GATE Mechanical Engineering (ME) 2023 Shift 1 Solved Paper

A vector field
𝐁(𝑥, 𝑦, 𝑧) = 𝑥 𝑖̂ + 𝑦 ĵ − 2𝑧 k̂
is defined over a conical region having height ℎ = 2, base radius 𝑟 = 3 and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin.
If 𝒏 denotes the unit outward normal to the curved surface 𝑆 of the cone, the value of the integral
${\int }_{\mathit{S}}\mathit{B}.\mathit{n}\mathit{d}\mathit{S}$
equals _________ . (Answer in integer)