GATE Real Analysis: Measure and Integration – Previous Year Questions
9 GATE previous year questions on Measure and Integration (Real Analysis, Mathematics) with answers and explanations, from every paper.
- GATE 2021 MA Q64 – For x∈(0,1), let n be the number of zeros immediately after the decimal point before the first nonzero decimal digit. Define f(x)=0 for rational x and…
- GATE 2022 MA Q38 – Continuous f:[−π,π]→ℝ satisfies f(x)>f(0)/2 for x <δ,0<δ<π. Put P (n,δ)(x)=(1+cos x−cosδ)ⁿ. Which integral necessarily tends to zero as n→∞?
- GATE 2023 MA Q16 – Let N⊆ℝ be non-Lebesgue-measurable. P:the irrational points of N form a measurable set. Q:the boundary of N has positive Lebesgue outer measure.…
- GATE 2023 MA Q17 – Measurable E k⊆[0,1] have measure 1/k². Define E= n k nE k and F= n k nE k. P:m(E)=0; Q:m(F)=0. Choose truth values.
- GATE 2023 MA Q47 – Let f n:ℝ→ℝ equal n²(x−n) on [n,n+1/n²], and zero elsewhere. Write m for Lebesgue measure. Which statements hold as n→∞?
- GATE 2023 MA Q48 – Write χ E for the indicator of E. Let f(x)= n=1(2n/n3) [2-(n+1),2-n](x) on [0,1]. P:f∈Lᵖ[0,1] for every 1<p<2. Q:f∈L¹[0,1]. Select all correct…
- GATE 2024 MA Q14 – Evaluate the source limit 0-1 0 e-x/[3x+x2+x+4]dx.
- GATE 2024 MA Q38 – Which condition suffices for f:[0,1]→ℝ to be Lebesgue measurable?
- GATE 2026 MA Q13 – Let C be the Cantor set. On [0,1], define f(x) = x²⁰²⁶ on C; cos(πx) on [0,1/2]∖C; sin(πx) on [1/2,1]∖C. Find its Lebesgue integral.