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GATE Engineering Mathematics: Numerical Methods: Error analysis, algebraic equations, interpolation, differentiation, integration, ODEs – Previous Year Questions

10 GATE previous year questions on Numerical Methods: Error analysis, algebraic equations, interpolation, differentiation, integration, ODEs (Engineering Mathematics, Civil Engineering) with answers and explanations, from every paper.

  1. GATE 2023 CE (CE1) Q36 (2 marks, Multiple choice) – A function f(x), that is smooth and convex-shaped between interval (x l, x u) is shown in the figure. This function is observed at odd number of…
  2. GATE 2023 CE (CE1) Q52 (2 marks, Numerical answer) – The differential equation, dudt + 2tu2 = 1, is solved by employing a backward difference scheme within the finite difference framework. The value of u…
  3. GATE 2024 CE (CE2) Q13 (1 mark, Multiple choice) – The second derivative of a function f is computed using the fourth-order Central Divided Difference method with a step length h. The CORRECT…
  4. GATE 2024 CE (CE1) Q11 (1 mark, Multiple choice) – The smallest positive root of the equation x5 - 5x4 - 10x3 + 50x2 + 9x - 45 = 0 lies in the range
  5. GATE 2024 CE (CE1) Q32 (1 mark, Numerical answer) – Consider the data of f(x) given in the table. i 0 1 2 --- --- --- --- x i 1 2 3 f(x i) 0 0.3010 0.4771 The value of f(1.5) estimated using…
  6. GATE 2025 CE (CE1) Q49 (2 marks, Numerical answer) – Consider the differential equation given below. Using the Euler method with the step size (h) of 0.5, the value of y at x = 1.0 is equal to (*rounded…
  7. GATE 2026 CE (CE2) Q12 (1 mark, Multiple choice) – A fifth-degree polynomial in x is defined for x > 0. All coefficients of the polynomial are positive. The first derivative of the polynomial is…
  8. GATE 2026 CE (CE1) Q28 (1 mark, Numerical answer) – It is given that x and y are integers in the following equation: (x + y - 7)2 + (y + 3x - 13)2 = 0 The value of (x3 + y3) is (*in integer*).
  9. GATE 2026 CE (CE1) Q48 (2 marks, Numerical answer) – Starting with the first approximation as x = 0.5, the second approximation for the root of the following function by the Newton-Raphson method is…
  10. GATE 2026 CE (CE1) Q49 (2 marks, Numerical answer) – Values of y for different values of x are tabulated below. x -2 1 2 --- --- --- --- y 28 4 16 If a second-degree interpolating polynomial P 2(x) is…