The GATE Grind

GATE Engineering Mathematics: Calculus – Previous Year Questions

20 GATE previous year questions on Calculus (Engineering Mathematics, Computer Science) with answers and explanations, from every paper.

  1. GATE 2017 CS Q38 (2 marks, Multiple choice) – The value of x 1 x7 - 2x5 + 1x3 - 3x2 + 2
  2. GATE 2016 CS Q13 (1 mark, Numerical answer) – x 4 (x - 4)x - 4 = .
  3. GATE 2015 CS Q12 (1 mark, Multiple choice) – x x1/x is
  4. GATE 2015 CS Q41 (2 marks, Numerical answer) – x=199 1x(x+1) = .
  5. GATE 2015 CS Q58 (2 marks, Numerical answer) – 1/2/ (1/x)x2 \, dx = .
  6. GATE 2018 CS Q26 (1 mark, Numerical answer) – The value of 0/4x(x2)\,dx correct to three decimal places (assuming that =3.14) is .
  7. GATE 2019 CS Q23 (1 mark, Multiple choice) – Compute x3x4-812x2-5x-3
  8. GATE 2026 CS (CS2) Q27 (1 mark, Multiple select) – For a real number a, let I(a)= -11(3x2-ax+1)\,dx. Which of the following statements is/are true?
  9. GATE 2026 CS (CS2) Q64 (2 marks, Numerical answer) – Consider a function f:(0,1)\0,1\ defined as follows. For a real number r(0,1), f(r)=1 if the second digit after the decimal point in r is one of the…
  10. GATE 2026 CS (CS1) Q32 (1 mark, Numerical answer) – Consider the function f:R R defined as follows: f(x) = cases c 1 ex - c 2 e(1x), & if x > 0 \\ 3, & otherwise cases where c 1, c 2 R. If f is…
  11. GATE 2026 CS (CS1) Q46 (2 marks, Multiple select) – Let f:R R be defined as follows: f(x) = ( x 2 - x)(x - x 2) Which of the following statements is/are true?
  12. GATE 2025 CS (CS2) Q12 (1 mark, Multiple choice) – The value of x such that x > 1, satisfying the equation 1x t t\,dt = 14 is
  13. GATE 2025 CS (CS1) Q31 (1 mark, Numerical answer) – Consider the given function f(x). f(x) = cases ax + b & for x < 1 \\ x3 + x2 + 1 & for x 1 cases If the function is differentiable everywhere, the…
  14. GATE 2024 CS (CS2) Q16 (1 mark, Multiple choice) – Let f(x) be a continuous function from R to R such that f(x)=1-f(2-x). Which one of the following options is the CORRECT value of 02 f(x)dx?
  15. GATE 2024 CS (CS1) Q11 (1 mark, Multiple choice) – Let f:RR be a function such that f(x)=\x,x3\, xR, where R is the set of all real numbers. The set of all points where f(x) is NOT differentiable is
  16. GATE 2023 CS Q28 (1 mark, Multiple select) – Let f(x) = x3 + 15x2 - 33x - 36 be a real-valued function. Which of the following statements is/are TRUE?
  17. GATE 2023 CS Q31 (1 mark, Numerical answer) – The value of the definite integral -33 -22 -11(4x2y - z3)dz\,dy\,dx is . (Rounded off to the nearest integer)
  18. GATE 2022 CS Q34 (1 mark, Numerical answer) – The value of the following limit is . x0+x1-e2x
  19. GATE 2021 CS Q30 (1 mark, Numerical answer) – Consider the following expression. x -3 2x+22-4x+3 The value of the above expression (rounded to 2 decimal places) is .
  20. GATE 2020 CS Q11 (1 mark, Multiple choice) – Consider the functions I. e-x II. x2- x III. x3+1 Which of the above functions is/are increasing everywhere in [0,1]?