GATE Engineering Mathematics: Numerical Methods: Linear and nonlinear algebraic equations, trapezoidal and Simpson's rule, single step methods for ODEs – Previous Year Questions

5 GATE previous year questions on Numerical Methods: Linear and nonlinear algebraic equations, trapezoidal and Simpson's rule, single step methods for ODEs (Engineering Mathematics, Biotechnology) with answers and explanations, from every paper.

1. GATE 2022 BT Q30 (1 mark, Numerical answer) – For x x+x-1=0, use Newton–Raphson with x 0=3. The value after one iteration (one decimal place) is .
2. GATE 2022 BT Q47 (2 marks, Multiple select) – For dy/dx=2x2-y2, y(1)=1. With implicit Euler y n+1=y n+hf(x n+1,y n+1) and h=0.5, the value(s) of y(1.5) is (are)
3. GATE 2026 BT Q51 (2 marks, Numerical answer) – Consider the equation dydx = 1x The value of the integral 12 dy using trapezoidal method and interval h = 0.25 is . (rounded off to two decimal…
4. GATE 2025 BT Q33 (1 mark, Numerical answer) – Consider a nonlinear algebraic equation, ex - 2 = 0. Using the Newton-Raphson method, with the initial guess of x 0 = 1, the approximated value of the…
5. GATE 2024 BT Q65 (2 marks, Numerical answer) – The absolute relative error in evaluating the integral 01 x2dx by the trapezoidal rule with the step size 0.25 is % (rounded off to 2 decimal places).