1
GATE ME 2015 Set 3
+1
-0.3
Let $$\phi$$ be an arbitrary smooth real valued scalar function and $$\overrightarrow V$$ be an arbitrary smooth vector valued function in a three dimensional space. Which one of the following is an identity?
A
$$Curl\left( {\phi \overrightarrow V } \right) = \nabla \left( {\phi Div\overrightarrow V } \right)$$
B
$${Div\overrightarrow V = 0}$$
C
$${Div\,\,Curl\,\,\overrightarrow V = 0}$$
D
$$Div\,\,\left( {\phi \overrightarrow V } \right) = \phi Div\overrightarrow V$$
2
GATE ME 2015 Set 2
+1
-0.3
Curl of vector $$\,V\left( {x,y,x} \right) = 2{x^2}i + 3{z^2}j + {y^3}k\,\,$$ at $$x=y=z=1$$ is
A
$$-3i$$
B
$$3i$$
C
$$3i-4j$$
D
$$3i-6k$$
3
GATE ME 2014 Set 2
+1
-0.3
Curl of vector $$\,\,\overrightarrow F = {x^2}{z^2}\widehat i - 2x{y^2}z\widehat j + 2{y^2}{z^3}\widehat k\,\,$$ is
A
$$\left( {4y{z^3} + 2x{y^2}} \right)\widehat i + 2{x^2}z\widehat j - 2{y^2}z\widehat k$$
B
$$\,\left( {4y{z^3} + 2x{y^2}} \right)\widehat i - 2{x^2}z\widehat j - 2{y^2}z\widehat k$$
C
$$2x{z^2}\widehat i - 4xyz\widehat j + 6{y^2}{z^2}\widehat k$$
D
$$2x{z^2}\widehat i + 4xyz\widehat j + 6{y^2}{z^2}\widehat k$$
4
GATE ME 2014 Set 3
+1
-0.3
Divergence of the vector field $${x^2}z\widehat i + xy\widehat j - y{z^2}\widehat k\,\,$$ at $$(1, -1, 1)$$ is
A
$$0$$
B
$$3$$
C
$$5$$
D
$$6$$
GATE ME Subjects
EXAM MAP
Medical
NEET