GATE Engineering Mathematics: Calculus: Gradient, divergence, curl, vector identities and integral theorems – Previous Year Questions
9 GATE previous year questions on Calculus: Gradient, divergence, curl, vector identities and integral theorems (Engineering Mathematics, Chemical Engineering) with answers and explanations, from every paper.
- GATE 2022 CH Q44 – The directional derivative of f(x, y, z) = 4x2 + 2y2 + z2 at the point (1,1,1) in the direction of the vector v = i - k is (rounded off to two decimal…
- GATE 2022 CH Q45 – Consider a sphere of radius 4, centered at the origin, with outward unit normal n on its surface S. The value of the surface integral S(2xi + 3yj +…
- GATE 2023 CH Q12 – The vector v is defined as v = zxi + 2xyj + 3yzk. Which one of the following is the CORRECT value of divergence of v, evaluated at the point (x, y, z)…
- GATE 2023 CH Q14 – For a two-dimensional plane, the unit vectors, (e r, e ) of the polar coordinate system and (i, j) of the cartesian coordinate system, are related by…
- GATE 2024 CH Q51 – Consider the line integral CF(r) dr, with F(r) = xi + yj + zk, where i, j and k are unit vectors in the (x, y, z) Cartesian coordinate system. The…
- GATE 2024 CH Q53 – Consider the function f(x, y, z) = x4 + 2y3 + z2. The directional derivative of the function at the point P(-1, 1, -1) along (i + j), where i and j…
- GATE 2025 CH Q12 – Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors i, j and k. Let vector a = 2i +…
- GATE 2025 CH Q36 – Consider a Cartesian coordinate system with orthogonal unit basis vectors i, j defined over a domain: x, y [0, 1]. Choose the condition for which the…
- GATE 2026 CH Q21 – A two-dimensional temperature profile is given as T = 2x2 + 3xy + y2. If i and j are the unit vectors along x and y directions, respectively, which…