GATE Engineering Mathematics: Calculus – Previous Year Questions
16 GATE previous year questions on Calculus (Engineering Mathematics, Mining Engineering) with answers and explanations, from every paper.
- GATE 2021 MN Q45 – For a fixed real constant b, evaluate x(xx2+b2-x4+b4).
- GATE 2022 MN Q11 – Evaluate x0[(1-x)n-1]/x.
- GATE 2022 MN Q13 – A 2π-periodic function is f(x)=−k for −π<x<0 and f(x)=k for 0<x<π, with constant k. Find its Fourier-series constant term.
- GATE 2022 MN Q42 – A continuous differentiable function on [3, 18] satisfies f(3)=−50 and f′(x)≤20. Find the greatest possible f(18), as an integer.
- GATE 2022 MN Q62 – Evaluate 01 x(1+x)\,dx, using the natural logarithm. Give two decimals.
- GATE 2023 MN Q21 – For x=r and y=r, find (x,y)/(r,).
- GATE 2023 MN Q39 – Evaluate ex-1+xe-1ex+xe\,dx. Each option is understood up to an additive constant.
- GATE 2023 MN Q40 – For f(x)= x + x-1 and real x, which statement is correct?
- GATE 2024 MN Q16 – Evaluate 0/4 x\,3x\,dx.
- GATE 2024 MN Q17 – For constant n, evaluate x0 n(5x)/(3x).
- GATE 2024 MN Q44 – Water enters the inverted conical tank at 300 m³/hour. The tank is 10 m across at the top and 15 m high as shown. Find water-level rise rate in m/min…
- GATE 2025 MN Q13 – For y=xx with x>0, find dy/dx.
- GATE 2025 MN Q29 – Evaluate x0(11x)/(5x) to one decimal.
- GATE 2025 MN Q58 – Find the area enclosed by y= x and y=8x2,to three decimals.
- GATE 2026 MN Q29 – For Fourier series on a symmetric interval, which statements are correct?
- GATE 2026 MN Q36 – For f(x,y)=x2+y2+xy-8x-7y, find the determinant of the Hessian at its stationary point.