Types of questions asked from each sectiond1zttcfb64t0un.cloudfront.net/Images/EE analysis...Signals and Systems Questions from Fourier and Z Transform Control Systems Questions from

Gate-14 Analysis , Questions & Solutions

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1

GATE 2014 – A Brief Analysis

(Based on student test experiences in the stream of EE on 1st

March, 2014 - Second Session)

Section wise analysis of the paper

Types of questions asked from each section

Engineering Mathematics There were questions from Algebra, Vector Calculus, Differential Equations, Probability

Networks Questions from basics concept Analog Circuits Questions from Amplifiers and Oscillator Digital Circuits Questions from Microprocessor Signals and Systems Questions from Fourier and Z Transform Control Systems Questions from Bode Plots, RH Criteria, Transfer Functions

Electrical Machines Questions from Single Phase Transformer, DC Machines

Power Systems Questions from Faulty Analysis, Economic Operation

Measurements Questions from Measuring Instruments Power Electronics Questions from Choppers, Rectifiers Field Theory Questions from Electric Field and Potential

1 Mark 2 Marks Total No of Questions Engineering Mathematics 2 3 5 Networks 2 2 4 Analog Circuits 1 2 3 Digital Circuits 1 2 3 Signals and Systems 6 4 10 Control Systems 2 3 5 Electrical Machines 3 3 6 Power Systems 2 6 8 Measurements 2 2 4 Power Electronics 2 2 4 Field Theory 2 1 3 Verbal Ability 2 2 4 Numerical Ability 3 3 6

30 35 65



2

Questions & Solutions 1st March ( Second Session )

1. In the given circuit if IR 25 .2

Then I = __________.

Sol. Given IR 252

V IR

I300 I 252

2I300 25I2

2I 50I 600 0. I 10A and 60A 10A is correct based on given direction. 2. A 3 , 50 Hz, 6 pole motor has rotor resistance of 0.1 , reactance 0.92 . The slip at

full load is 3%. Assume stator resistance & reactance are negligible. Find the ratio of maximum torque to full load torque.

Sol.

eff

mt flemax86

fl mt

2mt

2

ft

emax

efl

T 2 2 0.5129S 0.1086 0.03ST0.03 0.10S S

r 0.1S 0.1086x 0.92

S 3% 0.03T

1.9495.T

3. The incremental fuel costs of two generating plants are

1

21 1C 0.05Pg APg B

22 2 2C 0.10 Pg 3APg 2B

Where A, B are constants. 1 2Pg and Pg are power generated in plant 1 and 2. The two

plants optimally share 1000 MW at an incremental cost of 100Rs/MWh. The ratio of P1 : P2 is __________.

300 V

I

R



3

Sol. 21 1 1

22 2 2

C 0.05 Pg APg B

C 0.10 Pg 3APg 2B

1 2

1 2

1 2

11

1

1

22

2

2

2 1

2 1 1

21 2

1

2

Pg Pg 1000dC dC 100dPg dPdC 2 0.05 Pg A 100dPg0.1 Pg A 100 ___ 1dC 2 0.1 Pg 3A 100dP0.2 Pg 3A 100 ____ 2

subtracting 2 1 ,0.2 Pg 0.1 Pg 02Pg Pg Pg 800 MW

Pg 200 MWPg Pg 1000Pg 4 .Pg 1

4. In the following circuit the voltmeter reads __________V. Sol. From the given circuit, inside it is forming bridge circuit and it is balanced. So, the

voltmeter read zero. 5. If f(t) is continuous time signal, f( ) is Fourier transform defined by

j tf f t e dt

jutg t F u e du

The relation between f(t) and g(t) is given by

0.5

100 sin t

1j

1j 1j

1j

V



4

Sol. Consider,

jutg(t) F(u)e du

‘u’ is a dummy variable, replace it with ‘ ’

j t

j t

g(t) 1 F( )e d2 2

g( t) 1 F( )e d f (t)2 2

2 f (t) g( t)

6. A coin is tossed n times. The probability that difference between head and tail is (n-3) is

(A) n 3cn

(B) n2 (C) n 3

ncn 2

(D) 0.

Sol. 1 1p ,q 1 p2 2

Let random variable X = difference between heads and tails = 0, 1, 2, …, n

X ~ B u,p

n 3 n 3

n 3 3n

c c1 1P X n 3 n n .22 2

7. A rectifier circuit is shown below. The diode and thyristor are ideal. The load contains

R 10 and L 0.05H. The firing angle ' ' in degree to obtain a load voltage of 70 V is _________.

Sol.

mo

o

VV 1 cos2325 1 cos2

70 51.73 1 cos

o69.31

325sin314t Load~



5

8. The line integral of function F=yzi in anticlockwise direction along the circle 2 2x y 1 at z=1 is _________.

Sol. 2

C C 0

.F dr yzdx sin sin d

2 2C is circle x y 1. put x cos , y sin dx sin d , dy cos d

and lies between 0 to 2

2 cos2 1 d

2

2

0

1 sin 22 2

9. If 3

1X(z)1 z

be Z transform of causal signal x(n), then values of x(2), x(3) are

__________. Sol. Using long-division method,

3 6 9X(z) 1 z z z

x[2] 0; x[3] 1.

10. The matrix A is given as 0 1 1

A 6 11 66 11 5

The ratio of maximum eigen value to minimum eigen value is __________.

3 3 61 Z 1 z z

3

11 z

3

3 6

zz z

6

6 9

zz z

9z



6

Sol.

3 2

max

min

A I 0

0 1 1 0 06 11 6 0 0 06 11 5 0 0

1 16 11 6 06 11 5

6 11 6 01, 2, 3

1 0.3333

11. Consider the K map shown below. Its realization is given by____________. Sol. f C'A ' CB C B ex nor gate e 12. Consider the circuit shown

The transfer function of o

i

v ( )v ( )

gives bode plot as __________.

iV

1k

1 F

ccV

ccV

oV

fR

00 01 11 10

0 1 1

1 1 1C

AB

ABC

0

1

1 1

1 1

0100 11 10



7

Sol. The given circuit is LPF (Low Pass Filter)

03 6 3

in

V 1 1 1 1000V 1 SCR 1000 j1 j 10 10 1 j 10

1S1

1000

Corner frequency is at =1000 Low frequency gain=1{ =0} 13. The output 0V is ______________.

