GATE Engineering Mathematics: Numerical methods – Previous Year Questions

5 GATE previous year questions on Numerical methods (Engineering Mathematics, Metallurgical Engineering) with answers and explanations, from every paper.

1. GATE 2021 MT Q47 (2 marks, Numerical answer) – Use Newton–Raphson on f(x)=x- x with initial guess 0.5 radians. The root estimate after one iteration is (three decimal places).
2. GATE 2022 MT Q37 (2 marks, Multiple choice) – Which equation fails to converge to a root under Newton–Raphson iteration starting at x=0.5?
3. GATE 2022 MT Q61 (2 marks, Numerical answer) – Estimate the integral of f(x)=0.2+10x2 from 0 to 1 by the single-segment trapezoidal rule: (one decimal place).
4. GATE 2025 MT Q65 (2 marks, Numerical answer) – Two consecutive Newton–Raphson estimates of a root of f(x) are x i=8.5 and x i+1=13.5, with f(x i)=15. The first derivative f(x i) is (in integer).
5. GATE 2026 MT Q45 (2 marks, Numerical answer) – Taking the number of intervals as n=3, the value of 00.3e-x2\,dx using the trapezoidal method is . (Rounded off to two decimal places.)