n/w sample paper for gate

7/29/2019 n/w sample paper for gate

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SAIMEDHA HYD, Blore, TPT, VJA S Academy Page 1

GATE-IES-PSUs

NETWORK AND SYSTEMS 2

1. The equivalent inductance of the network is(a) L1 +L2 2M

(b) L1 +L2 + 2M(c) L1 +L2 M

(d) L1 +L22. Twelve 1 resistors are used as edge to form a cube. The resistance

between two diagonally opposite corners of cube is

(a)5

6 (b)

6

5 (c) 1 (d) None of these

3. The equivalent resistance as seen between the terminals (a, b) is

(a) 2

(b) 4

(c) 1

(d) Not possible

4. Which of the following networks in the equivalent of the circuit shown in

figure?

5. An ideal voltage source and ideal current source are connected in parallel

this circuit has

(a) a Norton equivalent but not Thevenin equivalent.

(b) a Thevenin equivalent but not Norton equivalent.

(c) Both the Thevenin and Norton equivalent.

(d) Neither Thevenin and Norton equivalent.

6. The total power consumed in the circuit shown in figure is (in between BC)

(a) 6 W

(b) 8W(c) 9 W

(d) 12 W

7. The time constant of the network shown in the fig. is

(a) 4RC

(b) 3RC

(c) 2RC

(d)2RC

3

L1

M

L1

a

2 2 2

1 1 1

b

I

J1

J1

2

J1

3

(a)

I

J1J1

2J1

3

(b)

I

J12

J1

3

J1(c)

I

J12

J1

3

J1 (d)

1J1

2 J1

3J1

4R

20 V 4R 2C

2

4 V+2 2A

B

C


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8. Impedance Z as shown in figure

(a) J 29 (b) J 9

(c) J 19 (d) J 39

9. When a unit impulse voltage is applied to an inductor of 4H, the energy

supplied by the source is

(a) (b) 5 J

(c)1

J8

(d)1

J2

10. Given two coupled inductors L1 and L2, their mutual Inductance

M satisfies

(a) 2 21 2M L L= + (b)1 2L LM

2

+>

(c) 1 2M L L> (d) 1 2M L L

11. The current I as marked in the figure is(a) 3A (b) 2A

(c) 1A (d) 0A

12. The Thevenin equivalent across AA is given by

(a) th th15

V 5V,R2

= =

(b) th th15

V 15V,R4

= =

(c) th th15

V 25V,R4

= =

(d) None of these

13. For the given graph the incidence matrix A is given by

1 1 0

(a) 0 1 1

1 0 1

1 0 1

(b) 1 1 0

0 1 1

1 1 0

(c) 0 1 1

1 0 1

(d) None of these

14. Consider the network graph shown in figure. Which one of the following is

not a tree of this graph? (GATE 2004)

15. For the graph shown below. Find the minimum number of branches that

may be added to make the resulting structure non planar

(a) 2 (b) 3

(c) 4 (d) None of these

J 2

J 10J 10

J 2J 5

V(t)=(t) 4 H

4 1 2

6A 1 3 3V

10 A

20 amp 5 5

A

(a) (b) (c) (d)

1 1

36

5 4

B

A C1

2 3


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16. The V-I relation for network is V = 52I, when R = 3 is connected as

shown the value of I is given by

(a) 5 (b)5

3

(c) 1 (d) 1

17. The natural frequency Sn of the given circuit is

(a) 1(b) 1

(c)1

2

(d) 2

18. Initial voltage on capacitor V0 as marked |V0|=5V. Vs = 8 u(t), where u(t)

is the unit step. The voltage marked V at t = 0+ is given by

(a) 1V

(b) 1V

(c)13

V3

(d)13

V3

19. Figure shows the waveform of the current passing through an inductor of

resistance 1 and inductance 2H. the energy absorbed by the inductor in

the first four seconds is(a) 144 J

(b) 98 J

(c) 132 J

(d) 168 J

20. A connected network of N>2 nodes has at most one branch directlyconnecting any pair of nodes. The graph of the network(a) must have at least N branches for one or more closed paths to exist.

(b) can have an unlimited number of branches.

(c) can only have at most N branches.

(d) can have minimum number of branches not decided by N.

