Gate Sample Papers

Gate Paper1

Q.1 - Q.20 Carry One Mark Each
1. If E denotes expectation, the variance of a random variable X is given by
2. The following plot shows a function y which varies linearly with x . The value of
4. lim is:
(A) 0.5 (B) 1 (C) 2 (D) not defined
5. Which one of the following functions is strictly bounded?
6. For the function , the linear approximation around 2 = is: - x e
7. An independent voltage source in series with an impedance Z R jX = + delivers a maximum average power to a load impedance Z when
(A) Z R jX = + (B) Z R =
L s s L s
(C) Z jX = (D) Z R jX = -
L s L s s
8. The RC circuit shown in the figure is
(A) a low-pass filter (B) a high-pass filter
(C) a band-pass filter (D) a band-reject filter
9. The electron and hole concentrations in an intrinsic semiconductor are n per cm at 300 K. Now, if acceptor impurities are introduced with a concentration of 3 N per cm where N n >> , the electron concentration per cm at 300 K will 3
+ 10. In a p n junction diode under reverse bias, the magnitude of electric field is maximum at
(A) the edge of the depletion region on the p-side
(B) the edge of the depletion region on the n-side
(C) the p n junction +
(D) the centre of the depletion region on the n-side
11. The correct full wave rectifier circuit is:
12. In a transconductance amplifier, it is desirable to have
(A) a large input resistance and a large output resistance
(B) a large input resistance and a small output resistance
(C) a small input resistance and a large output resistance
(D) a small input resistance and a small output resistance
13. X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two's complement format. The sum of X and Y represented in two's complement format using 6 bits is:
(A) 100111 (B) 001000 (C) 000111 (D) 101001
14. The Boolean function Y AB CD is to be realized using only 2-input NAND gates. The minimum number of gates required is:
(A) 2 (B) 3 (C) 4 (D) 5
15. If the closed-loop t ransfer function of a control syst em is given as
(A) an unstable system (B) an uncontrollable system
(C) a minimum phase system (D) a non-minimum phase system
16. If the Laplace transform of a signal y t is Y s s s = - then its final value is:
(A) -1 (B) 0 (C) 1 (D) unbounded
17. If R is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is NOT true?
(D) The mean square value of the process is R 0
18. If S f is the power spectral density of a real, wide-sense stationary random process, then which of the following is ALWAYS true?
19. A plane wave of wavelength is traveling in a direction making an angle 30° with positive x-axis and 90° with positive y-axis. The E field of the plane wave can be  represented as E is constant
20. If C is a closed curve enclosing a surface S, then the magnetic field intensity , H the current density J and the electric flux density D are related by
Q.21 - Q.75 Carry Two Marks Each
21. It is given that X x X are M non-zero, orthogonal vectors. The dimension of , ,…. the vector space spanned by the 2M vectors X X X X X X , ,… , , , … - - - is:
(A) 2M (B) M + 1 (C) M
(D) dependent on the choice of X X X , ,…
22. Consider the function f x x x = - - 2. The maximum value of f x in the closed interval 4, 4 - » ÿ / is:
(A) 18 (B) 10
(C) -2.25 (D) indeterminate
23. An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is:
(A) 0.5 (B) 0.18 (C) 0.12 (D) 0.06
24. The solution of the differential equation k y y = - under the boundary 2
conditions (i) y y = at x = y y = x y y 0 and (ii) at = 8 , where , k and are
constants, is
25. The equation - + - = 4 4 0 is to be solved using the Newton-Raphson
x method. If 2 = is taken as the initial approximation of the solution, then the next approximation using this method will be:
(A) 2
3 (B) 4 3 (C) 1 (D) 3 2
26. Three functions , and , which are zero outside the interval [0,T],
are shown in the figure. Which of the following statements is correct?
27. If the semi-circular contour D of radius 2 is as shown in the figure, then the value
(A) j p (B) -j p (C) - p (D) p
28. Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth of Filter 1 be and that of Filter 2 be . The value of is:
29. For the circuit shown in the figure, the Thevenin voltage and resistance looking into X-Y are:
(A) 4 , 2 (B) 2 4 , 3 V (C) 4 2 V , (D) 4V, 2
30. In the circuit shown, V is 0 volts at 0 t = sec. For t > 0, the capa citor current i t where t is in seconds, is given by ,
(A) 0.50 exp(-25t) mA (B) 0.25 exp(-25t) mA
(C) 0.50 exp(-12.5t) mA (D) 0.25 exp (-6.25t) mA
31. In the AC network shown in the figure, the phasor voltage V (in Volts) is:
(A) 0 (B) 5 30 ° (C) 12.5 30 ° (D) 17 30 °
32. A p n junction has a built-in potential of 0.8 V. The depletion layer width at a + reverse bias of 1.2V is 2 m. For a reverse bias of 7.2 V, the depletion layer
width will be:
(A) 4 m (B) 4.9 m (C) 8 m (D) 12 m
33. Group I lists four types of p-n junction diodes. Match each device in Group I with one of the option in Group II to indicate the bias condition of that device in its normal mode of operation.