1V

2V

R

R R

R

R

R

2R0V

0V

Rf

1K

inV

1 F

act as Buffer

0

in

V dBV

Actual Curve

Slope 20 dB decade

low frequency asymptote curve

o

3

1000



8

Sol.

o 1 2

o 1 2

2R RV 1 V V2R R

V 2 V V

14. Consider the circuit shown below. Given VC(0)=-2V . The value of current in the circuit

at t=0 is __________. Sol. Under steady state: When switch is opened: Laplace model

S

3 3 3

2 6 2

34

S S2

I 1 IV 100 2 SS Sc S

20 10 20 10 2 20 10 2 2100S 10 S S S S S

20 10V S V t 2 10 t.S

CV

t 0

t 0

cV

1 F

100

CV 2V

SV 0V

100SV

20 mA3

I

1 F 2 S

100SV20 mA

3



9

15. A 8 pole, 3 , 50Hz inductor motor runs at a speed of 700 rpm. The frequency of rotor current of motor is _______________.

Sol. S

S r

S

rotot

120f 120 50N 750 rpmP 8

N N 750 700 1SN 750 15

1F Sf 50 3.33 Hz.15

16. If xf x xe , the maximum value of function in interval 0, is (A) 1e (B) e (C) 11 e (D) 11 e Sol. x 1 xf x xe f x 1 x e 0 x 1

11 xf x x 2 e

11at x 1, f x 0

1The max imum value of the function is e 17. Power consumed by a balanced 3 3 wattmeter load is measured by two wattmeter

method. The reading of wattmeter one is twice that of second. The load angle in radians is given by _________.

Sol. The load impedance angle is 30o (or) c

6 . Then one watt meter reads twice of another

wattmeter in two-wattmeter method. 18. A wien bridge oscillator is given below. From the circuit the relation between 3 4R & R ; is given by.

1C

1R CCV

CCV 3R

4R2R2C



10

Sol. 3 1 2

4 2 1

1 1 2 2

R R CR R C

1 .R C R C

19. In the figure shown power is transferred among all the three elements. The power

absorbed by three elements is given by _____. Sol.

By KCL current through 15V battery 2A. Based on the directing given, 100V battery is absorbing the power and it is 100 × 10 =

1000 watts.

20. The solution in differential equation 2

2

d x 9xdt

with initial condition x(0)=1 and

t 0

dx 1dt

is given by ________.

Sol. 2

2

d x 9x 0dt

2A.E : m 9 0 m 3i

1 2General solution is x c cos 3t c sin 3t … (1)

1 2dxand 3c sin 3t 3c cos 3tdt

… (2)

Using given conditions, we get 1 2, c1c 13

1Solution is x cos 3t sin 3t3

10 A 8 A

80 V100 V

15 V

10A 8A

80 V

2A100 V

15 V



11

21. Consider the circuit shown. The magnitude at mid band voltage gain is ______. 22. In RH criteria if all the elements in a row are zero’s it indicates. (A) Roots lies on origin (B) Roots lies on positive real axis (C) Roots lie on imaginary axis (D) Roots lie on negative real axis. Sol. Roots lies on imaginary axis

23. If the roots of 2ax bx c are real and positive & a,b,c are real. Then 2ax b x c has

(A) no roots (B) 2 roots (C) 3 roots (D) 4 roots.

24. If 21z 98,

z

then 22

1zz

________.

Sol. 2

22

1 1z 98 z 98 2 96z z

25. In the press meet regarding the scam the minister said “the buck stops here”. What does

the minister mean. (A) He will return the money. (B) He will take the responsibility. (C) Money does not matters. (D) Stop the allegations. 26. In a tetrahedron with four triangular faces if a line is drawn connecting the corners of

tetrahedron. The total number of planes will be _______. 27. In a survey, 300 people are asked whether they own a vehicle are not. And the result is

shown below.

inV

10 K

C

CCV

C

feh 100

10 K

1 K C



12

The percentage of people do not own a scooter is _________.

Men Women

Car 40 34

Scooter 30 20

Both 60 46

Don’t own a vehicle 20 50

29. What is the value of resistor that shorted be placed in place of current source so that the

same amount of RMS current can flow ______________

Sol. or oror

or

V VI RR I

s

or

V 230R R 23I 10

30. In the network shown if 1F fault occur between 1G and bus A the voltage and current at

bust A is 1 1F FV & I . Also if fault occur between A and B, corresponding voltage at bus B

is 2 2F FV & I

Then (A).

1 1 2 2F F F FV leads I and V leads I

(B). 1 1 2 2F F F FV leads I and V lags I

(C). 1 1 2 2F F F FV legs I and V lags I

(D).1 1 2 2F F F FV lags I and V leads I

Sol. Faults at F1: VF1 leads IF1 Faults at F2: VF2 leads IF2 Note: Fault always demands reactive power.

10A230V

50Hz

E oE 0

1G2G

A B1F 2F



13

Questions & Solutions 2nd March ( First Session )

1. The line A to neutral voltage y 10 15 for a balanced 3-p star-connected load with phase

sequence ABC. The voltage of line B with respect to line C is given by

(A) 10 3 105 (B) 10 105 (C) 10 3 75 (D) -10 3 90

Sol. Star connected balanced load,

LL BC

B c

BC

V VV V

10 135 10 255

V 10 3 105

2. A 183-bus Power system has 150 PQ buses and 32 PV buses. In the general case, to

obtain the load flow solution using Newton-Raphson method in polar coordinates, the minimal number of simultaneous equations to be solved is ________.

3. Two matrices, p q

Ar s

2 2

2 2

p q pr qsB

pr qs r s

. If rank of A is N, then rank of B is

(A) N/2 (B) N-1 (C) N (D) 2N Sol.

