GATE Engineering Mathematics: Calculus and vector calculus – Previous Year Questions

10 GATE previous year questions on Calculus and vector calculus (Engineering Mathematics, Instrumentation Engineering) with answers and explanations, from every paper.

1. GATE 2021 IN Q12 (1 mark, Multiple choice) – For x n=0.5x n-1+1, n=1,2,, with x 0=0, the value of nx n is .
2. GATE 2021 IN Q33 (1 mark, Numerical answer) – The minimum of f(x)=-x2+10x+100 on [5,10] is .
3. GATE 2022 IN Q28 (1 mark, Numerical answer) – The global minimum of x3e- x for x(-,) occurs at x= (one decimal place).
4. GATE 2023 IN Q23 (1 mark, Multiple choice) – The limit x0x(1/x) is
5. GATE 2023 IN Q57 (2 marks, Numerical answer) – For g(x)=\(x-2)2,-2x+7\ on R, the minimum value is (one decimal place).
6. GATE 2024 IN Q46 (2 marks, Multiple choice) – Let C be the counterclockwise boundary of the rectangle with vertices (0,0),(2,0),(2,1),(0,1). The value of C(-ey\,dx+ex\,dy) is
7. GATE 2025 IN Q36 (2 marks, Multiple choice) – The outward surface integral S(2x+z)\,dy\,dz+(2x+z)\,dx\,dz+(2z+y)\,dx\,dy over the sphere S:x2+y2+z2=9 is
8. GATE 2025 IN Q38 (2 marks, Multiple choice) – The value of -(6x+4x)\,dx is
9. GATE 2026 IN Q12 (1 mark, Multiple choice) – Which one among the following statements is true for the function f(x)=x x ?
10. GATE 2026 IN Q53 (2 marks, Multiple select) – Given f(x,y)=x2-2xy+y2, the complete contour of the equation f(x,y)=1 is described by the option(s) .