21. In the figure below, the voltage across the 18 ohm resistor is 90 volts.

What is the total voltage across the combined circuit at terminal E and F

(a) 125 V

(b) 16 V

(c) 24 V

(d) 40 V

22. For the circuit shown below in the figure, the voltage V0 is

(a) 2 V (b) 1 V

(c) 1 V (d) None of these

R = 3+VN

I

2s 4s

6 A

18 90V

365

1E

F

2H 3

Vs 4 IS 1+

Vs 1V0

++

++

1

1 V

2 2

4V 2 V0 2V

+

+

+


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23. The impulse response of an R-L circuit is a

(a) rising exponential function (b) decaying exponential function

(c) step function (d) parabolic function

24. S is in position (a) for a long time. S moved to position (b) at t=0, At t = 0+,

the values of Ic andVL are

(a) 5, 0(b) 5, 0(c) 0.4(d) 2, 3

25. Given V2= 2 cos 2t = 2


5/14


31. Maximum power form a source having internal resistance Ri is delivered

to a resistive load RL if

(a) Ri = RL (b) Ri > RL (c) Ri < RL (d)

32. In the figure the transformer is ideal with adjustable turns ratio 2

1

N.

NThe

turns ratio 21

NN

for maximum power transfer to the load is

(a) 1 :1 (b) 100 :1

(c) 1 :100 (d) 1000 :1

33. Calculate the rms value of the given wave

(a) 2 6 A (b) 6 2 A

(c)4

A3

(d) 1.5A

34. For the figure given below which of these sets of E, R and C value will

ensure that the state equation is cdVc

1.25V 2dt

= + valied

(a) 2V, 1, 1.25F (b) 1.6 V, 0.8, 1F

(c) 1.6 V, 1, 0.8F (d) 2 V, 1.25, 1F

35. The Thevenin equivalent voltage Vm appearing between the terminals A

and B of the network shown is given by

(a) J16 (3J4) (b) J16 (J3+4)

(c) J6 (3+J4) (d) J6 (3J4)

36. The current I in the circuit will given by

(a) 5 amp (b) 1.2 amp

(c) 2.4 amp (d) 0.6 amp

37. The voltage of the source i.e. Vs, if i(t)= 20e2t

(a) 10e2t (b)10e2t

(c) 20e2t (b)20 e2t

38. Find the Thevenin voltage and resistance for the given circuit shown

below(a) th thR 58.82 ,V 117.64 V= =(b) th thR 117.64 ,V 58.82V= =(c) th thR 58.82V ,V 58.82V= =(d) th thR 117.64 ,V 117.64 V= =39. What will be the power dissipated in R in fig.

(a) 2.5 x 103 joule (b) 25 x 103 joule(c) .25 x 103 joule (b) None of these

(1 + J1)

100+J100 +

V

R+

VcC

1

2

I

10V 0. 2A 2I+

6 amp

6 ampT t

V2100

100IxxV

100

3K

A

+

B

Vx

Ix

1 m+

C = 20 F~100 sin 2 t

100


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40. Find the current at time t= 2 sec

(a) 2 amp. (b) 2 amp

(c) 1 amp (d) None of these

41. In above fig. current i at time t= 4 sec will be

(a) 5amp (b) 3amp

(c) 3 amp (d) 5amp

42. The Laplace transform of the function f(t) =2t 4tf(t) e = will be

(a)4s

2

1 e

2ss

+ (b)

24s

3

e

s

(c)4s

3

e

s

(d) does not exist

43. What will be the value of i(t) for t>0, the circuit fig.

(a)

t

.01[1 ( 2.5)]e .25

(b)t

.01[1 ( 2.5)]e .25

+

(c) does not exist (d) 5 u(t1)

44. What will be the value of Ldi

dtin fig.

(a) A/sec (b) 1 A/sec (c) 2 A/sec (d) 2 A/sec

45. The Y11-parameters for the given network shown below are

(a) 111 1 3

Y 6s2 5 5s

= + + +

(b) 111 1 1

Y 6s3 5 5s

= + + +

(c) 111 1 1

Y 6s3 5s 5

= + + + (d) 111

Y 6s5

= +

46. For the networks shown in the figures (a) and (b) to be duals, it is

necessary that R, L and C are respectively equal to

(a) 1 ,C andLR

(b) 1 1 1, andR L C

(c)1

R, ,and CL

(d)1 1

,L andR C

47. What will be the value of Rm between A and B for the given circuit shown

below

(a) 2R (b)R

(1 J)2

(c)R

(J 1)