2 2

2 2

p q pr qsB

pr qs r s

2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2

2

(p q )(r s ) (pr qs)(pr qs)

p r p s q r q s p r pqrs pqrs q s

p s q r 2pqrs

ps qr

p qA ps qr

r s

Rank of ‘B’ dependents on the value of (ps-qr) given that rank of ‘A’ is ‘N’. rank of B is also ‘N’. 4. The no-load speed of a 230V, separately excited D.C. motor is 1400 rpm. The armature

resistance drop and brush drop are neglected. The field current is kept constant at rated value. The torque of the motor in N-m for an armature current of 8A is ________.

AV 1015

BV 10135

cV 10255

cV

BCV



14

Sol.

b a60 E IP 60 PT TW 2 N 2 140060 230 .8

T 12.55 Nm2 1400

5. A state diagram of a logic gate which exhibits a delay in the output is shown in figure, where X is the don’t care condition and Q is the output represents the state.

(A) XOR (B) OR (C) AND (D) NAND. 6. For a fully transposed transmission line. (A) positive, negative and zero sequence impedances are equal (B) positive and negative sequence impedances are equal (C) zero and positive sequence impedances are equal (D) negative and zero sequence impedances are equal 7. A Single input single output feedback system has G(s) forward and H(s) feedback transfer

functions. It is given that G s H s 1. Which of the following is true, about the stability.

(A) It is always stable (B) Stable if all zeros of G(s) H(s) is in left half of s plane (C) Stable if all poles of G(s) H(s) is in left half of s plane (D) It is not possible to find stability from given information Sol. B 8. Life time of an electric bulb is a random variable with density f(x) = kx2, where x is in

years. If the minimum and maximum life times of bulb are 1 and 2 years respectively then the value of K is ________.

Sol. since f(x) is a p.d.f

11 0

11 0

Q 0

0x 1, 10 1Q 1 0x 1, 10 1



15

2

1

2 2

1

22

1

f (x)dx 1

kx dx 1

xk 13

k 3(8 1) 1 k3 7

9. The two signals S1 and S2 are applied to y and x deflection plates of an oscilloscope.

Then the wave form appeared on the screen is

(A) (B) (C) (D) Sol. A

Y

1

X

1

Y

1

X

1

Y

X1

1

Y1

X

1

1

1

T t

1S1

1

2S

T t

y

x

D

B

A

y2 2 1x y

x

Vy x V V tan

VA 0 1 1 0

B 1 1 2 45C 0 0 0

D 1 1 2E



16

10. A hollow metallic sphere of radius r is kept at potential of 1volt. The total electric flux

coming out of the concentric spherical surface of reading R(>r) is (A) 04 r (B) 2

04 r (C) 04 R (D) 204 R

Sol.

end

0

0

Q only upto surface.QV

4 rV 1V given

Q 4 r.

11. In a 8085 A microprocessor, the operation performed by instruction LHLD 2100H is (A) H H(H) 21 ,(L) 00 (B) H H(H) M(2100 ), (L) M(2101 ) (C) H H(H) M(2101) , (L) M(2100 ) (D) H(H) 00H, (L) 21 Sol. (H) M (2101)H (l) M (2100H) 12. The Torque-Speed characteristics of a motor m(T ) and load (TL) for two cases are shown

in the figure. (a) & (b). The load torque is equal to motor torque at points P, Q, R & S (a) (b) The stable points are (A) P&R (B) P &S (C) Q &R (D) Q& S Sol. P & R 13. The 1 , induction motor is provided with capacitor, centrifugal switch in series with

auxiliary winding. The switch is expected to operated at a speed of 0.7 NS, but due to initial functions of the switch fails to operate. The Torque-Speed char of the represented by

Speed

Torque

LT

MT

R

S

Speed

P

Q

TL

Torque

1V

R

r



17

(A) (B) (C) (D) Sol. B 14. A function f(t) is shown. The Fourier transform F(w) of f(t) is (A) real & even functions of (B) real & odd functions of (C) imaginary & odd functions of (D) imaginary & even functions of Sol. Given f(F) is real and odd signal. For such a signal the Fourier transform is imaginary and

odd. Ans :c. 15. For the signal f (t) 3sin8 t 6sin12 t sin14 t, the minimum sampling frequency (in

Hz). Satisfying the Nyquists crition is _______. Sol. Maximum frequency m max 8 ,12 ,14

m m

s m

14 f 7 Hzf 2F 14 Hz.

16. In a synchronous machine, hunting is predominately damped by (A) mechanical losses in the rotor (B) iron losses in rotor (C) Copper losses stator (D) Copper losses in rotor.

f (t)12

T2

t

12

T2

Torque

Speeds0.7 N sN

1

Torque

Speeds0.7 N sN

s0.7 N sN

Speed

Torque

Speed

Torque

s0.7N sN



18

Sol. Given signal x (F) can be shown as,

2

t t tx t rect ; x 2t rect t and x rect2 2 4

we know,trect sa

2

sin2x 2t rect t sa

22

similarly4sin 2t tx rect 4 s a 2

2 4 2t 4x 2t x sin2

sin 2 .2

17. An op-amp circuit is shown in figure. The output of the circuit for input vi is ____ .

(A) 2i

1

RR

(B) 2

i1

R1R

(C) 2i

1

R1R

(D) SatV

Sol. output of first op amp is nd

satV & 2 op amp ckt is not inversely amplifier.

o sat sat

RV 1 V VR

Output can’t be more than Vsat.

i

1R 2R

satV

RsatV

RsatV

satV

0V

x t

1

t11



19

18. A non ideal voltage source has a source impedance zs with a resistive load, then at what instant the maximum power is transferred to load.

(A) Load resistance is equal to source resistance (B) Load resistance is equal to complex conjugate of zs

(C) Load resistance is equal to magnitude of zs

(D) Load resistance is equal to source reactance. Sol. C

19. A signal is represented by 1 t 1

x(t)0 t 1

The Fourier transform of the convoled signal

ty(t) x(2 t) * x2

is

(A) 2

4 sin sin 22

(B) 4 sin2

(C) 2

4 sin (2 )

(D) 22

4 sin

Sol.

