1
GATE ECE 2015 Set 1
+1
-0.3
A vector $$\overrightarrow P$$ is given by $$\,\,\overrightarrow P = {x^3}y\overrightarrow a {}_x - {x^2}{y^2}\overrightarrow a {}_y - {x^2}yz\overrightarrow a {}_z.\,\,\,$$ Which one of the following statements is TRUE?
A
$$\overrightarrow P$$ is solenoidal, but not irrotational
B
$$\overrightarrow P$$ is irrotational, but not solenoidal
C
$$\overrightarrow P$$ is neither solenoidal nor irrotational
D
$$\overrightarrow P$$ is both solenoidal and irrotational
2
GATE ECE 2014 Set 4
Numerical
+1
-0
The magnitude of the gradient for the function $$f\left( {x,y,z} \right) = {x^2} + 3{y^2} + {z^3}\,\,$$ at the point $$(1,1,1)$$ is _________.
3
GATE ECE 2014 Set 4
Numerical
+1
-0
The directional derivative of $$f\left( {x,y} \right) = {{xy} \over {\sqrt 2 }}\left( {x + y} \right)$$ at $$(1, 1)$$ in the direction of the unit vector at an angle of $${\pi \over 4}$$ with $$y-$$axis, is given by ________.
4
GATE ECE 2014 Set 2
Numerical
+1
-0
If $$\,\overrightarrow r = x\widehat a{}_x + y\widehat a{}_y + z\widehat a{}_z\,\,\,\,$$ and $$\,\left| {\overrightarrow r } \right| = r,$$ then div $$\left( {{r^2}\nabla \left( {\ln \,r} \right)} \right)$$ = ________.
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
EXAM MAP
Joint Entrance Examination