2

(d) R

48. Given iL (0+)= 0, Vc(0)= 0 in the steady

state Vc equals to

(a) 200 V (b) 100 V

(c) 0V (d) 100 V

j R C L

Fig. (b)

R L C

V~+

Fig. (a)

JR

BR

R

JR

A

~+

V ZL

D L IL

100 V C

+

i3 A 5 10 2u(1t)t= 0

+

10

10

0.2H2u(t)

+

13

H12 V+

2+

6 V

i1 2H

1 s 4 2

L=3Ht

12 sin6

R=0.1

+ I1 I2

5H

2

j4

+5 1

F6

25

H2

V1 V2


7/14


49. A series R.L circuit is initially released. A step voltage is applied to the

circuit. If is the time constant of the circuit, the voltage across R and L

will be same at time t equal to

(a) elog 2 (b) e1

log2

(c) e1

log 2

(d) e1 1

log2

50. The rms voltage measured across on admittance (G+jB) is V. the reactive

power for the element is

(a) 2V B (b) 2V B (c) 2 2 2V G B+ (d) 2V (G jB)+

51. In a balanced Wheatstone bridge, if the positions of detector and sourceare interchanged, the bridge will still remain balanced. This inference canbe drawn from(a) reciprocity theorem (b) duality principle(c) compensation theorem (d) equivalence theorem

52. Which one of the following impedance values of load will cause maximumpower to be transferred to the load for the network shown in the givenfigure?

(a) (2+j2) (b) (2j2)(c) j2 (b) 2

53. Determine the Z-parameters of the T-network(a) 5, 8, 12, 0 (b) 13, 8, 8, 20(c) 8, 20, 13, 12 (d) 5, 8, 8,12

54. For a transfer function of a physical two-port network(a) all the zeros must lie only in the left half of S-plane(b) the poles may lie anywhere in the S-plane.(c) the poles lying on the imaginary axis must be simple.

(d) All of the above.55. In figure shown A1,A2,A3, are ideal ammeters. If A1 and A3, read 5 A and13A respectively reading of A2 will be(a) 8 A(b) 12 A(c) 18 A(d) Indeterminate unless the actual values of R, C and w are specified.

56. An iron core coil with 25 turns has an inductance of 0.625 mH. In order toobtain an inductance of 0.1 mH, the number of turns will have to bechanged to(a) 4 (b) 10 (c) 62.5 (d) 157

57. Two, two-port networks are connected in cascade. The combination is to be

represented as a single two-port network.teh parameters of the networkare obtained by multiplying the individual(a) Z-parameter matrix (b) h-parameter matrix(c) y- parameter matrix (d) ABCD parameter matrix.

58. In the circuit Vs = 10 cos t. Power drawn by the 2 ohm resistor 4 W. thepower factor is(a) 0.3 (b) 0.4(c) 0.6 (d) 0.8

2 J2 J2

~Vs+

J2 ZL

5 12

8

A1 A2

A3

1 L

Vs

s

+

2


8/14


59. For a current of 5A; what is the voltage across AB?(a) 40 V(b) 60 V(c) 60 V(d) 40 V

60. The inverse Laplace transform of 2 25(s 3)

(s 3) 5

+

+ +

(a) 5e3t (b) 3t5e cos5t (c)2 2

5

(s 3) 5+ +(d) 5e5t

61. The function of the given figure

(a)T 4 T 2 T

r(t) r t r t2 T 2 T 2

+

(b) ( )2 4 T 2

r(t) r t r t TT T 2 T

+

(c)

( )

T T T Tr(t) r t r t T

2 4 2 2

+

(d) None of the above

62. The equation of the waveform in terms of unit step function scan be

written as

(a) u(t1) + u(t2)u(t3)+u(t4)4u(t5)

(b) u(t+1) + 4(t+2)+4(t+3)+4(t+4)4(t5)

(c) u (t1) u(t2)44(t5)

(d) None of the above.

63. The unit step of the ramp is

(a) u(t4)+u(t3)

(b) 2[u(t3)u(t4)]

(c) 2(t4){u(t3)u(t4)} (d) 2{u(t3)u(t4)}

64. The Z-parameter representation of the 2-port network shown in the figure is

Z(s) 0(a)

0 Z(s)

0 Z(s)

(b)Z(s) 0

0 0(c)

0 0

(d)

65. A 2-port Network ha Z-parameters11 12

21 22

Z Z.