F.T

2

2x t t. sin

1 1 2 2x 2t . .sin sin2 2 2 2 2

2t 2 2x 2 2 2 sin 2 sin 22 2

t 2 2 4x t x sin sin 2 sin 2 sin .2 2 2

, 20. The driving point impedance z(s) for the given network is

(A) 2

4 2

s 1s s 1

(B) 4 2

3

s 3s 1s 2s

(C) 3

4 2

s 1s s 1

(D) 4 2

2

s 2s 4s 2

Sol.

Z(s)

1H 1H

1F1F

1

1 10

S S

1 S1S



20

2

22

2 2

4 2 2 4 2

32

1 1 s 1ss 1s s sz s s s

1 1 s 1 1 s s 2ss s s

s 2s s 1 s 3s 1.s 2ss s 2

21. For the given signal flow graph h0=b0-b1a1 & h1=b1. Then ratio of

C s

G s ?U s

(A) 0 12

0 1

b s bs a s a

(B) 1 02

1 0

a s as b s b

(C) 1 02

1 0

b s bs a s a

(D) 0 12

0 1

a s as b s b

Sol.

C sG s ; By signal flow graph.

G s

1 1 2 2P P ...T

F d.

1

1hpS

02 2

hpS

1

1a1S

2 1

012

aa1S S

01 12

012

hh a1S S ST

F aa15 S

1 1 02

1 0

h s a hs a s a

12 1 0 1 1 1 02 2

1 0 1 0

b s a b a b b s bTF s a s a s a s a

1h

U s

0h1

1a

0a

1

1s

11s

C s



21

22. A particle, starting from origin at t 0s, is travelling along x-axis with velocity

mV cos t .s2 2

At t=3s, the difference between the distance covered by the

particle and the magnitude of displacement from the origin is ______ Sol.

t 3

Time 3 sec3velocity cos t cos 2

2 2 2 2

t t

0 0

distance velocity time 3 2dxvelocitydt

displacement x volt cos t dt2 2

sin t2 sin t

2 22

3at t 3, displacement sin 12

3dis tan ce displacement 1 5.712.2

23. In a long transmission line, with r, ℓ, g & c are resistance, inductance, shunt conductance

& capacitance per unit length respectively. The condition for distortion less transmission is

(A) rc g l (B) r c l (C) rg c l (D) cg l

Sol. A 24. An LPF wattmeter, of p.f 0.2 is having three voltage settings, 300V, 150V & 75V and

two current settings 5A & 10A. The full scale reading is 150. If the watt meter is used with 150 voltage setting & 10A setting, the multiplying factor of the wattmeter is _________.

25. Let 2 2 2. fv x y y z z x, where f & v are scalar and vector fields respectively. If

v yi zj xk, then v. f is _________ . (A) 2 2 2x y y z z x (B) 2xy 2yz 2zx (C) x y z (D) 0 Sol. Given

2 2 2

2 2 2

.(fv) x y b z z xf .v v. f x y b z z x.



22

2 2 2

2 2 2

2 2 2

f i j k . y i 2 j xk V. f x y y z z xx y z

f (0) V. f x y y z z xV. f x y y z z x

26. A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20ms.

The resulting sample train is next applied to an ideal LPF with a cut off at 25Hz the filter output is seen to be a sinusoid frequency 20Hz. This means that x(t) has a frequency of

(A) 10Hz (B) 60Hz (C) 30Hz (D) 90Hz Sol.

3

s0

1 1Sampling frequency 50 Hzsampling period 20 10

f 50for a frequency f 25 Hz the sampling is Nyquest sampling.2 2

Q The filtered out sinusoidal signal has 20 Hz frequency, the sampling must be under sampling.

If the input signal i 0x t cos t is having its spectrum a follows: The output signal x[n] which is an under-sampled signal with sampled frequency 50 Hz is

as follows: The obtained output signal frequency = 20 Hz

0 050 f 20 f 30 Hz.

ix f

0f 0f f

0X f

050 f 50 0f 050 f 0f 50 050 f050 f

0f



23

27. The magnitude Bode plot of a network is shown in figure. The maximum phase angle m and the corresponding gain mG respectively are

(A) 30 & 1.73dB (B) 30 & 4.77dB

(C) 30 & 4.77dB

(D) 30 & 1.73dB

Sol.

1s1 3s 3G s K. 3k1 s s 1

Here K = 1

1 1T 3

1 1T

m

13

13

1B

4G s 343

mG 20 log 3 4.77 dB

28. A diode circuit feeds an ideal inductor as shown in figure. Given sV 100sin t V,

where r100 , L 31.83mHsec . The initial value of inductor current is zero. Switch

S is closed at t 2.5msec. The peak value of Li in A in the first cycle is ______. Sol.

sV 100.sin t 100 rad sec

m

L

Vi t 1 cos t

i t is max at t

20dB/dC G j

13

10log1

6

s

sV L

t 2.5ms

Li



24

m

max 3

2V 2 100IL 100 31.83 10

maxI 20A

29. Integration of the complex function 2

2

zf zz 1

in counter clockwise direction, around

z 1 1, is (A) i (B) 0 (C) i (D) 2 Sol.

2

2

zf (z) ; z 1 1z 1

For singularities, 2z 1 0

z 1 z 1 lies inside & z 1 lies outside of z 1 1

2 2

2

z zdz dzz 1 (z 1)(z 1)

2

2

zz 1

dz(z 1)

2 if (1) By cauchi 's int egral formula

12 i1 1

i

Q

Option ‘c’ is correct

30. A periodic signal is across the load. 1 sin t 0 t 6V t

1 sin t 6 t 12

. If M.I voltmeter

is connected across the load then the reading is

(A) 32 (B) 2

3 (C) 23 (D) 3

2

Sol. M.I instruments reads rms value

2

2 112

1 312 2

31. If the bridge shown iss balanced then the capacitance C1in F is ___________.

0.1 F

1C

105k

35k

Vsin t G



25

Sol. Bridge is balanced,

1 4 2 3

1

1

Z Z Z Z1 135K. 105K.

j 0.1 F j cc 0.3 F

32. A control system is described by 1 1 1

2 2 2

x x x0 1 0y 1 0

x x x1 1 1

For unit step input, the steady state error is

(A) 0 (B) 12

(C) 1 (D)

Sol.

