The GATE Grind

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

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

  1. GATE 2021 MT Q12 (1 mark, Multiple choice) – Which is a homogeneous function of degree three?
  2. GATE 2021 MT Q13 (1 mark, Multiple choice) – For vector field V(x,y,z) with components V x,V y,V z depending on x,y,z, its divergence is .
  3. GATE 2021 MT Q24 (1 mark, Numerical answer) – The value of x02(5x)/2x is (nearest integer).
  4. GATE 2021 MT Q36 (2 marks, Multiple choice) – The minimum value of y=x2-2x+4 is .
  5. GATE 2021 MT Q48 (2 marks, Numerical answer) – The work by F=2x i+3y j along a straight line from (0,0) to (1,2) is (nearest integer).
  6. GATE 2022 MT Q11 (1 mark, Multiple choice) – The Taylor series of f(x)=(x+1)/(ex+1) about x=0, truncated to its first two terms, is
  7. GATE 2022 MT Q23 (1 mark, Multiple choice) – A closed volume V is bounded by surface S with outward unit normal n. For vector field f and gradient operator , which theorem gives V( f)\,dV= S( n…
  8. GATE 2023 MT Q23 (1 mark, Multiple choice) – The value of x17x7-20x5+13x3x3+x-4 is
  9. GATE 2023 MT Q35 (1 mark, Numerical answer) – The maximum of f(x)=4x3-24x2+36 on [-1,5] is (nearest integer).
  10. GATE 2023 MT Q40 (2 marks, Multiple choice) – A fluid flow has velocity V=exyz(x i+z k). Its curl at (1,2,3) is
  11. GATE 2023 MT Q41 (2 marks, Multiple choice) – Let =xy i+yz j+xz k. The closed surface S is bounded by x=0,y=0,z=0,x=3,y=2,z=1, and n is its outward unit normal. The flux S n\,dS is
  12. GATE 2023 MT Q44 (2 marks, Multiple choice) – Match plots P–S in Section I (shown) with these functions in Section II: 1. y=2x/x 2. y=x2x 3. y= x/x 4. y=x x
  13. GATE 2024 MT Q12 (1 mark, Multiple choice) – Which Taylor series represents [(1+x)/(1-x)] about the origin for real x <1?
  14. GATE 2024 MT Q31 (1 mark, Numerical answer) – The divergence of V=x2y i+y3z j+z4 k at (1,1,1) is (nearest integer).
  15. GATE 2024 MT Q52 (2 marks, Numerical answer) – The integral 01xe-x\,dx is (two decimal places).
  16. GATE 2025 MT Q25 (1 mark, Multiple select) – Which of the following functions is/are expandable using Maclaurin series?
  17. GATE 2025 MT Q48 (2 marks, Numerical answer) – For the two-dimensional field T(x,y)=13xy(x+y), the magnitude of its gradient at (1,1) is (rounded to two decimal places).
  18. GATE 2025 MT Q52 (2 marks, Numerical answer) – The value of x06(x- x)x3 is (in integer).
  19. GATE 2026 MT Q13 (1 mark, Multiple choice) – Given w=f(ax+by), where a and b are constants, the value of b w x-a w y is .
  20. GATE 2026 MT Q32 (1 mark, Numerical answer) – The value of the scalar triple product a( b c) is . (Answer in integer.) Here a=2 i-3 j+4 k, b= i+2 j-3 k, and c=3 i+4 j- k, where i, j, k are…
  21. GATE 2026 MT Q65 (2 marks, Numerical answer) – Given the scalar field (x,y,z)=x2-yz, the magnitude of a vector in the direction of the most rapid increase of at P=(3,4,1) is . (Rounded off to two…