Group I Group II
(P) Zener Diode (1) Forward bias
(Q) Solar cell (2) Reverse bias
(R) LASER diode
(S) Avalanche Photodiode
(A) P - 1 Q - 2 R - 1 S - 2
(B) P - 2 Q - 1 R - 1 S - 2
(C) P - 2 Q - 2 R - 1 S - 1
(D) P - 2 Q - 1 R - 2 S - 2
34. The DC current gain of a BJT is 50. Assuming that the emitter injection
efficiency is 0.995, the base transport factor is:
(A) 0.980 (B) 0.985 (C) 0.990 (D) 0.995
35. Group I lists four different semiconductor devices. Match each device in Group I with its characteristic property in Group II.
Group I Group II
(P) BJT (1) Population inversion
(Q) MOS capacitor (2) Pinch-off voltage
(R) LASER diode (3) Early effect
(S) JFET (4) Flat-band voltage
(A) P - 3 Q - 1 R - 4 S - 2
(B) P - 1 Q - 4 R - 3 S - 2
(C) P - 3 Q - 4 R - 1 S - 2
(D) P - 3 Q - 2 R - 1 S - 4
36. For the Op-Amp circuit shown in the figure, V is:
(A) -2 V (B) -1 V (C) -0.5 V (D) 0.5 V
37. For the BJT circuit shown, assume that the of the transistor is very large and V V = 0.7 . The mode of operation of the BJT is:
(A) cut-off (B) saturation (C) normal active (D) reverse active
38. In the Op-Amp circuit shown, assume that the diode current follows the equation
39. In the CMOS inverter circuit shown, if the transconductance parameters of the NMOS and PMOS transistors are k k C C A V = = = = 40 / and n
(A) 0 A (B) 25 A (C) 45 A (D) 90 A
40. For the Zener diode shown in the figure, the Zener voltage at knee is 7V, the knee current is negligible and the Zener dynamic resistance is 10 . If the input voltage V range is from 10 to 16V, the output voltage V ranges from
(A) 7.00 to 7.29 V (B) 7.14 to 7.29 V
(C) 7.14 to 7.43 V (D) 7.29 to 7.43 V
41. The Boolean expression Y A B C D A B C D A B C D A B C D = + + + can be
minimized to
(A) Y A B C D A B C A C D = + +
(B) Y A B C D B C D A B C D = + +
(C) Y A B C D B C D A B C D = + +
(D) Y A B C D B C D A B C D = + +
42. The circuit diagram of a standard TTL NOT gate is shown in the figure. When V V = 2.5 , the modes of operation of the transistors will be:
43. In the following circuit, X is given by
(A) X A B C A B C A B C A B C = + + +
(B) X A B C A B C A B C A B C = + + +
(C) X AB BC AC = + +
(D) X A B B C A C = + +
44. The following binary values were applied to the X and Y inputs of the NAND latch shown in the figure in the sequence indicated below:
0, 1; 0, 0; 1, 1. X Y X Y X Y = = = = = =
The corresponding stable P, Q outputs will be:
(A) P = 1, Q = 0; P = 1, Q = 0; P = 1, Q = 0 or P = 0, Q = 1
(B) P = 1, Q = 0; P = 0, Q = 1; or P = 0, Q = 1; P = 0, Q = 1
(C) P = 1, Q = 0; P = 1, Q = 1; P = 1, Q = 0 or P = 0, Q = 1
(D) P = 1, Q = 0; P = 1, Q = 1; P = 1, Q = 1
45. For the circuit shown, t he counter state Q Q follows the sequence
(A) 00, 01, 10, 11, 00 … (B) 00, 01, 10, 00, 01 …
(C) 00, 01, 11, 00, 01 … (D) 00, 10, 11, 00, 10 …
46. An 8255 chip is interfaced to an 8085 microprocessor system as an I/O mapped I/O as shown in the figure. The address lines A and A of the 8085 are used by
0 1
the 8255 chip to decode internally its three ports and the Control register. The address lines A to A as well as the IO M signal are used for address decoding.
The range of addresses for which the 8255 chip would get selected is:
(A) F8H - FBH (B) F8H - FCH (C) F8H - FFH (D) F0H œ F7H
47. The 3-dB bandwidth of the low-pass signal e u t , where u t is the unit step - t function, is given by
(A) 1 (B) 1 2 1 - (C) 8 (D) 1 Hz
p p 2 Hz 2 Hz
48. A Hilbert transformer is a
(A) non-linear system (B) non-causal system
(C) time-varying system (D) low-pass system
49. The frequency response of a linear, time-invariant system is given by
The step response of the system is:
50. A 5-point sequence x n » ÿ / is given as
51. The z-transform X z » ÿ » ÿ X z = It is given / / of a sequence x n / is given by that the region of convergence of X z includes the unit circle. The value of 0 x / /
is:
(A) -0.5 (B) 0 (C) 0.25 (D) 0.5
52. A control system with a PD controller is shown in the figure. If the velocity error constant 1000 K = and the damping ratio 0.5, = then the values of K K are: and
53. The transfer function of a plant is T s = The second-order
approximation of T s using dominant pole concept is:
54. The open-loop transfer function of a plant is given as G s = If the plant is
2 s - 1 operated in a unity feedback configuration, then the lead compensator that an stabilize this control system is:
55. A unity feedback control system has an open-loop transfer function
. The gain K for which 1 1 s j = - + will lie on the root locus
s s s + + 7 12 2 of this system is:
(A) 4 (B) 5.5 (C) 6.5 (D) 10
56. The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function G s corresponding to this Bode plot is:
57. The state space representation of a separately excited DC servo motor dynamics is given as
58. In delta modulation, the slope overload distortion can be reduced by
(A) decreasing the step size (B) decreasing the granular noise
(C) decreasing the sampling rate (D) increasing the step size
