GATE Engineering Mathematics: Calculus: Gradient, divergence, curl, vector identities, line, surface and volume integrals – Previous Year Questions
7 GATE previous year questions on Calculus: Gradient, divergence, curl, vector identities, line, surface and volume integrals (Engineering Mathematics, Mechanical Engineering) with answers and explanations, from every paper.
- GATE 2022 ME (ME1) Q13 – Given a function = 12(x2 + y2 + z2) in three-dimensional Cartesian space, the value of the surface integral Sn \,dS, where S is the surface of a…
- GATE 2022 ME (ME1) Q48 – Consider two vectors: a = 5i + 7j + 2k, b = 3i - j + 6k Magnitude of the component of a orthogonal to b in the plane containing the vectors a and b is…
- GATE 2023 ME Q31 – A vector field B(x, y, z) = xi + yj - 2zk is defined over a conical region having height h = 2, base radius r = 3 and axis along z, as shown in the…
- GATE 2024 ME Q12 – The value of the surface integral S z\,dx\,dy where S is the external surface of the sphere x2 + y2 + z2 = R2 is
- GATE 2025 ME Q13 – The divergence of the curl of a vector field is
- GATE 2025 ME Q46 – The directional derivative of the function f given below at the point (1, 0) in the direction of 12(i + 3\,j) is (rounded off to 1 decimal place).…
- GATE 2026 ME Q12 – Let be a scalar function. Then, is