GATE Functional Analysis: Normed and Banach Spaces – Previous Year Questions

2 GATE previous year questions on Normed and Banach Spaces (Functional Analysis, Mathematics) with answers and explanations, from every paper.

1. GATE 2022 MA Q15 (1 mark, Multiple choice) – The unit sphere of a real normed space contains distinct x,y and their entire joining segment. Which holds?
2. GATE 2026 MA Q19 (1 mark, Multiple choice) – X = C¹([0,1],ℝ). Define p 1(x)= x(t) , p 2(x)= x(t) , and p₃ = p₁+p₂. Which statement is true?