59. The raised cosine pulse p t is used for zero ISI in digital communications. The expression for p t with unity roll-off factor is given by p t =
60. In the following scheme, if the spectrum M(f) of m t is as shown, then the spectrum Y f y t will be: of
61. During transmission over a certain binary communication channel, bit errors occurs independently with probability . p The probability of AT MOST one bit in error in a block of n bits is given by
(A) p (B) 1 - p n n
62. In a GSM system, 8 channels can co-exist in 200 KHz bandwidth using TDMA. A GSM based cellular operator is allocated 5 MHz bandwidth. Assuming a frequency reuse factor of 1 ,
5 i.e. a five-cell repeat pattern, the maximum number of
simultaneous channels that can exist in one cell is:
(A) 200 (B) 40 (C) 25 (D) 5
63. In a Direct Sequence CDMA system the chip rate is 1.2288 × 10 chips per
second. If the processing gain is desired to be AT LEAST 100, the data rate
(A) must be less than or equal to 12.288 × 10 bits per sec 3
(B) must be greater than 12.288 × 10 bits per sec 3
(C) must be exactly equal to 12.288 × 10 bits per sec
(D) can take any value less than 122.88 × 10 bits per sec.
64. An air-filled rectangular waveguide has inner dimensions of 3 cm × 2 cm. The wave impedance of the TE mode of propagation in the waveguide at a
frequency of 30 GHz is (free space impedance = 377 )
(A) 308 (B) 355 (C) 400 (D) 461
65. The H field (in A/m) of a plane wave propagating in free space is given by
The time average power flow density in Watts is:
66. The E field in a rectangular waveguide of inner dimensions a × b is given by
Where H is a constant, and a and b are the dimensions along the x-axis and the y-axis respectively. The mode of propagation in the waveguide is:
(A) TE (B) TM (C) TM (D) TE
67. A load of 50 is connected in shunt in a 2-wire transmission line of Z = 50 as
shown in the figure. The 2-port scattering parameter matrix (S-matrix) of the shunt element is:
68. The parallel branches of a 2-wire transmission line are terminated in 100 and 200 resistors as shown in the figure. The characteristic impedance of the line is
Z = 50 and each section has a length of . The voltage reflection coefficient
G at the input is:
69. A 2 dipole is kept horizontally at a height of above a perfectly conducting infinite ground plane. The radiation pattern in the plane of the dipole
E plane looks approximately as
70. A right circularly polarized (RCP) plane wave is incident at an angle of 60° to the normal, on an air-dielectric interface. If the reflected wave is linearly polarized, e the relative dielectric constant is:
(A) 2 (B) 3 (C) 2 (D) 3
Common Data Questions
Common Data for Questions 71, 72, 73:
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a
× cm - 4 2 Metal/Si /silicon (MOS) capacitor having an area of 1 10 . Assume that the permitivities of silicon and Si are 1 10 F/cm and 3.5 10 F/cm
respectively.
71. The gate oxide thickness in the MOS capacitor is:
(A) 50 nm (B) 143 nm (C) 350 nm (D) 1 m
72. The maximum depletion layer width in silicon is
(A) 0.143 m (B) 0.857 m (C) 1 m (D) 1.143 m
73. Consider the following statements about the C-V characteristics plot:
n S1: The MOS capacitor has an -type substrat e.
S2: If positive charges are introduced in the oxide, the C-V plot will shift to the left. Then which of the following is true?
(A) Both S1 and S2 are true (B) S1 is true and S2 is false
(C) S1 is false and S2 is true (D) Both S1 and S2 are false
Common Data for Questions 74, 75:
Two 4-ray signal constellations are shown. It is given that and constitute an
orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let denote the power spectral density of white Gaussian noise.
Constellation 2
Constellation 1
74. The ratio of the average energy of Constellation 1 to the average energy of Constellation 2 is:
a 2 (A) 4 (B) 4 (C) 2 (D) 8
75. If these constellations are used for digital communications over an AWGN
channel, then which of the following statements is true?
(A) Probability of symbol error for Constellation 1 is lower
(B) Probability of symbol error for Constellation 1 is higher
(C) Probability of symbol error is equal for both the constellations
N (D) The value of will determine which of the two constellations has a lower
probability of symbol error.
Linked Answer Questions: Q.76 to Q.85 Carry Two Marks Each
Statem ent for Linked Answer Questions 76 & 77:
Consider the Op-Amp circuit shown in the figure.
76. The transfer function is:
. If sin and sin , then the minimum and maximum values
f of (in radians) are respectively
Statement for Linked Answer Questions 78 & 79:
An 8085 assembly language program is given below.
Line 1: MVI A, B5H
2: MVI B, 0EH
3: XRI 69H
4: ADD B
5: ANI 9BH
6: CPI 9FH
7: STA 3010H
8: HLT
78. The contents of the accumulator just after execution of the ADD instruction in line 4 will be
(A) C3H (B) EAH (C) DCH (D) 69H
79. After execution of line 7 of the program, the status of the CY and Z flags will be
(A) CY = 0, Z = 0 (B) CY = 0, Z = 1 (C) CY = 1, Z = 0 (D) CY = 1, Z = 1

