1
GATE EE 2014 Set 2
+2
-0.6
The magnitude of magnetic flux density ($$\overrightarrow B$$) at a point having normal distance d meters from an infinitely extended wire carrying current of I A is $$\frac{\mu_0I}{2\mathrm{πd}}$$ (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4 A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. μ0 is permeability of free space. Assume $$\widehat i,\;\widehat j,\;\widehat k$$ to be unit vectors along x, y and z axes respectively. Assuming right handed coordinate system, magnetic field intensity, $$\overrightarrow H$$ at coordinate (2,1,0) will be
A
$$\frac3{2\mathrm\pi}\widehat k\;$$ Weber/m2
B
$$\frac4{3\mathrm\pi}\widehat i\;A/m$$
C
$$\frac3{2\mathrm\pi}\widehat k\;A/m$$
D
0 A/m
2
GATE EE 2014 Set 2
+1
-0.3
Which one of the following statements is true for all real symmetric matrices?
A
All the eigen values are real
B
All the eigen values are positive
C
All the eigen values are distinct
D
Sum of all the eigen values is zero
3
GATE EE 2014 Set 2
+1
-0.3
Minimum of the real valued function $$f\left( x \right) = {\left( {x - 1} \right)^{2/3}}$$ occurs at $$x$$ equal to
A
$$- \infty$$
B
$$0$$
C
$$1$$
D
$$\infty$$
4
GATE EE 2014 Set 2
+2
-0.6
To evaluate the double integral $$\int\limits_0^8 {\left( {\int\limits_{y/2}^{\left( {y/2} \right) + 1} {\left( {{{2x - y} \over 2}} \right)dx} } \right)dy,\,\,}$$ we make the substitution $$u = \left( {{{2x - y} \over 2}} \right)$$ and $$v = {y \over 2}.$$ The integral will reduce to
A
$$\int\limits_0^4 {\left( {\int\limits_0^2 {2udu} } \right)dv}$$
B
$$\int\limits_0^4 {\left( {\int\limits_0^1 {2udu} } \right)dv}$$
C
$$\int\limits_0^4 {\left( {\int\limits_0^1 {udu} } \right)dv}$$
D
$$\int\limits_0^4 {\left( {\int\limits_0^{21} {2udu} } \right)dv}$$
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