1T C SI A . BF

2

1 0 s 1 1 01 s 1s s 1

2 2

1 0 1 1TF ss s 1 s s 1

2 2

1 1G ss s 1 1 s s

1t 1t 1tp s 0 s 0 s 0

1 I 1k s. G s 1G s 1 s 1

p

1 1ess1 k 1 1

33. Find the Norton’s equivalent current source in Amperes at x & y terminals____________ Sol.

2.5V2.5

5

5

5V

x

y

5

5

2.5 2.5V

2.5

2.5V

5V

5

5

5V

5

5ISC5VISC

51A



26

34. The power delivered by the current source is ________W. Sol.

1 V VKCL at node V 21 1

3 2VV 1.5 V

Power delivered by current source is 2×1.5 = 3 W. 35. The table below has question wise data on the performance of students in an examination.

The marks for each question are also listed. There is no negative or partial marking in the examination.

Question Number

Marks Answered Correctly

Answered Wrongly

Not attempted

1 2 21 17 6

2 3 15 27 2

3 2 23 18 3

What is the average of the marks obtained by the class in the examination? (A) 1.34 (B) 1.74 (C) 3.02 (D) 3.91

Sol. 2 21 3 15 2 23 133Average marks : 3.0244 44

1 1

2A 1

1V

1V

1V 0V

1

1

2A1

1V

1V

V



27

36.

While trying to collectI

an envelop

from under the tableII

,

Mr. X fell downIII

and

was losing consciousness

IV.

Which of the above underlined parts of the sentences is NOT appropriate? (A) I (B) II (C) III (D) IV 37. If she _________ how to calibrate the instrument, she _________ done the experiment. (A) knows, will have (B) knew, had (C) had known, could have (D) should have known, would have Sol. C 38. Choose the word that is opposite in meaning to the word “coherent” (A) sticky (B) well-connected (C) rambling (D) friendly Sol. C 39. Which number does not belong to the series below? 2, 5, 10, 17, 26, 37, 50, 64 (A) 17 (B) 37 (C) 64 (D) 26 Sol. C 40. Consider the equation: (7526)8 - (Y)8=(4364)8, where (X)N stands for X to the base N.

Find Y. (A) 1634 (B) 1737 (C) 3142 (D) 3162 Sol. C

8

8

8

7 5 2 6

3 1 4 24 3 6 4

41. By the beginning of 20th century, several hypothesis were being proposed, suggesting a

paradigm shift in out understanding of the universe. However the clinching evidence was provided by experimental measurements of the positions of a star which was directly behind our sun.

Which of the following inference(s) may be drawn from the above paragraph? i. Our understanding of the universe changes based on the position of stars ii. Paradigm shift usually occur at the beginning of centuries iii. Stars are important objects in the universe iv. Experimental evidence was important in confirming this paradigm shift (A) i, ii & iv (B) iii only (C) i & iv (D) iv only Sol. C



28

42. The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/USD to Rs. 60/USD. India’s GDP in USD during the period 2012-2013

(A) increased by 5% (B) decreased by 13% (C) decreased by 20% (D) decreased by 11% Sol. B 43. The ratio of Male to Female students in a college for 5 years is plotted in the following

line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011?

(A) 1:1 (B) 2:1 (C) 1.5:1 (D) 2.5:1 Sol. C 44. A dance program is scheduled for 10.00 am. Some students are participating in the

program and they need to come 1 hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the program. The instruction you think that is appropriate for this is

(A) Students should come at 9.00 am and parents should come at 10.00 am (B) Participating students should come at 9.00 am accompanied by a parent and other

parents and students should come by 10.00 am (C) Students who are not participation should come by 10.00 am and they should not

bring their parents. Participating students should come at 9.00 am. (D) Participating students should come before 9.00 am. Parents who accompany them

should come at 9.00 am. All other should come at 10.00 am Sol. B

1

2

3

0

3.5

2.5

1.5

0.5

2008 2009 2010 2011 2012Rati

o of

Mal

e t

o F

em

ale

stu

dents



29

Questions & Solutions 2nd March ( Second Session )

1. A synchronous generator connected to an infinite bus having Ef = 1.3 P.U, XS = 1.1 P.U and delivering power 0.6 P.U. The reactive power delivered under this condition is ______. Neglect resistance of generator.

Sol: s

EV 1.3 1P sin 0.6 sinX 1.1

o

s

V30.5 Q Ecos VX

1Q 1.3cos(30.5) 11.1

Q 0.109p.u

2. Initially, the motor is rotating in clockwise direction with commutator brushes. If the rotor

winding is open circuited, system is made to run at fr by prime mover in antilock wise direction then frequency of voltage across slip rings is f1 and commutator brushes is f2.

Then f1 =__________ and f2 = _________. (A) 1 2f f , f (B) r rf f , f f (C) rf f , f (D) r rf f , f f

3. If the SCR shown has latching current of 40mA, and is triggered by a gate pulse of

50 sec, then Rmax = ________.

Sol: LI 40 mA

t 50 sec

maxR ?

t 3

3

V V L 200 10i(t) 1 eR R R 500

0.4 10

100VI

500

200MH

R

PrimeMover

rf 1f

Ac sup ply, f

2fInductionSlipring

Motor



30

631050 103 0.4100 10040 10 1 e

500 R

R 6.06k

4. A DC shunt machine has supply current of 50A and shunt field resistance is 125 and

armature resistance is 0.6 . The second machine is operating at 250V. The ratio of speed of machine as generator to as motor is _______.