Gate Paper2
Q.1 - Q.20 Carry One Mark Each.
1. The rank of the matrix
(A) 0
(B) 1
(C) 2
(D) 3
3. × • P ds , where P is a vector, is equal to
î — (A) P dl •
î — (B) P dl × × •
î — (C) P dl × •
——— (D) Pd •
4. A probability density function is of the form
The value of K is
(A) 0.5
(B) 1
(C) 0.5 a
(D) a
5. A solution for the differential equation
6. A low-pass filter having a frequency response H j A e = does not f j
produce any phase distortion if
7. The values of voltage across a tunnel-diode corresponding to peak and valley V currents are and respectively. The range of tunnel-diode voltage for
I V - which the slope of its characteristics is negative would be
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 and the output impedance of an ideal trans-
conductance (voltage controlled current source) amplifier are
Z Z = = (A) 0, 0
Z Z = = 8 (B) 0,
Z Z = 8 = (C) , 0
Z Z = 8 = 8 (D) ,
12. An n-channel depletion MOSFET has following two points on its curve:
V I mA = = (i) 0 at 12 and
V I = - = (ii) 6 Volts at 0
Which of the following Q-points will give the highest trans-conductance gain for small signals?
V = - (A) 6 Volts
GS
V = - (B) 3 Volts
GS
V = (C) 0 Volts
GS
V = (D) 3 Volts
GS
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)
1 0 0 1
0 d 0 0
0 0 d 1
1 0 0 1
(A) 2
(B) 3
(C) 4
(D) 5
14. Let be Fourier Transform pair. The Fourier Transform of the signal
15. The Dirac delta function t is defined as
16. If the region of convergence of x n x n + is 1 2 , < < z then the region of /
17. 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) 8
18. In the system shown below, x t t u t = sin . In steady-sate, the response
19. The electric field of an electromagnetic wave propagating in the positive z-direction is given by  The wave is
(A) linearly polarized in the z-direction
(B) elliptically polarized
(C) left-hand circularly polarized
(D) right-hand circularly polarized
20. 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
21. The eigenvalues and the corresponding eigenvectors of a 2 × 2 matrix are given by  Eigenvalue Eigenvector
The matrix is:
22. For the function of a complex variable ln W Z =
u = (where, and ), W u j Z x jy = + = + the 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
23. The value of the contour integral in positive sense is
25. 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.
Company % of computers supplied Probability of being defective
X 60% 0.01
Y 30% 0.02
Z 10% 0,03
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
26. For the matrix 4 2 the eigen value corresponding to the eigenvector 101 is: …
(A) 2
(B) 4
(C) 6
(D) 8
28. Consider the function f t having Laplace transform
The final value of f t would be:
(A) 0
(B) 1
29. As x is increased from to , -8 8 the function
(A) monotonically increases
(B) monotonically decreases
(C) increases to a maximum value and then decreases
(D) decreases to a minimum value and then increases
30. A two port network is represented by ABCD parameters given by
If port-2 is terminated by , R the input impedance seen at port-1 is given by
31. In the two port network shown in the figure below, z z are, respectively and
32. 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
33. A 2mH inductor with some initial current can be represented as shown below, where s is the Laplace Transform variable. The value of initial current is:
34. In the figure shown below, assume that all the capacitors are initially uncharged.
35. Consider two transfer functions
The 3-dB bandwidths of their frequency responses are, respectively
36. A negative resistance R is connected to a passive network N having driving
37. In the circuit shown below, the switch was connected to position 1 at 0 t and at  = t 0 , it is changed to position 2. Assume that the diode has zero voltage drop and a storage time . t For 0 , t t is given by (all in Volts)
38. 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 t o Hall effect acts in the direction
× (A) v B
× (B) B v
(C) along v
(D) opposite t o v
39. Find the correct match between Group 1 and Group 2:
Group 1 Group 2
(E) Varactor diode (1) Voltage reference
(F) PIN diode (2) High frequency switch
(G) Zener diode (3) Tuned circuits
(H) Schottky diode (4) Current controlled attenuator
(A) E - 4 F - 2 G - 1 H - 3
(B) E - 2 F - 4 G - 1 H - 3
(C) E - 3 F - 4 G - 1 H - 2
(D) E - 1 F - 3 G - 2 H - 4
- 40. A heavily doped n type semiconductor has the following data:
Hole-electron mobility ratio : 0.4
× 3 Doping concentration : 4.2 10 atoms/m 8
× 3 Intrinsic concentration : 1.5 10 atoms/m 4
- 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
41. For the circuit shown in the following figure, the capacitor C is initially uncharged.
