The GATE Grind

GATE Engineering Mathematics: Numerical Methods – Previous Year Questions

7 GATE previous year questions on Numerical Methods (Engineering Mathematics, Production and Industrial Engineering) with answers and explanations, from every paper.

  1. GATE 2021 PI Q63 (2 marks, Numerical answer) – At x = 0,1,…,10, y(x) values are 5,3,0,−5,−10,−6,0,5,11,18,30. Use the trapezoidal rule for 010y(x)dx, to one decimal.
  2. GATE 2022 PI Q12 (1 mark, Multiple choice) – Numerically integrate y = 2x+5 from x = 1 to 3 using ordinates at x = 1,2,3. Which statement is true?
  3. GATE 2023 PI Q27 (1 mark, Numerical answer) – Use Euler’s method for dy/dx=x3y-4, y(0) = 1, with step 0.1. Find y(0.1) to two decimals.
  4. GATE 2023 PI Q48 (2 marks, Numerical answer) – Apply Newton–Raphson to x5-15=0, starting at x₀ = 1. Find the first approximation x₁ to two decimals.
  5. GATE 2024 PI Q47 (2 marks, Numerical answer) – At x = 0,1,2,3,4, tabulated y values are 1,3,6,9,12. Use the trapezoidal rule for 04y(x)dx (one decimal).
  6. GATE 2025 PI Q43 (2 marks, Numerical answer) – Simpson’s 1/3 rule with four equal subintervals gives 13(x2-2x)dx=n/3. Find integer n.
  7. GATE 2026 PI Q15 (1 mark, Multiple choice) – Using numerical integration, which option most closely approximates 01e-x2dx?