The GATE Grind

GATE Numerical Analysis: Numerical Differentiation and Integration – Previous Year Questions

6 GATE previous year questions on Numerical Differentiation and Integration (Numerical Analysis, Mathematics) with answers and explanations, from every paper.

  1. GATE 2021 MA Q63 (2 marks, Numerical answer) – The quadrature ∫₀²x f(x)dx≈αf(0)+βf(1)+γf(2) is exact for every polynomial f of degree at most 2. Find 2β−γ.
  2. GATE 2022 MA Q44 (2 marks, Multiple choice) – A quadratic interpolant through (−1,f(−1)),(0,f(0)),(2,f(2)) approximates f′(0)=−(2/3)f(−1)+αf(0)+βf(2), for smooth f on (−3,3). Find 1/(αβ).
  3. GATE 2023 MA Q29 (1 mark, Numerical answer) – For fixed real c, the trapezoidal-rule value of ∫₀²(9x²−5cx⁴)dx equals the exact integral. Find c to two decimals.
  4. GATE 2023 MA Q50 (2 marks, Multiple select) – For h>0 define D hf(a)=[αf(a−h)+βf(a)+γf(a+2h)]/(6h). If this equals f′(a) for every real polynomial of degree at most 2 and every real a, which hold?
  5. GATE 2024 MA Q43 (2 marks, Multiple choice) – For f(x)= x + x−1 + x−2 on [−1,2], which listed quadrature rule gives the exact integral?
  6. GATE 2025 MA Q34 (1 mark, Numerical answer) – Quadrature ∫₋₁¹f(x)dx=αf(−1)+βf(1)+γf′(−1)+δf′(1) is exact through degree three. Find 9(α²+β²+γ²+δ²) (integer).