At 0, t = the switch S is closed. The voltage V across the capacitor at
C = t 1 millisecond is:
C=1 F
42. 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:
43. 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. n this numbering system, the BCP code 100010011001 corresponds to the
following number in base-5 system
(A) 423
(B) 1324
(C) 2201
(D) 4231
44. An I/O peripheral device shown in figure (b) below is to be interfaced to an 8085 microprocessor. To select the I/O device in the I/O address range D4 H œ D7 H, its chip-select CS should be connected to the output of the decoder shown in
figure (a) below:
45. For the circuit shown in figure below, two 4-bit parallel-in serial-out shift registers loaded with the data shown are used to feed the data to a full adder. Initially, all
the flip-flops are in clear state. After applying two clock pulses, the outputs of the full-adder should be
46. A 4-bit D/A converter is connected to a free-running 3-bit UP counter, as shown in the following figure. Which of the following waveforms will be observed at ? V
47. Two D-flip-flops, as shown below, are to be connected as a synchronous counter that goes through the following Q Q sequence
The inputs D D respectively should be connected as and
48. Following is the segment of a 8085 assembly language program:
LXI SP, EFFF H
CALL 3000 H
3000 H : LXI H, 3CF4 H
PUSH PSW
SPHL
POP PSW
RET
On completion of RET execution, the contents of SP is:
(A) 3CFO H
(B) 3CF8 H
(C) 3FFD H
(D) EFFF H
49. The point P in the following figure is stuck-at-1. The output f will be
(A) ABC
(B) A
(C) ABC
(D) A
50. A signal m t with bandwidth 500 Hz is first multiplied by a signal g t where The resulting signal is then passed through an ideal lowpass filter with bandwidth 1 kHz. The output of the lowpass filter would be:
51. The minimum sampling frequency (in samples/sec) required to reconstruct the following signal from its samples without distortion.
52. A uniformly distributed random variable X with probability density function Where u is the unit step function is passed through a transformation given in
the figure below. The probability density function of the transformed random variable Y would be
53. A system with input
(A) linear, stable and invertible
(B) non-linear, stable and non-invertible
(C) linear, stable and non-invertible
(D) linear, unstable and invertible
54. The unit-step response of a system starting from rest is given by
The transfer function of the system is:
55. The Nyquist plot of G j H j for a closed loop control system, passes through - 1, 0 j point in the GH plane. The gain margin of the system in dB is equal to
(A) infinite
(B) greater than zero
(C) less than zero
(D) zero
56. The positive values of —K" and —a" so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are
(A) 1, 0.75
(B) 2, 0.75
(C) 1, 1
(D) 2, 2
57. The unit impulse response of a system is:
For this system, the steady-state value of the output for unit step input is equal to
(A) -1
(B) 0
(C) 1
8 (D)
58. The transfer function of a phase-lead compensator is given by
The maximum phase-shift provided by such a compensator is:
59. A linear system is described by the following state equation
The state-transition matrix of the system is:
60. The minimum step-size required for a Delta-Modulator operating at 32 K
samples/sec to track the signal (here u t is the unit-step function)
So that slope-overload is avoided, would be
61. A zero-mean white Gaussian noise is passed through an ideal lowpass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period  = t 0.03 msec. The samples so obtained would be
(A) correlated
(B) statistically independent
(C) uncorrelated
(D) orthogonal
62. A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate as
(A) 6000 bits/sec
(B) 4500 bits/sec
(C) 3000 bits/sec
(D) 1500 bits/sec
63. The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following  condition, (here W is message bandwidth and is carrier frequency both in
rad/sec)
64. In the following figure the minimum value of the constant —C", which is to be
65. A message signal with bandwidth 10 kHz is Lower-Side Band SSB modulated with  carrier frequency f 10 Hz. The resulting signal is then passed through a  Narrow-Band Frequency Modulator with carrier frequency f 10 Hz.
The bandwidth of the output would be:
× (A) 4 10 Hz
× (B) 2 10 Hz
× (C) 2 10 Hz
× (D) 2 10 Hz 1
66. A medium of relative permittivity 2 forms an interface with free-space. A
point source of electromagnetic energy is located in the medium at a depth of 1 meter from the interface. Due to the total internal reflection, the transmitted beam has a circular cross-section over the interface. The area of the beam cross-section at the interface is given by
