GATE | Electronics and Communication Question Paper 2006
Q.1 — Q.20 Carry One Mark Each.
1. The rank of the matrix
1 1 1
1 -1 0 is:
1 1 1
(A) 0
(B) 1
(C) 2
(D) 3
2. VxVxP, wherePisa vector, is equal to
(A) PxVxP-V2P
(B) V2P+V(V.P)
(C) V2P+VxP
(D) v(v.P)-v2P
3. [[(vxP).ds, where P is a vector, is equal to
(A) 4P.dI
(B) VxVxP.dI
(C) 4VxP.dI
(D) [[[V.Pdv
4. A probability density function is of the form
p(x) = Ke aix1 XE
The value of K is
(A) 0.5
(B) 1
(C) O.5cL
(D) x
5. A solution for the differential equation k(t)+2x(t) = 5(t) with initial condition x(0 —) = 0 is:
(A) e 2u(t)
(B) e2u(t)
(C) e u(t)
(D) &u(t)
6. A low-pass filter having a frequency response H(ja) = A(ai)edoes not produce any phase distortion if
(A) A(a) = Cai2,Ø(ai) = kai3
(B) A(a) = Cai2,Ø(ai) = ko.
(C) A(a)=Ca,Ø(a)=ka2
(D) A(a)=C, )=ka1
7. The values of voltage (V3) across a tunnel-diode corresponding to peak and valley currents are V, and V1 respectively-:- The range of tunnel-diode voltage VD for which the slope of its IVD characteristics is negative would be
(A) V3<O
(B) O<VJ<V?
(C) V,V<V
(D) VdVV
8. The concentration of minority carriers in an extrinsic semiconductor under equilibrium is:
(A) directly proportional to the doping concentration
(B) inversely proportional to the doping concentration
(C) directly proportional to the intrinsic concentration
(D) inversely proportional to the intrinsic concentration
9. Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the
(A) diffusion current
(B) drift current
(C) recombination current
(D) induced current
10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a reduction of the effective base-width caused by
(A) electron-hole recombination at the base
(B) the reverse biasing of the base-collector junction
(C) the forward biasing of emitter-base junction
(D) the early removal of stored base charge during saturation-to-cutoff switching.
11. The input impedance (Z,)and the output impedance (Z0)of an ideal transconductance (voltage controlled current source) amplifier are
(A) Z,=0,Z0=0
(B) Z,=O,Z0=oo
(C) Z,=oo,Z0=O
(D) Z = 00, =
12. An n-channel depletion MOSFET has following two points on its ID VGS curve:
(i) VGS = 0 at ID = l2mA and
(ii) VGS = —6 Volts at ID =
Which of the following Q-points will give the highest trans-conductance gain for small signals?
(A) VGS = —6 Volts
(B) VGS = —3 Volts
(C) VGS = 0 Volts
(D) VGS = 3 Volts
13. The number of product terms in the minimized sum-of-product expression obtained through the following K-map is (where “d” denotes don’t care states)
1001
0d00
00d 1
1001
(A) 2
(B) 3
(C) 4
(D) 5
14. The Dirac delta function 8(t) is defined as
(A) 8(t)=1 t=O.
L° otherwise
100 t=O
(B) 8(t)=.
