GATE- IN 2005

7/27/2019 GATE- IN 2005

1/25

2005 IN

IN 1/25

www.gatehelp.com

Q.1 - Q.30 carry one mark each

Q.1 Let A be a3 3# matrix with rank 2. Then AX 0= has

(A) Only the trivial solution X 0=

(B) One independent solution

(C) Two independent solutions

(D) Three independent solutions

Q.2 Identify which one of the following is an eigenvector of the matrix A1

1

0

2=

> H

(A) [ ]1 1 T (B) [ ]3 1 T

(C) [ ]1 1T

(D) [ ]2 1T

Q.3 If .......f a x a x y a xy a yn n nn

nn

0 11

11= + + + +

where ( )a i to n 0i = are constants, then

xxf

yyf

2

2

2

2+ is

(A)nf

(B)fn

(C) nf (D) n f

Q.4 Ifa vector ( )tR has a constant magnitude, then

(A)dt

dR

R 0: = (B)dtd

RR 0# =

(C)dt

dR R

R: (D)

dtd

R RR

# =

Q.5 The value of the integralx

dx121

1

# is

(A) 2 (B) Does not exist

(C) 2 (D) 3

Q.6 The probability that there are 53 Sundays in a randomly chosen leap year is

(A)71 (B)

141

(C)281 (D)

72

7/27/2019 GATE- IN 2005

2/25

2005 IN

IN 2/25

www.gatehelp.com

Q.7 A mass of 10 kg is measured with an instrument and the readings are normally dis-tributed with respect to the mean of 10 kg. Given that

( / ) .exp d22 2 0 62

=# and that 60 per cent of the readings are found to be within

0.05 kg from the mean, the standard deviation of the data is(A) 0.02 (B) 0.04

(C) 0.06 (D) 0.08

Q.8 The measurements of a source voltage are 5.9 V, 5.7 V and 6.1 V. The sample stan-dard deviation of the readings is

(A) 0.013 (B) 0.04

(C) 0.115 (D) 0.2

Q.9 The diameter of an aluminium sphere is found to be 50 mm at an atmospheric pres-sure of105 Pa. The bulk modulus for aluminium is 68.6 GPa. The change in the diameterof the sphere in microns, when placed in vaccum is

(A) 0.018 (B) 0.024

(C) 0.032 (D) 0.038

Q.10 In a flyball-type angular speed magnitude measuring device, the centrifugal force,

given 106 2

, where is the angular speed in rad/s, is transmitted to a spring with thenon-linear characteristic F x16 2 2= , where F is the applied force and x is the spring com-pression in meters. The sensitivity of the device in .mm s is

(A) 1

(B)21

(C)31

(D)41

Q.11 In a variable-area flowmeter (rotameter), the inlet tube diameter is the same as thatof the effective float diameter and the tube taper is small. When the volume flow rate ofa fluid is Q1, the float stands at a height of 70 mm from the inlet and when the volumeflow rate of the fluid is Q2, the float moves to a height of 20 mm from the inlet. The ratioof the flow rates /Q Q1 2 is

(A) 3.5 (B) 0.29

(C) 0.082 (D) 12.3

7/27/2019 GATE- IN 2005

3/25

2005 IN

IN 3/25

www.gatehelp.com

Q.12 In a falling-ball viscometer, the ball attains terminal velocities of 0.01 m/s for oil Aand 0.002 m/s for oil B. Assuming the oils have the same density and oil A has kinematicviscosity of /m s5 10 3 2#

, the kinematic viscosity of oil B in /m s2 is

(A) 15 10 3# (B) 20 10 3#

(C) 25 10 3#

(D) 30 10 3#

Q.13 The peak value of the output voltage V0 across the capacitor shown in the figure fora 2230:9 transformer and a 230 V, 50 Hz, input assuming 0.7 V diode drop and an idealtransformer, is

(A) 12.73 (B) 11.33

(C) 7.6 (D) 9.0

Q.14 Identify the transfer function corresponding to an all-pass filter from the following.

