1
GATE CE 2025 Set 2
MCQ (More than One Correct Answer)
+1
-0

Consider a velocity vector, $\vec{V}$ in ( $\mathrm{x}, \mathrm{y}, \mathrm{z}$ ) coordinates given below. Pick one or more CORRECT statement(s) from the choices given below:

$$ \vec{V}=u \vec{x}+v \vec{y} $$

A
z-component of Curl of velocity; $\nabla \times \vec{V}=\left(\frac{\partial u}{\partial x}-\frac{\partial u}{\partial y}\right) \vec{z}$
B
z-component of Curl of velocity; $\nabla \times \vec{V}=\left(\frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}\right) \vec{z}$
C
Divergence of velocity; $\nabla \cdot \vec{V}=\left(\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}\right)$
D
Divergence of velocity; $\nabla \cdot \vec{V}=\left(\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}\right)$
2
GATE CE 2023 Set 2
MCQ (Single Correct Answer)
+1
-0.33
Let πœ™ be a scalar field, and 𝒖 be a vector field. Which of the following identities is true for div(πœ™π’–)?
A
div(πœ™π’–) = πœ™div(𝒖) + 𝒖 β‹… grad(πœ™)
B
div(πœ™π’–) = πœ™div(𝒖) + 𝒖 Γ— grad(πœ™)
C
div(πœ™π’–) = πœ™grad(𝒖) + 𝒖 β‹… grad(πœ™)
D
div(πœ™π’–) = πœ™grad(𝒖) + 𝒖 Γ— grad(πœ™)
3
GATE CE 2017 Set 2
Numerical
+1
-0
The divergence of the vector field $$\,V = {x^2}i + 2{y^3}j + {z^4}k\,\,$$ at $$x=1, y=2, z=3$$ is ________.
Your input ____
4
GATE CE 2012
MCQ (Single Correct Answer)
+1
-0.3
For the parallelogram $$OPQR$$ shown in the sketch. $$\,\overrightarrow {OP} = a\widehat i + b\widehat j$$ and $$\,\overrightarrow {OR} = c\widehat i + d\widehat j.\,\,$$ The area of the parallelogram is GATE CE 2012 Engineering Mathematics - Vector Calculus Question 5 English
A
$$ad-bc$$
B
$$ac+bd$$
C
$$ad+bc$$
D
$$ab-cd$$
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