GATE Engineering Mathematics: Calculus – Previous Year Questions

12 GATE previous year questions on Calculus (Engineering Mathematics, Production and Industrial Engineering) with answers and explanations, from every paper.

1. GATE 2021 PI Q35 (1 mark, Numerical answer) – Find the minimum of f(x,y,z)=x2+5y2+5z2-4x+40y-40z+300 (integer).
2. GATE 2022 PI Q45 (2 marks, Numerical answer) – Evaluate x1(x3-3x+2)/(x3-x2-x+1) to one decimal.
3. GATE 2023 PI Q13 (1 mark, Multiple choice) – For 0<x1, (1+x)/x=1+bx+cx2+. Find b and c, respectively.
4. GATE 2023 PI Q36 (2 marks, Multiple choice) – z(x,y)=ex-2y, x(t)=et, y(t)=e-t, with all variables real. Find dz/dt.
5. GATE 2024 PI Q11 (1 mark, Multiple choice) – Find the coefficient of z³ in the Taylor expansion of sin z around z = 0.
6. GATE 2024 PI Q12 (1 mark, MTA) – F=(100x+100y) i+(-50x+200y) j. Evaluate C F d l along an anticlockwise circle of radius 2, with d l=dx i+dy j.
7. GATE 2024 PI Q27 (1 mark, Multiple select) – f(x,y)=u(x,y)+iv(x,y) is analytic, with real x,y,u,v. Which ONE OR MORE equations hold?
8. GATE 2024 PI Q32 (1 mark, Numerical answer) – x1(x2-2ax+b)/(x-1)=8. Find a − b (integer).
9. GATE 2025 PI Q12 (1 mark, Multiple choice) – For orthogonal Cartesian unit vectors i,j,k, find the curl of -2y i+x j.
10. GATE 2025 PI Q37 (2 marks, Multiple choice) – Which function is analytic in z = x + iy, with i=-1?
11. GATE 2025 PI Q44 (2 marks, Numerical answer) – Find the rate of change of f=x2+2y2+z at (1,1,1) in the direction 3 i+4 k (integer).
12. GATE 2026 PI Q34 (1 mark, Numerical answer) – Evaluate C(2x\,dx+2y\,dy+2z\,dz), where C is a semicircle in z = 0 starting at (0,0,0) and ending at (1,0,0). Give an integer.