Q.1
Del operator is also known as _________
  • a) Divergence operator
  • b) Gradient operator
  • c) Curl operator
  • d) Laplacian operator
Q.2
The gradient of a scalar field V is a vector that represents both magnitude and the direction of the maximum space rate of increase of V.
  • a) True
  • b) False
Q.3
The gradient is taken on a _________
  • a) tensor
  • b) vector
  • c) scalar
  • d) anything
Q.4
Find the gradient of a function V if V= xyz.
  • a) yz ax + xz ay + xy az
  • b) yz ax + xy ay + xz az
  • c) yx ax + yz ay + zx az
  • d) xyz ax + xy ay + yz az
Q.5
Find the gradient of V = x2 sin(y)cos(z).
  • a) 2x siny cos z ax + x2 cos(y)cos(z) ay – x2 sin(y)sin(z) az
  • b) 2x siny cos z ax + x2 cos(y)cos(z) ay + x2 sin(y)sin(z) az
  • c) 2x sinz cos y ax + x2 cos(y)cos(z) ay – x2 sin(y)sin(z) az
  • d) x siny cos z ax + x2 cos(y)cos(z) ay – x2 sin(y)sin(z) az
Q.6
Find the gradient of the function W if W = ρzcos(ϕ) if W is in cylindrical coordinates.
  • a) zcos(ϕ)aρ – z sin(ϕ) aΦ + ρcos(ϕ) az
  • b) zcos(ϕ)aρ – sin(ϕ) aΦ + cos(ϕ) az
  • c) zcos(ϕ)aρ + z sin(ϕ) aΦ + ρcos(ϕ) az
  • d) zcos(ϕ)aρ + z sin(ϕ) aΦ + cos(ϕ) az
Q.7
If W = xy + yz + z, find directional derivative of W at (1,-2,in the direction towards the point (3,6,9).
  • a) -0.6
  • b) -0.7
  • c) -0.8
  • d) -0.9
Q.8
Electric field E can be written as _________
  • a) -Gradient of V
  • b) -Laplacian of V
  • c) Gradient of V
  • d) Laplacian of V
Q.9
Let F = (xyax + yx2 ay, F is a not a conservative vector.
  • a) True
  • b) False
Q.10
State whether the given equation is a conservative vector.
  • a) True
  • b) False
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