# GATE EE 2002

 Question 1
A current impulse $5\delta \left ( t \right )$, is forced through a capacitor C. The voltage $V_{c}\left ( t \right )$, across the capacitor is given by
 A 5t B 5u(t) - C C $\frac{5}{C}t$ D $\frac{5u(t)}{C}$
Signals and Systems   Introduction of C.T. and D.T. Signals
Question 1 Explanation:
$V_c(t)=\frac{1}{C}\int_{-\infty }^{t}i(t)dt=\frac{1}{C}\int_{-\infty }^{t}5\delta (t)dt=\frac{5}{C}u(t)$
 Question 2
Fourier Series for the waveform, f(t) shown in figure is A $\frac{8}{\pi ^{2}}\left [ \sin \left ( \pi t \right )+\frac{1}{9}\sin \left ( 3\pi t \right )+\frac{1}{25}\sin \left ( 5\pi t \right )+.... \right ]$ B $\frac{8}{\pi ^{2}}\left [ \sin \left ( \pi t \right )-\frac{1}{9}\cos \left ( 3\pi t \right )+\frac{1}{25}\sin \left ( 5\pi t \right )+.... \right ]$ C $\frac{8}{\pi ^{2}}\left [ \cos \left ( \pi t \right )+\frac{1}{9}\cos \left ( 3\pi t \right )+\frac{1}{25}\cos \left ( 5\pi t \right )+.... \right ]$ D $\frac{8}{\pi ^{2}}\left [ \cos \left ( \pi t \right )-\frac{1}{9}\sin \left ( 3\pi t \right )+\frac{1}{25}\sin \left ( 5\pi t \right )+.... \right ]$
Signals and Systems   Fourier Series
Question 2 Explanation:
$\because$ f(t) is an even function with half waves symmetry,
$\therefore$ dc term as well as sine terms=0
Only the cosine terms with odd harmonics will be present.

 Question 3
The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by
 A B - N + 1 B B + N C N - B + 1 D N - 2B -1
Electric Circuits   Magnetically Coupled Circuits, Network Topology and Filters
Question 3 Explanation:
 A A circle of unit radius B An ellipse C A parabola D A straight line inclined at $45^{\circ}$ with respect to the x-axis
$\therefore \;\; \text{Phase difference}=0^{\circ} \text{also} f_x=f_y.$
Given a vector field $\vec{F}$, the divergence theorem states that
 A $\int _S\vec{F}\cdot d\vec{S}=\int _V\vec{\triangledown }\cdot \vec{F}dV$ B $\int _S\vec{F}\cdot d\vec{S}=\int _V\vec{\triangledown }\times \vec{F}dV$ C $\int _S\vec{F}\times d\vec{S}=\int _V\vec{\triangledown }\cdot \vec{F}dV$ D $\int _S\vec{F}\times d\vec{S}=\int _V\vec{\triangledown }\times \vec{F}dV$