(A) ss

11

+

(B) ss

11

2

++

(C)s1

1+

(D)s

s1

+

Q.15 Given the discrete-time sequence [ ]x n [2, 0, 1, 3, 4, 1, 1], ( )X ej= is

(A) 8 (B) 6

(C) 8 (D) 6

Q.16 A voltage signal ( ) sinV t A B t = + is fed to an oscilloscope with the coupling modeset to DC, other settings being appropriate. The displayed wave can be expressed as

(A) sinA B t+ (B) sinB t

(C) A (D) sinA B t+

7/27/2019 GATE- IN 2005

4/25

2005 IN

IN 4/25

www.gatehelp.com

Q.17 An 8-bit 2s complement representation of an integer is FA (hex). It decimal equiva-lent is

(A) 10 (B) 6

(C) 6+ (D) 10+

Q.18 For N-bit Successive Approximation ADCs other parameters such as clock frequencyremaining constant, the conversion time is proportional to

(A) N2 (B) N

(C) log N (D) N

Q.19 The time period of a square wave in the audio frequency range is measured usingan 8085 microprocessor by feeding the square wave to one of the four interrupts, namely,

RST 7.5, RST 6.5, RST5.5, or INT. The algorithm used starts a timer at the beginningof a time period, stops the timer at the beginning of the next time period and reads thetimer values for time measurement. Which of the following interrupts should be selectedor this application ?

(A) INTR (B) RST 5.5

(C) RST 6.5 (D) RST 7.5

Q.20 An 8-bit micro-controller has an external RAM is the memory map from 8000H to9FFFh. The number of bytes this RAM can store is

(A) 8193 (B) 8191

(C) 8192 (D) 8000

Q.21 In an 8085 microprocessor, which one of the following is the correct sequence of themachine cycles for the execution of the DCR M instruction ?

(A) op-code fetch

(B) op-code fetch, memory read, memory write

(C) op-code fetch memory read

(D) op-code fetch memory write, memory write

Q.22 A thermometer at room temperature C30c is dipped suddenly into a bath of boil-ing water at C100c . It takes 30 seconds to reach . C96 5c . The time required to reach atemperature of C98c is

7/27/2019 GATE- IN 2005

5/25

2005 IN

IN 5/25

www.gatehelp.com

(A) 32.5 s (B) 34.6 s

(C) 35.6 s (D) 38.6 s

Q.23 In the circuit shown in the given figure the input voltage ( )V tin is given by 2 ( )sin t100

. For RL in the range 0.5 k to 1.5 k to 1.5 k, the current through RL is.

(A) 2 (100 )sin t mA+ (B) 2 (100 )sin t mA

(C) 0.5 (100 )sin t mA+ (D) 1.5 (100 )sin t mA

Q.24 A single input single output linear system is described by the equationsdtdx

Ax bu = + and ,y cx du = + where A is an n n#6 @ matrix and xand b are n 1#6 @ vectors. The transfer function is given by(A) [ ]c sI A b1 (B) [ ]c sI A b d 1 +

(C) [ ]c sI A b (D) [ ]c sI A b d +

Q.25 A control loop structure is shown in the figure with FC, FT, TC and TT denotingFlow Controller, Flow Transmitter, Temperature Controller and Temperature Transmitterrespectively. This loop is an example of

(A) Ratio Control (B) Feed forward Control

(C) Split Range Control (D) Cascade Control

7/27/2019 GATE- IN 2005

6/25

2005 IN

IN 6/25

www.gatehelp.com

Q.26 The P wave, QRS complex and T wave in one heart cycle of the ECG waveform cor-respond respectively to

(A) Polarization of atria; depolarization of vetricles and repolarization of atria

(B) Polarization of atria; polarization of vetricles and repolarization of atria

(C) Depolarization of atria; depolarization of ventricles and repolarization of atria

(D) Depolarization of atria; repolarization of ventricles and depolarization of atria.

Q.27 Choose the correct match for signals biological activity

P. EEG

Q. EOG

R. EMG

S. EGG

1. Eye movement

2. Gastric motility

3. Muscle activity

4. Brain activity

5. Heart activity

6. Bladder activity

The matching pairs are

(A) P-4, Q-5, R-4, S-3 (B) P-4, Q-1, R-3, S-2

(C) P-3, Q-2, R-6, S-1 (D) P-2, Q-3, R-1, S-6

Q.28 A cranial generator has a peak-to-peak voltage of 100 V and a source resistance of10 k. If the electrode resistance are 20 k, the voltage across the amplifier terminals withan input impedance of 10 M, is

(A) 93.5 V (B) 95.5 V

(C) 97.5 V (D) 99.5 V

Q.29 The longitudinal mode separation in a gas laser with a cavity length of 0.4 m (givenvelocity of light /m s3 108#= ) is

(A) 374 MHz (B) 375 MHz

(C) 748 MHz (D) 750 MHz

Q.30 The continuous-time signal ( )x ta t

12 2= +

has the Fourier transform expa

a _ i.

