GATE Engineering Mathematics: Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial derivatives, Multiple integrals, Fourier series – Previous Year Questions

12 GATE previous year questions on Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial derivatives, Multiple integrals, Fourier series (Engineering Mathematics, Electrical Engineering) with answers and explanations, from every paper.

1. GATE 2017 EE Q27 (1 mark, Numerical answer) – Let I = c R xy2\,dx\,dy, where R is the region shown in the figure and c = 6 10-4. The value of I equals . (Give the answer up to two decimal places.)
2. GATE 2017 EE Q36 (2 marks, Multiple choice) – A function f(x) is defined as f(x) = cases ex, & x < 1 \\ x + ax2 + bx, & x 1 cases, where x R. Which one of the following statements is TRUE?
3. GATE 2017 EE Q52 (2 marks, Numerical answer) – Only one of the real roots of f(x) = x6 - x - 1 lies in the interval 1 x 2 and bisection method is used to find its value. For achieving an accuracy…
4. GATE 2015 EE Q12 (1 mark, Multiple choice) – If a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statements is TRUE?
5. GATE 2016 EE Q37 (2 marks, Numerical answer) – Let S = n=0 nn where < 1. The value of in the range 0 < < 1, such that S = 2 is .
6. GATE 2018 EE Q21 (1 mark, Multiple choice) – Let f be a real-valued function of a real variable defined as f(x)=x2 for x0, and f(x)=-x2 for x<0. Which one of the following statements is true?
7. GATE 2018 EE Q28 (1 mark, Numerical answer) – Let f be a real-valued function of a real variable defined as f(x)=x-[x], where [x] denotes the largest integer less than or equal to x. The value of…
8. GATE 2021 EE Q23 (1 mark, Numerical answer) – Suppose the circles x2+y2=1 and (x-1)2+(y-1)2=r2 intersect each other orthogonally at the point (u,v). Then u+v= .
9. GATE 2021 EE Q36 (2 marks, Multiple choice) – In the open interval (0,1), the polynomial p(x)=x4-4x3+2 has
10. GATE 2024 EE Q31 (1 mark, Numerical answer) – Consider the complex function f(z)= z+ez2. The coefficient of z5 in the Taylor series expansion of f(z) about the origin is (rounded off to 1 decimal…
11. GATE 2024 EE Q44 (2 marks, Multiple select) – Consider the function f(t)=((0,t))2 for -<t<, where (a,b) denotes the maximum of a and b. Which of the following statements is/are true?
12. GATE 2026 EE Q65 (2 marks, Numerical answer) – The integral 1 0x2026(1+x2026)(1+x2)dx evaluates to . (Round off to two decimal places)