Z Z

If the network is

augmented by adding an impedance R at the input port as shown, the

Z-parameters of the augmented network will be

11 12

21 22

Z R Z R(a)

Z R Z R

+ + + +

11 12

21 22

Z R Z R(b)

Z Z R

+ + +

11 12

21 22

Z R Z(c)

Z Z

+

11 12

11 22

Z Z R(d)

Z R Z

+ +

B

+

+A

V1= 10 I

10 V

1

T/2 T t

V

2

01 2 3 4 t

R 11 12

21 22

Z Z

Z Z 2

V t

1 2 3 4 5 t

II

II

I1 I2*

z(s)+ +

V1 V2


9/14


66. The ABCD parameters of the 2-powrt network, shown in the figure are

0 Z(a)

1 2

2 Z

(b) 11

z

11

(c) zz 2

2 0

(d) 1 1

z z

67. The 2-port network of fig. (1) has Y-parameter11 12

21 22

Y Y.

Y Y

The network is

excited as shown in fig. (2). If Ix = 1y, the current 1 drawn from the source

would be

(a) V(Y11 + Y12 + Y21+ Y22)

(b) V(Y11 + Y22)

(c) V(Y11)

(d) V(Y11 + Y22 + Y12 Y21)

68. D.C component of the waveform shown below is

(a) 0.5 V (b) 1.5 V

(c) 2.5V (d) 3.5V

69. D.C. component of the waveform shown below is

(a) 1.372 A (b) 6.36 A(c) 0.318 A (d) 0.159 A

70. Calculate the value of current i

(a) 5 A (b) 2 A

(c) 3 A (d) 8 A

71. Calculate the value of VR for the circuit given below

(a) 3 V (b) 19 V

(c) 9V (d) 19 V

72. Consider the circuit shown below

The voltage V1 and V2 are related as(a) V1= 6ia 8 + V2 (b) V1= 6ia + 8 + V2(c) V1= 6ia + 8 + V2 (d) V1= 6i 8 + V2.

42

0 2 4 6 8 t

f t

F E

D

i

CA

B2A 8A

4A6A

1A

1 k5V

+Vx

3 k

8 k

4 k6VD

8V

B

CE

A

V1 6 8V V2

616 V ia

e V

10

0 2 3 rad

z I2+ +

V1 Z V2

I1

2-port

Networ 21

Fig.(1)Fig.(2)

2-port

Networ1V

I+

Iy

Ix


10/14


73. Let i(t) = 3 te100t A and V(t) = 0.6(0.01t) e100t V for the network of fig.

shown below. The power being absorbed by the network element at t =5

ms is

(a) 18.4 W (b) 9.2 W

(c) 16.6 W (b) 8.3 W

74. The dependent source in fig. shown below(a) delivers 80 W (b) delivers 40 W

(c) absorbs 40 W (d) absorbs 80 W

75. The incidence matrix of a graph is as given below

1 0 0 0 1 0 0 1

0 1 0 0 1 1 0 0A

0 0 1 0 0 1 1 1

0 0 0 1 0 0 1 0

=

The number of possible tree are

(a) 40 (b) 70

(c) 50 (d) 24076. The f-cut set matrix of a graph shown below with respect to chosen tree is

as given below

F

1 1 0 1 0 0

Q 1 0 1 0 1 0

0 0 0 1 1 0

=

The oriented graph of the network is

77. For the 2-port as given below [ ]a2 0

Y mS0 10

=

The value 0

s

V

Vis

(a)3

3.2(b)

1

16

(c)2

33(d)

1

17

78. For the circuit shown below

(a) Power absorbed by the dependent source is 80W(b) Power delivered by the dependent source is 80W

(c) Power absorbed by the independent source is 80W

(d) Power delivered by the independent source is 80W

79. For the circuit given below, the power absorbed by the load RL is

(a) 4W (b) 8W

(c) 2W (d) None of these

i

N+V

1

4 6 5

1 3

(a) (b) (c) (d)

[ ]aY '60 A B

300+

V0

Vs + 100

A B

I

2V 1 2I RL=2

+

5V1= 20 V

5

A

1V

5

5

+

5V1 = 20V


11/14


80. For the circuit shown below. Power is delivered by

(a) Dependent source of 192W

(b) Dependent source of 368W

(c) Independent source of 192W

(d)Independent source of 436W

81. Calculate the Y parameter for the given network

(a)2.5 3.5

1.5 4.5

(b)2.5 3.5

0.5 3.5

(c)1.5 3.0

1.0 4.5

(d) None of these

82. For the circuit arrangement shown below. Calculate the value of R under

maximum power transfer condition

(a) 9 (b) 25(c) 0 (d) None of these

83. The given symbol represents

(a) Practical battery

(b) Ideal battery(c) Both (a) and (b)