5. Two resistance 250 and 300 having tolerance 1% connected in parallel. The

equivalent resistance has a tolerance of _______. (A) 5% (B) 1% (c) 1.2% (D) 2% Sol: 1

2

R 250 1%R 300 1%

1 2T

1 2

T

T

R RRR R250 300R

550R 136.36

T

RTT

R%E 100R

T 1 T 2

1 1 2 2

R R R R. . 100R R R R

1 R11

2 R 212

RT

R 250 1R 2.5100 100

R 300 1R 3100 100

136.36 2.5 136.36 3% 1%250 250 300 300

6. Horizontally spaced conductors of a 1- , line having line frequency 50Hz, outer diameter

1.6 cm and spacing between center is 6mts. The capacitance to neutral per km of each line is

(A) 94.2 10 F (B) 124.2 10 F (C) 98.4 10 F (D) 128.4 10 F

Sol: 12

9on

2 2 8.854 10C 8.4 10 F/ kmD 6ln lnr 0.008



31

7. In the network shown, C 1 1 1 2 2 2V A sin t A sin t then A1=________,

A2 = ______. (A) 2, 1.98 (B) 2.5, 4.2 (C) 5, 1.98 (D) 5, 6.4

Sol: By Super position theorem Step (1)

1CV t due to 20 sin 10t voltage source

1

1C

11 1j cH transfer function 1 R.j c 1 1 10jR

j c1V t 20 sin 10t Tan 10101

Step(2) 2CV t due to10 sin t

2

2

2

C

C

C 22

2

10 0 1V 0.2j1 0.2j

2jV1 0.2j

2V sin 5t1 0.2

1.96 sin 5t

By super position theorem

1 2C C C 1 2V t V t V t 2sin 10t 1.96sin 5t .

8. Consider the following 1 , full bridge phase controlled rectifier, which is operating at o30 and ripple free current in inductor. The input side power factor is

Sol: Given o30 In 1 full bridge rectifier input p.f= 0.9 cos

=0.9×cos30

IPF 0.78

~

20 sin10t

CV 1F

1H

10sin 5t

1

2CV j0.210 0

j 51



32

9. Two ammeters X and Y having internal impedance 1.2 and 1.5 and drawing full load current are 150mA and 250mA respectively. A shunt resistance is connected to each of the ammeter to extend the range to 15A. If both ammeters connected in parallel along with shunt resistances and drawing a supply current of 15A. What is the reading indicated by meter x. _______.

10. A 3 alternator has solidly grounded neutral and its ratings are 100MVA, 25kV. The

zero, positive and negative sequence reactances are 0.2 P.U, 0.2 P.U, 0.05 P.U. What is the fault current in amps if a bolted single line to ground fault occurred at the terminals of unloaded generator.

Sol:

a1a0 a1 a2

a0 a1 a2

a a0 a1 a2 a1

base

fault Base pu

Ea 1I 2.22puZ Z Z 0.2 0.2 0.005

For a SLG I I IPhasecurrent in a is I I I I 3I 6.66pu

Base VAI 2309.4A3 Basevoltage

I I I 2309.4 6.66 15380.61A

11. In the network shown, the total power dissipated is 1 kW. XL=__________.

Sol: 2 2

2 2

P 2 1 10 R 1000R 3.1559

V 200Z 20 R LI 10

XL 19.749

12. Given 2

k1 G(s)H(s)s(s 2)(s 2s 4)

. If the system is marginally stable, then k =

___________.

:

V

10A2A

C1XR

LX

1

2XC200 V



33

Sol: 1 G s H s 0

2

2

3 2 2

4 3 2

K1 0s s 2 s 2s 4

s s 2 s 2s 4 K 0

s s 2s 2s 4s 4s 8 K 0

s 4s 8s 8s K 0

4

3

2

1

0

s 18 Ks 48 0s 6K

48 4Ks 06

s

For marginally stable, 48 4K 06

48 4K 048 4K K 12

13. Given G(s)H(s) = 2

5(s 4) .s(s 0.25)(s 4s 25)

The constant gain term and highest corner

frequency in it bode plot are (A) 3, 0.25 (B) 16, 4 (C) 3.2, 5 (D) 16, 5 Sol:

2

2

5 S 4G S H S

S S 0.25 S 4S 25

first convert into time cons tan t formS5 4 14G S H S

S 4 SS 0.25 1 25 1 S0.25 25 5

2

S15 4 4 4.

S 4 S25 S 1 1 S0.25 25 5

2

2

n n

S3.2 14

S 4 SS 1 1 S0.25 25 5

2 4, 5425

2 0.45

cons tan t gain 3.2highest corner frequency is5 rad sec.



34

14. The POS representation of SOP= (0,1,3,7,11) is ________.

15. The values of Rs is _______ to avoid burnout of zener diode.

16. Let 1t and 2t be time duration of positive and negative part cycle. Then 1 2t tRCe

Sol: satTP

VV4

sat

TPVL2

sat1

sat

sat sat

sat sat

1

V LTPt RClnV UTP

V V / 2RClnV V / 4

t 0.69Rc

1 2

sat2

sat

sat sat

satsat

t tRc

2

V UTPt RCln

V LTP

V V / 4RClnVV2

t 0.916RC e 0.7977

:

SR

LR

20 V2

5V1 W4

R

oVC

3k

1k

1k



35

17. A 1 , AC voltage regulator has 1 sR 5 , L 16mH. V 230 V. What is the maximum value of so that device voltage is 0 all throughout and RMS current under above conditions

(A) 30o, 46 A (B) 45o, 23 A (C) 30o, 32 A (D) 45o, 32 A 18. In a 1 , 2 winding transformer, if V is doubled and f increased by 10%, then hysteresis

and eddy current losses are (A) +10%, +21% (B) -10%, -21% (C) +11%, -21% (D) -11%, +21% 19. Two alternators having no load frequencies 51.5 Hz, and 51 Hz. Their droop constants are

1Hz/MW each. Load sharing is 2.5 MW. The steady state frequency is _____ when generators are operating at droop characteristics.

