GATE 2008 EC Question Paper

1 to 20 Carry One Mark Each

2. The system of linear equations
4x+ 2y= 7
2x+ y= 6

has
(A) a unique solution (B) no solution
(C) an infinite number of solutions (D) exactly two distinct solutions
3. The equation sin(z)= 10has
(A) no real or complex solution
(B) exactly two distinct complex solutions
(C) a unique solution
(D) an infinite number of complex solutions
4. For real values of x, the minimum value of the function f(x)= exp(x)+ exp(-x) is
(A) 2 (B) 1 (C) 0.5 (D) 0

10. The impulse response h(t) of a linear time-invariant continuous time system is
described by h(t)= exp(αt)u(t)+ exp(βt)(-ut)where u(t) denotes the unit step
function, and α and β are real constants. This system is stable if
(A) α is positive and β is positive (B) α is negative and β is negative
(C) α is positive and β is negative (D) α is negative and β is positive

13. Which of the following is NOT associated with a p-n junction?
(A) Junction capacitance (B) Charge Storage Capacitance
(C) Depletion Capacitance (D) Channel Length Modulation
14. Which of the following is true?
(A) A silicon wafer heavily doped with boron is a p+ substrate
(B) A silicon wafer lightly doped with boron is a p+ substrate
(C) A silicon wafer heavily doped with arsenic is a p+ substrate
(D) A silicon wafer lightly doped with arsenic is a p+ substrate
15. For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is
(A) 360º (B) 180º (C) 90º (D) 45

18. A silicon wafer has 100nm of oxide on it and is inserted in a furnace at a
temperature above 1000ºC for further oxidation in dry oxygen. The oxidation
rate
(A) is independent of current oxide thickness and temperature
(B) is independent of current oxide thickness but depends on temperature
(C) slows down as the oxide grows
(D) is zero as the existing oxide prevents further oxidation

49. An 8085 executes the following instructions
2710 LXI H, 30A0H
2713 DAD H
2714 PCHL
All addresses and constants are in Hex. Let PC be the contents of the program
counter and HL be the contents of the HL register pair just after executing PCHL.
Which of the following statements is correct
(A) PC 2715H = (B) PC 30A0H = (C) PC 6140H = (D) PC 6140H =
HL 30A0H = HL 2715H = HL 6140H = HL 2715H

55. Consider the following assertions
S1: For Zener effect to occur, a very abrupt junction is required
S2: For quantum tunneling to occur, a very narrow energy barrier is required
Which of the following is correct?
(A) Only S2 is true
(B) S1 and S2 are both true but S2 is not a reason for S1
(C) S1 and S2 are both true and S2 is a reason for S1
(D) Both S1 and S2 are false

56. The two numbers represented in signed 2’s complement form are
P 11101101 and Q 11100110 = = . If Q is subtracted from P, the value obtained in
signed 2’s complement form is
(A) 100000111 (B) 00000111 (C) 11111001 (D) 11111100

61.A rectangular waveguide of internal dimensions (a 4cm and b 3 = = ) is to be
operated in TE11 mode. The minimum operating frequency is
(A) 6.25GHz (B) 6.0GHz (C) 5.0GHz (D) 3.75GHz
62. One of a loss-less transmission line having the characteristic impedance of 75Ω
and length of 1cm is short-circuited. At 3GHz, the input impedance at the other
end of the transmission line is
(A) 0 (B) Resistive (C) Capacitive (D) Inductive
63. A uniform plane wave in the free space is normally incident on an infinitely thick
dielectric slab (dielectric constant ε =
r 9 ). The magnitude of the reflection
coefficient is
(A) 0 (B) 0.3 (C) 0.5 (D) 0.8
64. In the design of a single mode step index optical fiber close to upper cut-off, the
single mode operations is NOT preserved if
(A) Radius as well as operating wavelength are halved
(B) Radius as well as operating wavelength are doubled
(C) Radius is halved and operating wavelength is doubled
(D) Radius is doubled and operating wavelength is halved
65. At 20GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70%
efficiency is
(A) 15dB (B) 25dB (C) 35dB (D) 45dB
66. Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3dB cut-off frequency of fc. The noise power at the filter output is
(A) K (B) Kfc (C) K fcπ (D) ∞
68. Four messages band limited to W, W, 2W and 3W respectively are to be
multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth
required for transmission of this TDM signal is
(A) W (B) 3W (C) 6W (D) 7W

A speech signal, band limited to 4kHz and peak voltage varying between +5V and
-5V is sampled at the Nyquist rate. Each sample is quantized and represented by
8 bits.
71. If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth
required for distortion free transmission is
(A) 64kHz (B) 32kHz (C) 8kHz (D) 4kHz
72. Assuming the signal to be uniformly distributed between its peak values, the
signal to noise ratio at the quantizer output is
(A) 16dB (B) 32dB (C) 48dB (D) 64dB

73. The number of quantitization levels required to reduce the quantization noise by
a factor of 4 would be
(A) 1024 (B) 512 (C) 256 (D) 64

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