1
GATE ME 2024
+1
-0.33

The value of the surface integral

where S is the external surface of the sphere x2 + y2 + z2 = R2 is

A

0

B

$4 \pi R^{3}$

C

$\frac{4\pi}{3} R^{3}$

D

$\pi R^{3}$

2
GATE ME 2020 Set 1
Numerical
+1
-0

For three vectors $$\vec A = 2\hat j - 3\hat k,\vec B = - 2\hat i + \hat k\ and\;\vec C = 3\hat i - \hat j,$$ where î, ĵ and k̂ are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of $$\left( {\vec {A.} \left( {\vec B \times \vec C} \right) + 6} \right)$$ is _______.

3
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
$$Div\,\,\left( {\phi \overrightarrow V } \right) = \phi Div\overrightarrow V$$
4
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
$$3i-6k$$
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