The signal ( )cosx t bt has the Fourier transform

7/27/2019 GATE- IN 2005

7/25

2005 IN

IN 7/25

www.gatehelp.com

(A) exp expa

a b a b2

+ +_ _i i8 B(B) exp exp

aa a

2

+ _ _i i8 B(C) exp cos

aa b

_ i

8 B(D) exp expa a b a b2 +_ _i i8 B

Q.31 to Q.80 carry two marks each

Q.31 Using the given data points tabulated below, a straight line passing through theorigin is fitted using least squares method. The slope of the line is

x 1.0 2.0 3.0

y 1.5 2.2 2.7(A) 0.9 (B) 1.0

(C) 1.1 (D) 1.5

Q.32 Consider the circle z i5 5 2 = in the complex plane ( , )x y with z x iy = + . Theminimum distance from the origin to the circle is

(A) 5 2 2 (B) 54

(C) 34 (D) 5 2

Q.33 Let z z3 = , when z is a complex number not equal to zero. Then z is a solution of

(A) z 12 = (B) z 13 =

(C) z 14 = (D) z 19 =

Q.34 Given a real-valued continuous function ( )f t defined over [ , ]0 1 , ( )limt

f x d x 1

t o

t

0"# is

(A) 3 (B) 0

(C) ( )f 1 (D) ( )f 0

Q.35 The curves, for which the curvature at any point is equal to cos2, where is theangle made by the tangent at that point with the positive direction of the x-axis, are(given ''/ [ ( ) ]y y1 /2 3 2 = + , where 'y and ''y are the first and second derivatives ofy withrespect to x )

7/27/2019 GATE- IN 2005

8/25

2005 IN

IN 8/25

www.gatehelp.com

(A) Circle (B) Parabolas

(C) Ellipses (D) Hyperbolas

Q.36 The general solution of the differential equation ( )D D y4 4 02 + = , is of the form

(given /D d dx = ), and C1 and C2 are constants.

(A) C e x12 (B) C e C e x x1

22

2+

(C) C e Cxex12

2

x2

+ (D) C e Cxex12

2

x2

+

Q.37 A scalar field is given by f x y/ /2 3 2 3= + , where x and y are the Cartesian coordinates.The derivative off along the line y x= directed away from the origin, at the point (8, 8)is.

(A) 3

2

(B) 2

3

(C)3

2 (D)2

3

Q.38 A temperature sensor having a range of 0-100 Cc has a worst case accuracy specifica-tion of . %1 0! of true or . %0 3! of full scale, whichever is higher. The sensitivity of thesensor is experimentally obtained by taking its readings at true temperature C25c and

C75c . The maximum error in sensitivity, expressed as percentage of its ideal value is

(A) . %0 105! (B) . %0 21!

(C) . %1 05! (D) . %2 1!

Q.39 Position sensor units having a constant sensitivity of 1V/ mm are used for feedbackin number of position controlled system units, each having an overall forward path dc gainof 50. If the random dc bias errors in the outputs of various sensor units are characterizedas normal with mean 0 and standard deviation ( ) 0.01 V, for a constant set point of 5V,the true position outputs of the various controlled system units can be characterized asnormal with.

(A) mean of 5.0 of 0.01

(B) mean of 0.0, of 0.01

(C) mean of 5.0, of 0.0098

(D) mean of 4.902, of 0.0098

Q.40 A surface height profile is given by, ( )siny a bl

xx

2 0 1# #= + where , ,a b l are

7/27/2019 GATE- IN 2005

9/25

2005 IN

IN 9/25

www.gatehelp.com

constants and x is the horizontal coordinate. The roughness of the surface, based an ab-solute deviation, is

(A) b2

(B) b4

(C) b6

(D) b8

Q.41 A mercury barometer reads h mm Hg with the temperature of the mercury at T Cc. The barometer reading corrected for the standard temperature 0 Cc with denoting thevolumetric expansion coefficient of mercury in 0 C 1c is

(A)T

h1 +

(B) ( )h T +

(C) ( )h T1 + (D) ( )h T

Q.42 The fundamental period of the sequence [ ] 3 (1.3 0.5 )sinx n n = + 5 (1.2 )sin n+ is

(A) 20 (B).1 32

(C).1 22

(D) 10

Q.43 An analog low-pass filter is needed with the following specifications:

Pass-band: . ( )H j0 9 1# # , 0 2 1000## #

Stop-band: ( ) .H j 0 2# , 2 1500#$ .