67. A medium is divided into regions I and II about 0 x plane, as shown in the figure below. An electromagnetic wave with electric field
incident normally on the interface form region-I. The electric field E in region-II  at the interface is:
68. When a plane wave traveling in free-space is incident normally on a medium
e = having 4.0, the fraction of power transmitted into the medium is given by
69. A rectangular waveguide having TE mode as dominant mode is having a cutoff frequency of 18-GHz for the TE mode. The inner broad-wall dimension of the  rectangular waveguide is:
70. A mast antenna consisting of a 50 meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of 600 kHz. The radiation resistance of the antenna in Ohms is:
Common Data Questions:
Common Data for Questions 71, 72, 73:
In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters:
The capacitance C can be assumed to be infinite.
In the figure above, the ground has been shown by the symbol
71. Under the DC conditions, the collector-to-emitter voltage drop is:
(A) 4.8 Volts
(B) 5.3 Volts
(C) 6.0 Volts
(D) 6.6 Volts
72. If is increased by 10% , the collector-to-emitter voltage drop
(A) increases by less than or equal to 10%
(B) decreases by less than or equal to 10%
(C) increases by more than 10%
(D) decreases by more than 10%
73. The small-signal gain of the amplifier is:
(A) -10
(B) -5.3
(C) 5.3
(D) 10
Common Data for Questions 74, 75:
74. The impulse response of filter matched t o the signal s t g t t g t 2 * is
given as:
75. An Amplitude Modulated signal is given as One set of possible values of t he modulating signal and modulation index would be
(A) , 0.5 t
(B) , 1.0 t
(C) , 2.0 t
(D) t , 0.5 2
Linked Answer Questions: Q.76 to Q.85 Carry Two Marks Each.
Statement for Linked Answer Questions 76 & 77:
A regulated power supply, shown in figure below, has an unregulated input (UR) of 15
Volts and generates a regulated output V Use the component values shown in the figure.
In the figure above, the ground has been shown by the symbol
76. The power dissipation across the transistor Q1 shown in the figure is:
(A) 4.8 Watts
(B) 5.0 Watts
(C) 5.4 Watts
(D) 6.0 Watts
77. If the unregulated voltage increases by 20%, the power dissipation across the transistor Q1
(A) increases by 20%
(B) increases by 50%
(C) remains unchanged
(D) decreases by 20%
Statement for Linked Answer Questions 78 & 79:
The following two questions refer to wide sense stationary stochastic processes
78. It is desired to generate a stochastic process (as voltage process) with power spectral density
By driving a Linear-Time-Invariant system by zero mean white noise (as voltage process) with power spectral density being constant equal to 1. The system which can perform the desired task could be:
(A) first order lowpass R-L filter
(B) first order highpass R-c filter
(C) tuned L-C filter
(D) series R-L-C filter
79. The parameters of the system obtained in Q.78 would be
(A) first order R-L lowpass filter would have R = 4 L = 4H
(B) first order R-C highpass filter would have R = 4 C = 0.25F
(C) tuned L-C filter would have L = 4H C = 4F
(D) series R-L-C lowpass filter would have R = 1 , L = 4H, C = 4F
Statement for Linked Answer Questions 80 & 81:
< Consider the following Amplitude Modulated (AM) signal, where : f B
m = + p p x t f t f t 10 1 0.5 sin2 cos2
80. The average side band power for the AM signal given above is:
(A) 25
(B) 12.5
(C) 6.25
(D) 3.125
81. The AM signal gets added to a noise with Power Spectral Density S f given in the figure below. The ratio of average sideband power t o mean noise power
would be:
Statem ent for Linked Answer Questions 82 & 83:
Consider a unity-gain feedback control system whose open-loop transfer function is:
82. The value of —a" so that the system has a phase margin equal to 4 is
approximately equal to
(A) 2.40
(B) 1.40
(C) 0.84
(D) 0.74
83. With the value of —a" set for a phase-margin of , the value of unit-impulse = response of the open-loop system at 1 t second is equal to
(A) 3.40
(B) 2.40
(C) 1.84
(D) 1.74
Statem ent for Linked Answer Questions 84 & 85:
A 30-Volts battery with zero source resistance is connected to a coaxial line of  = characteristic impedance of 50 Ohms at 0 t second terminated in an unknown resistive load. The line length is that it takes 400 s for an elect romagnetic wave to travel from = µ source end to load end and vice-versa. At 400 , t s the voltage at the load end is found to be 40 Volts.
84. The load resistance is
(A) 25 Ohms
(B) 50 Ohms
(C) 75 Ohms
(D) 100 Ohms
85. The steady-state current through the load resistance is:
(A) 1.2 Amps
(B) 0.3 Amps
(C) 0.6 Amps
(D) 0.4 Amps

