The GATE Grind

GATE Engineering Mathematics: Numerical Methods: Algebraic equations, integration, ODEs and finite-difference methods – Previous Year Questions

6 GATE previous year questions on Numerical Methods: Algebraic equations, integration, ODEs and finite-difference methods (Engineering Mathematics, Chemical Engineering) with answers and explanations, from every paper.

  1. GATE 2022 CH Q28 (1 mark, Numerical answer) – The area of a circular field is 25 m2. The radius, r, is to be determined using the Newton-Raphson iterative method. For an initial guess of r = 2.500…
  2. GATE 2022 CH Q46 (2 marks, Numerical answer) – The equation dydx = xy2 + 2y + x - 4.5 with the initial condition y(x = 0) = 1 is to be solved using a predictor-corrector approach. Use a predictor…
  3. GATE 2023 CH Q37 (2 marks, Multiple choice) – Simpson's one-third rule is used to estimate the definite integral I = -111 - x2\,dx with an interval length of 0.5. Which one of the following is the…
  4. GATE 2024 CH Q50 (2 marks, Numerical answer) – The Newton-Raphson method is used to solve f(x) = 0, where f(x) = ex - 5x. If the initial guess x(0) = 1.0, the value of the next iterate, x(1),…
  5. GATE 2025 CH Q46 (2 marks, Numerical answer) – The Newton-Raphson method is used to find the root of f(x) x2 - x - 1 = 0. Starting with an initial guess x(0) = 1, the second iterate x(2) is…
  6. GATE 2026 CH Q35 (1 mark, Numerical answer) – Using single step trapezoidal rule, the value of 00.5 (1 + 16x - 20x2)\,dx is (rounded off to two decimal places).