5. GATE 2026 PH Q27 (1 mark, Multiple select) – For which of the following functions does the Laplacian vanish?
  6. GATE 2025 PH Q61 (2 marks, Numerical answer) – Consider \1,x,x2\. An orthonormal basis on [-1,1] uses normalization -11x2[f(x)]2dx=1. If the basis is (3/2,5/2x,1221/N(5x2-3)), the value of N (in…
  7. GATE 2024 PH Q30 (1 mark, Multiple select) – Consider I= V2(1/r)\,dV where r=x2+y2+z2. Which statement(s) is/are correct?
  8. GATE 2024 PH Q45 (2 marks, Multiple select) – F=(2xz+3y2) y+4yz2 z. The path A → B → C → D → A is the unit square in z = 0. Which option(s) is/are true?