Engineering Mathematics
Probability and Statistics
Marks 1Marks 2
Differential Equations
Marks 1Marks 2
Transform Theory
Marks 1Marks 2
Complex Variable
Marks 1Marks 2
Linear Algebra
Marks 1Marks 2
Vector Calculus
Marks 1Marks 2
Numerical Methods
Marks 1Marks 2
1
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)
2
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 ____
3
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
$$ab-cd$$
4
GATE CE 2011
MCQ (Single Correct Answer)
+1
-0.3
If $$\overrightarrow a $$ and $$\overrightarrow b $$ are two arbitrary vectors with magnitudes $$a$$ and $$b$$ respectively, $${\left| {\overrightarrow a \times \overrightarrow b } \right|^2}$$ will be equal to
A
$${a^2}\,{b^2} - {\left( {\overrightarrow a .\,\overrightarrow b } \right)^2}$$
B
$$ab - \overrightarrow a .\,\overrightarrow b $$
C
$${a^2}\,{b^2} + {\left( {\overrightarrow a .\,\overrightarrow b } \right)^2}$$
D
$$ab + \overrightarrow a .\,\overrightarrow b $$
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