(d) None of these

84. The number of edges in a compete graph of n vertices is

(a) n(n1) (b)n(n 1)

2

(c) n (d) n1

85. In the circuit shown below, the switch is closed at t= 0. The current

through the capacitor will decrease exponentially with a time constant

(a) 0.5s (b) 1 s (c) 2 s (d) 10 s

86. The 2-port network shown in the circuit given below is connected in

parallel with another 2-port network which has y11 = y12 = y21 = y22 Y

The y-parameters of the composite network will satisfy which one of thefollowing?

(a) y11= Y +g (b) y12= Y +g

(c) y21= Y +g (d) y22= Y +g

500 A 200

+

40V 2Ix 400+

16

10V RL=25

R

Vs +

10V 1 1F

1t = 0

2 4

1 3y =

2

V2V1

gV1


12/14


87. Consider the following circuit:

If V1 = 5V and V2 = 3 V, then what is the input

impedance of the CRO in the above circuit(a) 1 M (b) 1.5 M

(c) 3 M (d) 5 M


What is power delivered t resistor R in the above circuit?

(a) 15W

(b) 0 W

(c) 15 W

(d) Cannot be determined unless the value of R is known


What is the current in the above circuit?

(a) 0A (b) 2.05 A (c) 0.37 A (d) 1.5A


For the above circuit, which one of the following statements is correct? The

voltage V0 is independent of R, if the input signal frequency

(a)1

isLC

(b)1

is2 LC

(c) is LC (d) has any value

91. For the circuit shown below, the Thevenins resistance across the terminal

A & B is

(a) 0.5 k (b) 0.2 k (c) 1 k (d) 0.11 k

30 60

R60 120

30V

RL V0~V1

R

C L

+

2k

5V+3VAB2k 1k

V1 V2

~

1M

CRO

10 10 6

60V 20 20 15A 41


13/14


92. Consider the following statements:

Superposition theorem is applicable to a linear network in determining

1. The current responses

2. The voltage responses

3. The power responses

Which of the statements given above are correct?

(a) 1 and 2 (b) 1,2 and 3 (c) 1 and 3 (d) 2 and 393. For the circuit given above, what is the expression for the voltage V?

(a) Vi + Vc (b) Vc

(c) c cdV

RC V 0dt

= (d) c cdV

RC V 0dt

+ =

94. Which one of the following statements is not

correct?

(a) A tree contains all the vertices of its graph

(b) A circuit contains all the vertices of its graph

(c) The number of f-circuits is the same as the number of chords

(d) There are at least two edges in a circuit

95. In a series RLC circuit, the locus of the tip of the admittance phasor in thecomplex plane as the frequency is varied, is

(a) A semicircle in the upper half of the G-B plane having the centre at

1,0

R

and radius1

R

(b) A circle in the upper half of the G-B plane having the centre at

1,0

(2R)

and radius1

(2R)

(c) A semicircle in the bottom half of the G-B plane having the centre

at

1

,0(2R)

and radius

1

(2R)

(d) A semicircle in the upper half of the G-B plane having the centre at

1,0

R

and radius

1

R

96.

A step voltage is applied to the circuit shown above. What is the transientcurrent response of the circuit?(a) Undamped sinusoidal (b) Overdamped(c) Underdamped (d) Critically damped97. Kirchoffs laws fail in case of(a) Non-linear networks (b) Linear networks(c) Dual networks (d) Distributed parameter networks

98. The Nodal method of circuit analysis if based on(a) KVL and Ohms law (b) KCL and Ohms law(c) KCL and KVL (d) KCL, KVL and Ohm/s law

R R

+

Vi C VVc C

+

R L C

2 1H 1F


14/14


99. Substitution theorem applies to(a) linear networks(b) non-linear networks(c) linear time-invariant networks(d) any network.

100. The voltage of the source i.e. Vs, if i(t)= 20e2t

(a) 10e2t (b)10e2t

(c) 20e2t (b)20 e2t

Any doubts Please send it to this mail

[email protected]

+

1

II t

Vs

1H

4

I2F

n/w sample paper for gate

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