GATE Engineering Mathematics: Calculus – Previous Year Questions
26 GATE previous year questions on Calculus (Engineering Mathematics, Electronics and Communication Engineering) with answers and explanations, from every paper.
- GATE 2017 EC Q36 – Let f(x) = ex + x2 for real x. From among the following, choose the Taylor series approximation of f(x) around x = 0, which includes all powers of x…
- GATE 2017 EC Q40 – Starting with x = 1, the solution of the equation x3 + x = 1, after two iterations of Newton-Raphson's method (up to two decimal places) is .
- GATE 2015 EC Q12 – A function f(x) = 1 - x2 + x3 is defined in the closed interval [-1, 1]. The value of x, in the open interval (-1, 1) for which the mean value theorem…
- GATE 2015 EC Q38 – Which one of the following graphs describes the function f(x) = e-x(x2 + x + 1)?
- GATE 2015 EC Q39 – The maximum area (in square units) of a rectangle whose vertices lie on the ellipse x2 + 4y2 = 1 is .
- GATE 2016 EC Q13 – Given the following statements about a function f : R R, select the right option: P: If f(x) is continuous at x = x 0, then it is also differentiable…
- GATE 2016 EC Q15 – Consider the plot of f(x) versus x as shown below. [Figure: f(x) is zero at x = -5, then falls to -2 and stays flat for a while, rises through 0 at x…
- GATE 2016 EC Q36 – The integral 12 D (x + y + 10) \, dx \, dy, where D denotes the disc: x2 + y2 4, evaluates to
- GATE 2018 EC Q16 – Consider p(s)=s3+a 2s2+a 1s+a 0 with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(s)…
- GATE 2018 EC Q22 – Let f(x,y)=ax2+by2xy, where a and b are constants. If f x= f y at x=1 and y=2, then the relation between a and b is
- GATE 2018 EC Q34 – Taylor series expansion of f(x)= 0xe-(t22)dt around x=0 has the form f(x)=a 0+a 1x+a 2x2+ The coefficient a 2 (correct to two decimal places) is equal…
- GATE 2018 EC Q62 – Let r=x2+y-z and z3-xy+yz+y3=1. Assume that x and y are independent variables. At (x,y,z)=(2,-1,1), the value (correct to two decimal places) of r x…
- GATE 2019 EC Q29 – The value of the integral 0 y xx\,dx\,dy is equal to .
- GATE 2019 EC Q36 – Consider a differentiable function f(x) on the set of real numbers such that f(-1)=0 and f'(x) 2. Given these conditions, which one of the following…
- GATE 2020 EC Q13 – The partial derivative of the function f(x,y,z)=e1-x y+xze-1/(1+y2) with respect to x at the point (1,0,e) is
- GATE 2020 EC Q61 – For the solid S shown below, the value of Sx\,dx\,dy\,dz (rounded off to two decimal places) is .
- GATE 2022 EC Q36 – The function f(x)=8 e x-x2+3 attains its minimum over the interval [1,e] at x= . (Here e x is the natural logarithm of x.)
- GATE 2022 EC Q45 – Consider the following series: n=1ndcn For which of the following combinations of c,d values does this series converge?
- GATE 2022 EC Q53 – The value of the integral D 3(x2+y2)\,dx\,dy, where D is the shaded triangular region shown in the diagram, is (rounded off to the nearest integer).
- GATE 2023 EC Q12 – The rate of increase, of a scalar field f(x,y,z)=xyz, in the direction v=(2,1,2) at a point (0,2,1) is
- GATE 2023 EC Q55 – The value of the integral Rxy\,dx\,dy over the region R, given in the figure, is (rounded off to the nearest integer).
- GATE 2024 EC Q36 – Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the 60N latitude circle, that contains the…
- GATE 2025 EC Q12 – Consider the following series: (i) n=11 n (ii) n=11n(n+1) (iii) n=11n! Choose the correct option.
- GATE 2025 EC Q25 – Consider the function f:RR, defined as f(x)=2x3-3x2-12x+1. Which of the following statements is/are correct? (Here, R is the set of real numbers.)
- GATE 2025 EC Q51 – Consider a non-negative function f(x) which is continuous and bounded over the interval [2,8]. Let M and m denote, respectively, the maximum and the…
- GATE 2026 EC Q61 – Consider the square region R in the X-Y plane as shown with the dark shading in the Figure. The value of R(x2+y2-1)\,dx\,dy is . (rounded off to two…