Gate - Electronics and Communication - Analog - Sample Paper

Que. 1      A cascade amplifier stage is equalent to
A         a comman emittor stage followed by a common  base stage
B         a comman base stage followed by a common emittor stage
C         a common base stage followed by an emittor follower
D         an emittor follower stage followed by a common base stage

Que. 2     In order to make Q point independent and varitions B in a transistor amplifier,it
is   necessary to make

A         R (b)<<  B R(c)
B         (D)R < or =  B R(c)
C         (D)R(b) < or =  B R
D         R(b) < or =  B R(c)

Que. 3     Input resistance of a common base transistor ckt is of the order of

A         0The output resistance of a common base transistor ckt is of
the order of
B         50-100 ohm
C         100-150 ohm
D         150-200 ohm

Que. 4     The emitter coupled pair of BJTs gives a linear transfer relation between
the   differential output voltage and input voltage only when the magnitude
of V(id) is less   alpha times the thermal voltage, where alpha is

A         4
B         3
C         2
D         1

Que. 5     Maximum efficiency of half wave rectifier is

A         33.33%
B         40.6%
C         50%
D         68%

Que. 6     If the input ac is 10Vrms the maximum voltage that will appear across
the diode of a   half wave rectifier with a capacitor input filter will

be
A         10v
B         14v
C         20v
D         28v

Que. 7     The three stage cascaded amplifier of identical non-interacting FET common
source stage   has all over an voltage gain of 1000 and overall bandwidth
of 25*10^6rad/sec given   g(m) =5mA/v the shunt capacitance of each stage
is given by

A         20PF
B         10PF
C         3.2PF
D         1.6PF

Que. 8     When a +ve gate voltage is applied to MOSFET it is said to operate in

A         enhancement mode
B         depletion mode
C         conduction mode
D         none of these

Que. 9     the tunned ckt for good stability should have

A         low C
B         low r
C         high Q
D         low L

Que. 10     by varying which one of the following the RR feedback oscillator are usually
tunned

A         load impedance
B         bras
C         lore
D         none of these

Que. 11     An operational amplifier has a slow rate of 100V/micre sec. for a freq.
of 10mhz the maximum value of the sine wave output voltage will be

A         100v
B         50/(pi)^v
C         10v
D         5v

Que. 12     the number of flipflop required to build a mod-15 counters is

A         4
B         5
C         6
D         7

Que. 13     The maximum overall efficiency of a transformer coupled class A amplifier
is

A         78.5%
B         25%
C         50%
D         85%

Que. 14     In an FET as V(GS) is changed from zero to increasing reverse biased the
value of g(m)

A         increases
B         decreases
C         remain constant
D         falls suddenly to zero

Que. 15     given for an FET g(m)  =95mA/v total capacitance =500pf for a voltage
gain of -30 the bandwidth will be

A         100khz
B         630khz
C         3mhz
D         19mhz

Que. 16     for the resonent ckt shows w =10^5,Q=50,R=400 thevalue of C is given by