LO otherwise
(C) 8(t) = = . and [8(t)dt = 1
L otherwise
(D) 8(t)=4°° t=O and [8(t)dt=1
L otherwise
15. The open-loop transfer function of a unity-gain feedback control system is given by The gain margin of the system in dB is given by
(A) 0
(B) 1
(C) 20
(D)
16. The electric field of an electromagnetic wave propagating in the positive zdirection is given by
E=asin(at—flz)+asinot—flz+. The wave is
(A) linearly polarized in the z-direction
(B) elliptically polarized
(C) left-hand circularly polarized
(D) right-hand circularly polarized
17. A transmission line is feeding 1 Watt of power to a horn antenna having a gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is:
(A) 10 Watts
(B) 1 Watt
(C) 0.1 Watt
(D) 0.01 Watt
18. The eigenvalues and the corresponding eigenvectors of a 2 x 2 matrix are given by Eigenvalue Eigenvector
A1=8
A2=4 v2=[hil
The matrix is:
(A) 6 2 L2 6
(B) 6 L6 4
(C) r L 2
(D) 8 L8 4
19. For the function of a complex variable W = lnZ (where, W=u+jv and Z=x+jy),the u=constant lines get mapped in Z-plane as
(A) set of radial straight lines
(B) set of concentric circles
(C) set of confocal hyperbolas
(D) set of confocal ellipses
20. Three companies, X, Y and Z supply computers to a university. The percentage of computers supplied by them and the probability of those being defective are tabulated below. Given that a computer is defective, the probability that it was supplied by Y is:
(A) 0.1
(B) 0.2
(C) 0.3
(D) 0.4
21. For the matrix [ jthe eigenvalue corresponding to the eigenvector is:
(A) 2
(B) 4
(C) 6
(D) 8
22. For the differential equation + k2y = 0 the boundary conditions are Company °h of computers supplied Probability of being defective
X 60°h 0.01
Y 30°h 0.02
Z 10°h 0.03
(i) y=Oforx=Oand
(ii) y=Oforx=a
The form of non-zero solutions of y (where mvaries over all integers) are m,rx
(A) y=AmsIn
m a
m,rx
(B) y= AmCO5
m a
(C) Y=4m
mrx
(D) y=Amea
23. Consider the function f (t) having Laplace transform
2 2 Re[sl>O
S +a)0
The final value of f(t)would be:
(A) 0
(B) 1
(C) —1 f(oo) 1
(D)
24. As x is increased from — to 00, the function ex f(x)= 1 + ex
(A) monotonically increases
(B) monotonically decreases
(C) increases to a maximum value and then decreases
(D) decreases to a minimum value and then increases
25. The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by
(A) RL network only
(B) RC network only
(C) LC network only
(D) RC as well as RL networks
26. In the figure shown below, assume that all the capacitors are initially uncharged. If v,(t)=lOu(t) Volts,v0(t) is given by
(A) Se °°° Volts
(B) 8(1 — e °°°) Volts
(C) 8u(t) Volts
(D) 8 Volts
27. Consider two transfer functions G1(S)=s2+as+b and G2(S)=s2+as+b• Vo(t) The 3-dB bandwidths of their frequency responses are, respectively
(A) %Ja2 _4b,%Ja2 +4b
(B) %Ja2 + 4b, %Ja2 — 4b
28. A negative resistance Rneg is connected to a passive network N having driving point impedance Z1 (s)as shown below. For Z2 (s)to be positive real,
Z2(s)
(A) R I<ReZ1(ja),Va neg —
(B) R I —
(C) R 1< ImZ1(ja),va neg —
(D) R <zz (jai),Vai neg— 1
29. In the circuit shown below, the switch was connected to position 1 at t < 0 and at t = 0, it is changed to position 2. Assume that the diode has zero voltage drop and a storage time t5. For 0 < t < t5,v is given by (all in Volts)
(A) v=—5
(B) v=–5
(D) —5 <v <0
30. The majority carriers in an n-type semiconductor have an average drift velocity v in a direction perpendicular to a uniform magnetic field B. the electric field E induced due to Hall effect acts in the direction
(A) v x B
(B) Bxv
(C) along v
(D) opposite to v
31. A heavily doped n—type semiconductor has the following data: Hole-electron mobility ratio : 0.4
Doping concentration : 4.2x 108 atoms/m3
Intrinsic concentration : 1.5x 10 atoms/m3
The ratio of conductance of the n —type semiconductor to that of the intrinsic semiconductor of same material and at the same temperature is given by
(A) 0.00005
(B) 2,000
(C) 10,000
(D) 20,000
32. For the circuit shown below; assume that the zener diode is ideal with a breakdown voltage of 6 Volts. The waveform observed across R is:
(A)6V
(B)l2sinot R VR
(C)12V
33. A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-5 number is represented by its corresponding 3-bit binary code.
For example, the base-5 number 24 will be represented by its BCP code 010100. In this numbering system, the BCP code 100010011001 corresponds to the
following number in base-5 system
(A) 423
(B) 1324
(C) 2201
(D) 4231