The minimum order N of the Butterworth filter to approximate the above is(A) 6 (B) 11

(C) 12 (D) 15

Q.44 A discrete-time system is shown in the figure. The system function, ( )H z , of thenetwork is given by

(A)k z

k z1 1 2 1

1

+

^ h(B)

kz

k z

1

11

2 1

+

^ h

7/27/2019 GATE- IN 2005

10/25

2005 IN

IN 10/25

www.gatehelp.com

(C)kz

k z

1

1 11

2 1

^ h(D)

kzk z

1 11

+

Q.45 In the circuit shown in the figure, the switch S is closed at time t 0= .The supplycurrent at t 0= + and the capacitor voltage at t"3 are, respectively

(A) 0 and V (B)RV and

R RVR

1 1 2

2

+

(C) R R

V

and R R

VR1 2 1 2

2

+ + (D) R

V

andV1

Q.46 The cell of a Field Programmable Gate Array is shown in the figure.It has three 2-to-1-multiplexers with their select lines , ,G G G 4and0 1 2 digital signal input lines ,I I I I and,0 1 2 3.The logical function that relates the output O to the select an signal input lines is

(A) G G I G G I G G I G G I 0 1 2 0 1 3 2 1 0 2 1 1+ + +

(B) G I G G G I G G I G 0 2 0 1 2 0 2 1 1 0+ + + +

(C) G G I G G I G G I G G I 0 2 0 0 2 1 2 1 2 2 1 3+ + +

(D) G G I G G I G G I G G I 2 1 2 2 1 3 2 0 0 0 2 1+ + +

Q.47 The input-output characteristic of a Schmidt trigger has a hysteresis band of . V0 1!. If the input voltage is 5 ( )sin t100 , the delay between the corresponding zero cross-overpoints of the output and input signals is

(A) 6.37 s (B) 0.02 s

7/27/2019 GATE- IN 2005

11/25

2005 IN

IN 11/25

www.gatehelp.com

(C) 63.7 s (D) 2.0 s

Q.48 In the circuit shown in the figure the input voltage Vi is a symmetrical saw-toothwave of average value zero, positive slope and peak-to-peak value 20 V. The average value

of the output, assuming an ideal operational amplifier with peak-to-peak symmetricalswing of 30 V, is

(A) 5 V (B) 10 V

(C) 5 V (D) 7.5 V

Q.49 In the instrumentation amplifier shown in the figure if the switch SW is changedform position A to B, the values of the amplifier gain G before and after changing theswitch respectively are

(A) 45, 95 (B) 50, 100

(C) 100, 200 (D) 90, 180

Q.50 Figure shows a circuit which has a coil of resistance R and inductance L. At reso-nance, the Q-factor of the coil is given by

7/27/2019 GATE- IN 2005

12/25

2005 IN

IN 12/25

www.gatehelp.com

(A)V

V V0b l (B) VV0

(C)V

V V0

0b l (D) VV

0

Q.51 For the circuit shown in the figure, IDSQ (in mA) and VGSQ (in V) are related through2 ( )I V4DSQ GSQ

2= + .

The following data is given :

15 1.0 , 6.5 , 2.0 , 1.0 ,V R R R k V, R M M kDD D S 1 2 = = = = =8 .I mADSS = The value ofI ,DSQ assuming the gate current is negligible, is approximately

equal to.

(A) 5 mA (B) 2.0 nA

(C) 2.3 A (D) 3.4 mA

Q.52 In the circuit shown in the figure, assuming ideal diode characteristics with zero for-ward resistance and 0.7 V forward drop, the average value ofV0 when the input waveform

is as shown, is

7/27/2019 GATE- IN 2005

13/25

2005 IN

IN 13/25

www.gatehelp.com

(A) 0.7 V (B) 1.0 V

(C) 2.0 V (D) 2.7 V

Q.53 For the RC circuit shown in the figure, the condition for obtaining an attenuation,V Vout in , of 1/3 at a frequency rad/s is

(A) CR3 1 0 = (B) CR2 1 0 =

(C) CR3 2 0 = (D) CR 1 0 =

Q.54 The bridge shown in Fig. Q 54 is balanced. The dissipation factor for the unknown

lossy capacitor Rj C

1x

x+ is

(A) R C2 3 (B) RR C

2

12

3

(C) R C3 3 (D) RR

2

1

7/27/2019 GATE- IN 2005

14/25

2005 IN

IN 14/25

www.gatehelp.com

Q.55 Three parallel-plate air capacitors of equal plate area A are formed, as shown in theFig, a for measuring zero mean vibrational displacement. The Capacitors have three sepa-rate fixed plates and one common moving plate, which are connected as shown in Fig. b .When the displacement, x is zero, the distance separating the fixed plates from the com-mon moving plate is the same, equal to d. The circuit is excited by a sinusoidal voltage