A         250PF
B         1000PF
C         500PF
D         1.25PF

Que. 17     In a class A amplifierusing a transistor under ideal condition the maximum
ac power   delivered is 1 watt the maximum transistor dissipation capability
has to be

A         1watt
B         2watt
C         3watt
D         4watt

Que. 18     two binary signals A and B are compared the output expression when the
two signals are   equal is given by

A         ab' +a'b
B         ab + (ab)'
C         (ab)'
D         ab

Que. 19     the most widely used universal gate are

A         OR and AND gates
B         NOR and NAND gates
C         NOR and AND gates
D         NAND and OR gates

Que. 20     the microprocessor contains ROM  chip contains?

A         control function
B         airthmatic function
C         instructions to execute data
D         memory function

Que. 21     Carry-look ahead is type ofadder in which

A         inputs to several stages are examined
B         carries are produced simultaneously
C         carries are produced before hand
D         none of these

Que. 22     Logic shift affects

A         odd positions
B         all positions
C         even positions
D         new positions

Que. 23     Programmable logic array uses

A         ROM matrices
B         PROM matrices
C         RAM matrices
D         solo memory

Que. 24     Race condition can be avoided by introducing......... between the flipflop

A         harmonic suppressor
B         deacceleration
C         delay
D         dusting

Que. 25     An amplifier has an open loop gain of 100, an input impadence of 1kohm,and
an output       impedance of 100ohm.a feedback network with a feedback
fector of 0.99 is connected to       the amplifier in a voltage series
fedback mode the new input and output impedance respectively are

A         10 ohm and 1 ohm
B         10 ohm and 10 kohm
C         100 ohm and 1 ohm
D         100 kohm and 1 kohm

Que. 26     In a twin wire transmisssion line in the air the adjacent voltage maximum
are at 12.5cm   and 27.5cm the operating freq. is

A         300mhz
B         1Ghz
C         2Ghz
D         6.28Ghz

Que. 27     The band width of an N stage tunedamplifire with each stage having a
 band width of   B, is given by

A         B/n
B         B/(sqrt)n
C         B[(sqrt)2^[1/n]-1
D         B/[(sqrt)(/2^[1/n]-1]

Que. 28     the resolution of a 12-bit D/A convertor using a binary ladder with 10v
as the full   scale output will be

A         2.44mA
B         3.50mA
C         4.32mA
D         5.12mA

Que. 29     the number of comparetor ckt requires to build a 3-bit simultaneous A/D
convrtor is

A         7
B         8
C         15
D         16

Que. 30     A magnetic drum of 8 inches diameter has 100 tracks and storage density
of 200bits/inches    its storage capacity will be

A         502400 bits
B         8402 bits
C         1004800 bits
D         202400 bits

Que. 31     the function of inhabit line in a memory in

A         to write 1 in a core
B         to read 1 in a core
C         to write 0 in a core
D         to stop writing 1 in a core

Que. 32     the storage time of transistor is the part of the

A         turn on time
B         turn off time
C         fall time
D         rise time

Que. 33     if the turn on time of a transistor is decreases its turn on time

A         decreases
B         increases
C         is not affected
D         infinite
Que. 34     for an input pulse train of clock period T,the delay produced by an n
stage shift   resister

A         (n-1)
B         2n
C         (n+1)T
D         2nT

Que. 35     If the memory chip size is 256*1 bits,then the member of chips required
to make   up 1k bytes of memory is

A         32
B         24
C         12
D         8

Que. 36     In sign magnitude numbers

A         the leading bit stands for the sign
B         the leading bit is part of the magnitude
C         the leading bit is always zero
D         the leading bit is always

Que. 37     what is dule of  X + X'Y =X + Y

A         X + Y = XY
B         X' + XY = XY
C         X(X' + Y) = XY
D         X'(X + Y) = X + Y

Que. 38     The "Pinch off" voltage of a JFET is 0.5 volts. Its "Cut Off" votage is

A         (0.5)^1/2 v
B         2.5 v
C         5.0 v
D         (5.0)^3/2 v

Que. 39     four independent message have bandwidth of 100hz, 200hz, and 400hz,respectively
each   is sampled at the Nyquist rate and the samples are time division
multiplexed and   transmitted sample rate is

A         1600
B         800
C         400
D         200

Que. 40     in the CMOS  inventor  1. Both are enchancement Type  2. One transistor
is N Channel and the other  3. Both are N Channel with one enchancement
and the other depletion type 4. one is enchancement and the other depletion
type Of the above 4 statment the only true one are

A         4
B         1 and 2
C         1 and 3
D         none of these