GATE Engineering Mathematics: Calculus – Previous Year Questions
16 GATE previous year questions on Calculus (Engineering Mathematics, Biomedical Engineering) with answers and explanations, from every paper.
- GATE 2020 BM Q19 – Which functions are odd? P=sin t, Q=cos t, R=sin t+cos t, S=sin t cos t.
- GATE 2020 BM Q55 – Find the magnitude of the gradient of f(x,y)=x²+y² at (1,1), to two decimals.
- GATE 2020 BM Q56 – Evaluate Rxy\,dx\,dy over the first-quadrant part of the unit disc, to three decimals.
- GATE 2021 BM Q12 – For V(x,y)=(x2+y2)/2, find its directional derivative at (1,1) in direction 3y i-3x j.
- GATE 2021 BM Q31 – Find the minimum of f(x 1,x 2,x 3)=12(x 12+x 22+x 32)-2(x 1+x 2+x 3), rounded to the nearest integer.
- GATE 2022 BM Q12 – Evaluate dx/2x-x2, where c is an integration constant.
- GATE 2022 BM Q13 – For vector field V=a i+b j+c k, identify the invalid differential operation.
- GATE 2022 BM Q26 – For real x, select all even functions, on their stated natural domains.
- GATE 2022 BM Q51 – Using the divergence theorem, evaluate outward flux S F n\,dA across the closed surface of x2+y2 z2,0 z3, for F=4x i+3z j+5y k. Round to the nearest…
- GATE 2023 BM Q15 – For f(x,y)=ex y, evaluate 2 f/( x y) at x=0,y=/2.
- GATE 2023 BM Q53 – For f(x)=x⁴−x² on the real line, which statements are correct?
- GATE 2024 BM Q50 – For F=(x+y) i+(x+y) j, evaluate F d r counterclockwise around the unit square (0,0),(1,0),(1,1),(0,1). Give an integer.
- GATE 2025 BM Q18 – A real function f is continuous and differentiable with f′(x)≠0 everywhere. For finite real a≠b, which always holds?
- GATE 2025 BM Q32 – For f(x)=x-1/x, evaluate x0[f(1+ x)-f(1)]/ x.
- GATE 2026 BM Q17 – For f(x,y)=x2y+3y2x, evaluate 2f/ x2 at (1,1).
- GATE 2026 BM Q40 – For f(x,y)=x2+y2, evaluate PQ f d l along the quarter-unit-circle path shown, from P=(1,0) to Q=(0,1).