GATE Engineering Mathematics: Numerical Methods – Previous Year Questions

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

1. GATE 2022 AG Q21 (1 mark, Numerical answer) – For x-4x+1=0, use Newton–Raphson once from x 0=.2. Give the next estimate to three decimals.
2. GATE 2022 AG Q48 (2 marks, Numerical answer) – Instrument power (W) at times0,.6,1.2,1.8,2.4,3.0,3.6 s is 8.6,9.2,7.8,6.4,7.2,8.6,11.2. Use Simpson’s1/3 rule to find energy in J, to two decimals.
3. GATE 2023 AG Q50 (2 marks, Numerical answer) – For dy/dx=2x+y,y(0)=1,use fourth-order Runge–Kutta to find y(.2),to three decimals.
4. GATE 2026 AG Q15 (1 mark, Multiple choice) – For 2x+4y=-7 and 3x+5y=1,Gauss elimination is performed without pivoting. What diagonal entries remain after forward elimination?
5. GATE 2026 AG Q50 (2 marks, Numerical answer) – Use Newton–Raphson for e-x-x=0 with initial guess x 0=2. Find the first iterate x 1,to two decimals.