The GATE Grind

GATE Engineering Mathematics: Numerical Methods – Previous Year Questions

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

  1. GATE 2020 BM Q28 (1 mark, Numerical answer) – Starting at a finite positive value, the iteration xₙ₊₁=(xₙ+1/xₙ)/2 converges to what value?
  2. GATE 2024 BM Q12 (1 mark, Multiple choice) – Which Newton–Raphson iteration solves x=2cos x?
  3. GATE 2025 BM Q57 (2 marks, Numerical answer) – Use one Newton–Raphson iteration for x³−2x−5=0 from x0=3. Give x1 to two decimal places.
  4. GATE 2026 BM Q39 (2 marks, Multiple choice) – Use Newton–Raphson to solve x=e-2x starting from x0=0. Find the first iterate x1.