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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 𝜙 be a scalar field, and 𝒖 be a vector field. Which of the following identities is true for div(𝜙𝒖)?
A
div(𝜙𝒖) = 𝜙div(𝒖) + 𝒖 ⋅ grad(𝜙)
B
div(𝜙𝒖) = 𝜙div(𝒖) + 𝒖 × grad(𝜙)
C
div(𝜙𝒖) = 𝜙grad(𝒖) + 𝒖 ⋅ grad(𝜙)
D
div(𝜙𝒖) = 𝜙grad(𝒖) + 𝒖 × grad(𝜙)
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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GATE CE 2025 Set 2 (1) GATE CE 2023 Set 2 (1) GATE CE 2017 Set 2 (1) GATE CE 2012 (1) GATE CE 2011 (1) GATE CE 2009 (1) GATE CE 2003 (1) GATE CE 1999 (1) GATE CE 1996 (1) GATE CE 1995 (1)
GATE CE Subjects
Engineering Mechanics
Strength of Materials Or Solid Mechanics
Structural Analysis
Construction Material and Management
Reinforced Cement Concrete
Steel Structures
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Hydrology
Irrigation
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
Engineering Mathematics
General Aptitude