1
GATE EE 2007
MCQ (Single Correct Answer)
+1
-0.3
Divergence of the vector field $$\overrightarrow V\left(x,y,z\right)=-\left(x\cos xy\;+\;y\right)\;\widehat i\;+\;\left(y\cos xy\right)\;\widehat j\;+\;\left(\sin\;z^2\;+\;x^2\;+\;y^2\right)\widehat k$$\$ is
A
$$2z\cos z^2$$
B
$$\sin xy\;+\;2z\;\cos z^2$$
C
$$x\sin xy\;-\;cosz$$
D
none of these
2
GATE EE 2004
MCQ (Single Correct Answer)
+1
-0.3
A parallel plate capacitor is shown in Fig. It is made of two square metal plates of $$400$$ $$mm$$ side. The $$14$$ $$mm$$ space between the plates is filled with two layers of dielectrics of $${\varepsilon _r} = 4,6\,\,mm$$ thick and $${\varepsilon _r} = 2,8\,\,mm$$ thick. Neglecting fringing of fields at the edges, the capacitance is
A
$$1298\,pF$$
B
$$944\,pF$$
C
$$354\,pF$$
D
$$257\,pF$$
3
GATE EE 2002
MCQ (Single Correct Answer)
+1
-0.3
Given a vector field $$\overrightarrow F ,$$ the divergence theorem states that
A
$$\oint {\overrightarrow F .d\overrightarrow s = \int\limits_v {\Delta \,\,.\,\,\overrightarrow F \,dv} }$$
B
$$\int\limits_s {\overrightarrow F .\,\,d} \overrightarrow s = \int\limits_v {\Delta \times \overrightarrow F \,\,dV}$$
C
$$\int\limits_s {\overrightarrow F \times \,d} \overrightarrow s = \int\limits_v {\Delta \,\,.\,\,\overrightarrow F \,\,dV}$$
D
$$\int\limits_s {\overrightarrow F \times \,d} \overrightarrow s = \int\limits_v {\Delta \,\, \times \overrightarrow F \,\,dV}$$
4
GATE EE 1997
MCQ (Single Correct Answer)
+1
-0.3
In a uniform electric field, field lines and equipotentials
A
are parallel to one another
B
intersect at $$45^\circ$$
C
intersect at $$30^\circ$$
D
are orthogonal
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