Sol:

01 1 02 201 1 01 2

1 2

01 11 2

1

1 2

1 2

1 2

f f f ff f P f P

f ff 51.5 1.P 51 1.P droopcons tan t

P P 0.5P P 2.5P 1.5MW,P 1MWf 51.5 1.5 50Hz

20. Thevenin voltage and resistance across x and y terminal are Sol:

xy oc

xy xyin

xy

2

xy

V V

V Vsin tV1 2 1 2

V 2sin t

2R 1 41

21. A stepup chopper supplying a load at 400V and operating at 250V. The off time of

switch is 20μ sec and inductor current is continuous and ripple free. The frequency of chopper in kHz is ___________________.

1x

y

sin t

1: 2



36

Sol: Vo = 400V

s

off

V 250VT 20 secf ?

so

V 250V 1 D1 D 400

offoff

5

(1 D) 0.625TT (1 D).T T

1 DT 3.2 10 sec

1f f 31.25kHzT

22. A single phase induction motor operating at 0.6pf lagging and supplying a load of 12MW.

A capacitor is connected to improve the power factor to 0.8lag. The reactive power supplied by the capacitor is _______.

Sol: 1 2Q P{tan tan } 12{tan53.13 tan36.86} 7MVAR 23. The two wattmeter readings when a 3 power is measured by two wattmeters are 100W

and 250W. The load power factor is ______. Sol: 2-Watt meter method:

1

2

1 3 1 2

1 2

1 1 2

1 2

W 100 WW 250W

V / W Wphase angle tanW W

36.58

3 / W WPower factor cos cos tanW W

cos( 36.58) p.f 0.8

24. A 3 , star load drawing power at V 0.9pu, 0.8 pf lag. The base values are 100MVA,

437.38 A. The line to line voltage in kV is __________.

Sol: l l L LV ? S 3V .I

6

LL

S 100 10V 132kV3I 3 437.38



37

25. A 3 , 4-pole induction generator is operating at 1f . If load is partially removed, operating at 2f speed is maintained at 1500 rpm in both cases. Choose the correct one

(A) 1 2 1 2f , f 50, f f (B) 1 2f 50, f 50 (C) 1 2 2f , f 50, f 51 (D) 1 2f 50, f 50 Sol: In induction generator, speed always >Ns.

s1

N N Pf 50 Hz

120

Also 2f 50Hz but when load disconnected speed becomes more 2 1f f 26. 20 pole, alternator is having 180 identical stator slots with 6 conductors in each slot. All

the coils of a phase are in series generated voltage is 1V if it is1 . If coils are now connected to realize 3 , star, generator voltage is 2V . Assume full pitch single layer

winding 1

2

VV

(A) 13

(B) 12

(C) 3 (D) 2

27. Shunt reactors are used in high voltage transmission systems to (A) limit short circuit current (B) limit over voltage at load side under light load limit (C) limit series compensation (D) compensate for high voltage drop under heavily loaded condition 28. Two inductors connected in series resulted net inductance as 380μH and 240μH. The

coupled inductance in μH is ____________. Sol: 1 2

1 2

L L 2M 380L L 2M 240

4M 140M 354H

29. In a 1 , induction motor, Vf

is maintained constant from zero frequency to base

frequency. At low frequency (A) stator flux increases from rated value (B) stator flux decreases from rated value (C) motor saturates (D) ϕ remains constant from rated value

Sol: V Bm ,f

Q Hence saturated

30. The state model of a control system has 1 0 1A , B

1 1 1

. The state transition

matrix is

(A) t

t t

e 0te e

(B) t

t t

e 0e e

(C) t t

t

e te0 e

(D) t

2 t t

e 0t e e



38

Sol: 1

1 s 0 10SI A

0 s 11

1

2

2

t1At 1

t t

s 1 0 s 1 011 s 1 1 s 1s 1

1 0s 1

1 1s 1s 1

e 0e L SI A

te e

31. A 1000/100 V, 50 kVA, two winding transformer is reconnected as auto transformer. Its

kVA rating is Sol: 1000V/100V, 50 kVA is connected As auto transformer

2 2AutoTransformerKVA V I

1100 500550 kVA

32. The steady state error for unit step input applied to a block whose transfer function is

2

4T ss 0.4s 4

is

(A) 0 (B) 1 (C) 0.5 (D) ∞ Sol: Steady state error for type-1, unit step input is 0. 33. A LTI system has impulse response 5t 3t 5 th t e u t and y t e e . It’s input is

(A) 3te u t (B) 3t2e u t (C) 5te u t (D) 5t2e u t

Sol:

5t

3t 5t

1h t e u t H ss 5

1 1 2y t e e y ss 3 s 5 s 3 s 5

y 0H s

x s

100 V

1100 V

1000 V



39

34. Given 1 1 0

x x u0 3 1

&

y 0 1 x.

The system is (A) Controllable, observable (B) Controllable, but not observable (C) Not controllable, not observable (D) Not controllable, but observable

Sol: c

c

T T T0

0

0 1Q B AB

1 3

Q 0, controllable

0 0Q C A C

1 3

Q 0, not observable

35. A saw tooth waveform shown below is applied to moving iron meter. It’s reading is

________. Sol:. M.I meter will read RMS value

mRMS

V 100V 57.73volts3 3

36. The minimum value for the function 23x 1 occurs at

(A) 1 (B) 0 (C) -∞ (D) ∞

Sol: 23f (x) x 1

for x 1, f (x) 0for x 0, f (x) 1for x 1, f (x) 1.59for x 2, f (x) 1.08for x 3, f (x) 2.52

for x 4, f (x) 2.92:::

for x , f(x)

