GATE Engineering Mathematics: Calculus – Previous Year Questions

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

1. GATE 2021 AG Q12 (1 mark, Multiple choice) – For integer x>1, evaluate x[1/x2+2/x2++(x-1)/x2+1/x].
2. GATE 2022 AG Q13 (1 mark, Multiple choice) – Which expression is the Maclaurin expansion of f(x), assuming the series converges to the function?
3. GATE 2022 AG Q22 (1 mark, Numerical answer) – Find the slope of f(x)=2x4-3x2+5x at x=2. Give an integer.
4. GATE 2022 AG Q36 (2 marks, Multiple choice) – Which statement describes (x-2)2(x+2)2?
5. GATE 2023 AG Q12 (1 mark, Multiple choice) – Find x0(1+x-1)/x.
6. GATE 2023 AG Q13 (1 mark, Multiple choice) – Evaluate I= 0/2( x+ x)2/1+2x\,dx.
7. GATE 2024 AG Q21 (1 mark, Multiple select) – A continuously differentiable function y=f(x) satisfies which listed conditions at a point of inflection? Select all that apply.
8. GATE 2024 AG Q47 (2 marks, Numerical answer) – Approximate e2x at x=1/2 using the first four Taylor terms about 0. Report to three decimals.
9. GATE 2025 AG Q36 (2 marks, Multiple choice) – Find the sum n=0r qn=1+q+q2++qr.
10. GATE 2025 AG Q37 (2 marks, Multiple choice) – Evaluate x0(x x- x)/(x2 x).
11. GATE 2025 AG Q38 (2 marks, Multiple choice) – For u=x4+y4+3x2y2,find (x u x+y u y)-1.
12. GATE 2026 AG Q36 (2 marks, Multiple choice) – Evaluate I= 01 01x(xy)\,dx\,dy.