.sinV ti Neglecting fringe effects and the possibility of saturation of the opamp output,the output voltage V0 normalised by Vi for a displacement x is

(A)dx

21 + (B)

dx

21

2+

(C)d

xx

22

2 (D)21

Q.56 Figure given below shows an ultrasound flowmeter with the transducers separatedby a distance L 25= mm with the line joining the transducers making an angle 60c withthe direction of the flow. The transit time difference between upstream and downstreammeasurements is 10 ns with the sound velocity in the medium being 1000 m/s. Assumingthat the size of the transducers is very small as compared to the diameter of the pipe, the

flow velocity is

(A) 0.2 m/s (B) 2 m/s

(C) 0.4 m/s (D) 40 m/s

7/27/2019 GATE- IN 2005

15/25

2005 IN

IN 15/25

www.gatehelp.com

Q.57 The asymptotic magnitude Bode plot of an open loop system ( )G s with K 0> andall poles and zeros on the left handside of the S-plane is shown in the figure. It is com-pletely symmetric about c . The minimum absolute phase angle contribution by ( )G s isgiven by

(A) .68 6c (B) 90c

(C) .101 4c (D) 180c

Q.58 The Routh-Hurwitz array is given for a third order characteristics equation.

s

s

s ( )

b

a c

k

k

1 0 0

0 0

36

0

3

2

1

0

s

The coefficients a,b,c and k are such that , , ,a b k c 3 0 0 0> > >= and c is a function of

k. The root locus for the corresponding characteristic equation is as shown in the given

figure. The values ofk and c for critical stability respectively are

(A) 6 and 6 (B) 6 and 2(C) 3 and 2 (D) 3 and 3

Q.59 The transfer function of the open loop system ( )G s which is represented by the signalflow shown the figure below is

7/27/2019 GATE- IN 2005

16/25

2005 IN

IN 16/25

www.gatehelp.com

(A)G H G H

G G1 1 1 2 2

1 2

+ +(B)

G H G HG G

1 1 1 2 21 2

+

(C)( )( )G H G H

G G1 11 1 2 2

1 2

+ +(D)

( )( )G H G H G G

1 1 1 1 21 2

+ + +

Q.60 The open loop part of a unity feed back control system ( )G s is unstable and has twopoles on the right hand side of the S-plane. However, the closed loop system is stable. Thenumber of encirclements made by the Nyquist plot of the ( , )1 0 point in the ( )G s plane is

(A) 2 (B) 0

(C) 3 (D) 1

Q.61 Consider a unity feedback control system whose forward path transfer function( ) /G s K s 2= . The steady state error, for a step input is

(A) 1.0 (B) 3

(C) 0.0 (D) does not exist

Q.62 A single stack stepper motor has 4-stator slots and 18 permanent magnet type rotorpole faces. The step size under half stepping scheme is

(A) 5c (B) 10c

(C) 15c (D) 20c

Q.63 Two ionic species A and B of masses in the ratio 1:2 and of equal charge are simul-taneously accelerated in a time of flight mass-spectrometer. When ion A reaches the endof a 1 m drift tube, ion B would be at a distance of

(A) m2 (B) m2 1

(C) m2

1

(D) m2

1

Q.64 A spectrophotometer is used to measure concentration of a molecule in a solutionbased on Beers law using a cuvette of path length 10 mm and detectable absorbance of0.01. The molar absorptivity of the solution is 104 litres/mol/cm. The minimum concentra-tion of the solution that can be detected is

(A) 1 mol/litre (B) 2 mol/litre

7/27/2019 GATE- IN 2005

17/25

2005 IN

IN 17/25

www.gatehelp.com

(C) 5 mol/litre (D) 10 mol/litre

Q.65 The maximum solid angle of acceptance of light coupled into a step index fibre hav-ing core and cladding refractive indices of 1.48 and 1.45 respectively, is

(A) 0.28 steradians (B) 0.30 steradians

(C) 0.32 steradians (D) 0.34 steradians

Q.66 A microprocessor has an instruction XOR ( , )r r1 2 , which performs an Exclusive ORoperation of registers ,r r1 2 and stores the result in r1. After the following instructions areexecuted.

