1
GATE ME 2012
MCQ (Single Correct Answer)
+1
-0.3
For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }},0} \right)$$ is given by
A
$${{1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat j}$$
B
$${{1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat j}$$
C
$${\widehat k}$$
D
$${{1 \over {\sqrt 3 }}\widehat i + {1 \over {\sqrt 3 }}\widehat j + {1 \over {\sqrt 3 }}\widehat k}$$
2
GATE ME 2008
MCQ (Single Correct Answer)
+1
-0.3
The divergence of the vector field $$\left( {x - y} \right)\widehat i + \left( {y - x} \right)\widehat j + \left( {x + y + z} \right)\widehat k$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
3
GATE ME 2005
MCQ (Single Correct Answer)
+1
-0.3
Stokes theorem connects
A
a line integral and a surface integral
B
a surface integral and a volume integral
C
a line integral and a volume integral
D
gradient of a function and its surface integral.
4
GATE ME 1996
MCQ (Single Correct Answer)
+1
-0.3
The expression curl $$\left( {grad\,f} \right)$$ where $$f$$ is a scalar function is
A
Equal to $${\nabla ^2}f$$
B
Equal to $$div\left( {grad\,f} \right)$$
C
A scalar of zero magnitude
D
A vector of zero magnitude
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