37. Minimum value of 3 2x 3x 24x 100 in range [-3,3] is (A) 20 (B) 16 (C) 28 (D) 32

m sec

100

0 20 40



40

Sol: Let f(x) = 3 2x 3x 24x 100

2

3 2

3 2

2

f '(x) 3x 6x 24 0x 2, 4

f ''(x) 6 x 6f''( 2) 12 6 18 0&

f ''(4) 24 6 18 0f(x) has min. at x 4min value f (4) 4 3(4 ) 24(4) 100

64 48 96 100 20End valuesf ( 3) ( 3) 3( 3) 24( 3) 100

27 27 72 100 118f (3) 3

23(3 ) 24(3) 10027 27 72 100 28

min 20,118,28 20

38. The solution to 2

22

d y dyx x y 0dx dx

is

(A) xe (B) 2x (C) 1x

(d) ln x

Sol: 2

22

d y dyx x y 0dx dx

2 2

Z

2 2

2

2

2 2

z z log x log x 21 2 1 2 1

(x D xD 1)y 0Put x e (or) Z logx

xD , x D ( 1)d dwhere D &

dx dz( 1) 1 y 0

1 y 0

( 1) 0for C.F

1 0 1 1cC.F c e c e c e c e c xx

We have to find 1 2c & c by applying given initial conditions suitable answer will be 1x

39. All the values of ii (A) Purely imaginary (B) Real & non negative (C) On unit circle (D) Equal is real & imaginary parts



41

Sol: All values of ii

Let ii logii e

2

i log i

i log1 i 2n2

i2

e

e ; n Z

e ; n z

1

We have log z log z i 2nwhere

ytanx

Real & non negative 40. The switch in circuit shown below initially at 1 and moved to 2 after longtime. CV (t)

______. Sol: When switch is in position When switch is in position 2

t2RC

c o1 o2 o1V V V V e

R 2

R

CV

CO1VO2V

1

TR

c o1V Vo1V

R

cVo2V

R

01V



42

41. JK Flip flop is realized using T flip flop. Which of the following represents the correct implementation?

(A) (B) (C) (D) Sol: 1T JQ KQ

JK Q T00 0 000 1 001 0 001 1 110 0 110 1 011 0 011 1 1

42. A input x(t) = 2+5sin 100t sampled at 400 Hz and applied input to block whose transfer

function is

N

1

1 Z .N 1 Z

Where N is samples/cycle. The value of y(n) under steady state is

__________. 43. The invalid state is 8-4-2-1. Binary coded decimal is. (A) 1000 (B) 1001 (C) 0011 (D) 1100 Sol: 1100 12

in BCD, 0001 0010

J

K

T Q

Q

Q

T Q

Q

J

K

T Q

Q

Q

J

K

J

T Q

Q

K



43

44. For the ckt-shown, out to be clipped. iV must outside range

(A) -1 to -2 (B) +1 to -2 (C) -2 to -4 (D) +2 to -4 Sol: Vi must outside range -2 to -4

45. 12 12 12 ....

(A) 4 (B) 3 (C) 3.52 (D) ∞

Sol:

2

2

2

x 12 12 12 ....... 12 x

x 12 xx x 12 0x 4x 3x 12 0x x 4 3 x 4 0x 4, 3x 4 is correct answer

46. The BJT shown below is in active region. The maximum value of CR is

CE satV 0.2 BE activeV 0.7 50 Sol: CE BEV (sat) 0.2V, V (A ct) 0.7 V, 50.

B

C

CEC

C

5 0.7I 2.15mA2k

I 107.5mA 0.1075A5 V (sat) 5 0.2Max.R 44.65

I 0.1075

10 K

10 K

AC 1V 2V

CR

2k

5V

5V



44

47. If the potential difference between one of the plates and the nearest surface of dielectric surfaces is 2V. Then 1 2: is

(A) 1 : 4

(B) 2 : 3

(C) 3 : 2

(D) 4 : 1

48. In figure I, B at a distance from conductor carrying current I is oI .2 d

In figure II, H at

(2,1,0) is

(A) 3 k2

(B) 4 i2

(C) 3 k2

(D) 0

49. Who _______ was coming to see us this evening. (A) you said (B) did you say (C) did you say that (D) had you said 50. If 2x 2x 3 11, x is real, then 2 3x x x (A) 2, 4 (B) 2, 14 (C) 4, 52 (D) 14, 52 Sol: 2

2

2

2

x 2x 3 11

x 2x 3 11x 2x 3 11 0x 2x 8 0x 4, 2

3 2

3 2

3 2

x x x

x 4

4 4 4 64 16 4

52 52x 2

2 2 2

8 4 2 14

1 210V

d 2

d

dX

I

oIB2 d

fig I

2,1,0

4A

y

x

4A

2

fig II



45

51. The contents of Accumulator after the execution of 2000 XRA A 2001 MVI B04 2002 MVI A03 2005 RAR 2006 DCR 13 2007 JNZ 2005 200A HLT

Sol:

f 0,1,3,7,11f ' cd' ab bc ' ac 'f c ' d a ' b ' b ' c a ' c

52. Let X be random variable with p.d.f

f(x) 0.2 x 1

0.1 1 x 40 else where

P 0.5 x 5 __________

Sol: f (x) 0.2; x 10.1;1 x 40; else where

5

0.51 4 5

0.5 1 41 4 5

0.5 1 41 4

0.5 1

P(0.5 x 5) f (x)dx

f (x)dx f (x)dx f (x)dx

0.2dx 0.1dx 0dx

0.2x 0.1x0

(0.2 0.1) (0.4 0.1)0.4

53. A 10 kHz, even symmetric square wave is passed through a BFP with center frequency 30 kHz and 3 dB pass band 6 kHz. The output frequency is

(A) nearly 0 (B) highly attenuated square wave at 10 kHz (C) perfect sine wave at 30 kHz (D) perfect cosine wave at 30 kHz.

00 01 11 1000 1 1 1 001 0 0 1 011 0 0 0 010 0 0 1 0

00 01 11 1000 1 1 1 001 0 0 1 011 0 0 0 010 0 0 1 0

cd

ab

Types of questions asked from each sectiond1zttcfb64t0un.cloudfront.net/Images/EE analysis...Signals and Systems Questions from Fourier and Z Transform Control Systems Questions from

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