XOR ( , )r r2 1XOR ( , )r r1 2

XOR ( , )r r2 1

Which one of the following is true ?

(A) Content of register r1 is half sum ofr1 and r2

(B) Content of register r2 is half sum ofr1 and r2

(C) Content of registers r1 and r2 remain unaltered

(D) Contents of registers r1 and r2 are swapped

Q.67 In a 8085 microprocessor the value of the stack pointer (SP) is 2010 and that of DE

register pair is 1234H before the following code is executed. The value of the DE registerpair after the following code is executed is

LXI H, 0000H

PUSH H

PUSH H

POP B

DAID SP

XCHG

(A) 200EH (B) 200CH

(C) 2010H (D) 1232H

Q.68 For the digital counter shown in the figure with outputs , , , ......,Q Q Q0 1 2 Where Q0indicates the LSB of the count value, the correct statement when the switch Sw is closed, is

7/27/2019 GATE- IN 2005

18/25

2005 IN

IN 18/25

www.gatehelp.com

(A) Counter outputs are both even and odd numbers

(B) Counter outputs are only odd numbers

(C) Counter outputs are only even numbers

(D) Counter stops counting

Q.69 A combinational logic circuit has three inputs A, B and C and one output Y. Theoutput Y 1= when at least two inputs are 1. Otherwise, Y 0= . In its minimized SOP re-alization, the maximum number of the two-input terms is.

(A) 1 (B) 2

(C) 3 (D) 4

Q.70 Notwithstanding overflow, the addition and subtraction of K-bit signed binary num-ber can be realized using One K-bti full adder and

(A) K 2-Input AND Gates (B) K 2-Input NOR Gates

(C) K 2-Input OR Gates (D) K 2-Input XOR Gates

Q.71 Figs. ( )a and ( )b depict a simplified representation of the effect of series mode volt-age noise on 2-wire transmission of analog signals. I and V represent information sourcestransmitting in voltage and current modes, RL is the load resistance and R1 and RV are

the corresponding source resistances. For comparable full scale readings, let V IRL= . Alsolet R R100 L1 = and /R R 100V L= For a given noise voltage magnitude e, the errors causedby e are Ve1 and Ve2 in the displayed voltages V1 and V2 respectively. The ratio /V Ve e1 2 is

7/27/2019 GATE- IN 2005

19/25

2005 IN

IN 19/25

www.gatehelp.com

(A) 0.01 (B) 1

(C) 100 (D) 0 4

Q.72 The output from a 633 nm He-Ne laser comes out from the mirror with a beam di-ameter of 1 mm and diverges to the far field. It is brought to a focus by a convex lens offocal length of 17 mm. The spot size diameter of the beam at the focal point is

(A) 20 m (B) 26 m

(C) 52 m (D) 13 m

Q.73 The exact diffusion potential across an electrochemical cell membrane due to Na+ion concentration is 60 mV. In Case I, two silver electrodes are used to measure the po-tential and is Case II, one silver electrode and one gold electrode are used. In case I, thediffusion potential is measured as 60 mV without error. The concentration ratio of Na+ions across the membrane, and the voltage error in Case II are respectively

(A) 10; 0 mV (B) 10; 1150 mV

(C) 10; 700 mV (D) 10; 2300 mV

Q.74 The two-wattmeter method is used to measure power in a balanced 3-phase circuit,drawing lagging current. The power factor if one of the wattmeters reads zero is

(A) 0.5 (B) 0.8

(C) 1.0 (D) 0.0

Q.75 Identify the logic gate given in the figure.

7/27/2019 GATE- IN 2005

20/25

2005 IN

IN 20/25

www.gatehelp.com

(A) NOR (B) NAND

(C) AND (D) OR

Common Data for Questions 76, 77, 78

The temperature-emf characteristics of iron-constantan and copper-constantan junctions,

with the reference junctions at C0c , are given by 5.3E T V1C = and 43E T VCC = , over

an appropriate temperature range, where T is in Cc . It is known that AD 590 is an IC

temperature sensor with can drive a current of (273 T) A+ at T Cc into an appropriate

load resistance.

Q.76 An iron-constantan themocouple has its measuring junction in a both whose tem-perature can vary between 100 Cc , the maximum error, expressed as a percentage of the

emf developed, due to ambient temperature variation in the range C0c , is

(A) 8.182 (B) 22.5

(C) 45 (D) 81.82

Q.77 A thermocouple is made using a copper and an iron wire. Its measuring junction iskept at a temperature of C100c and the reference junction is kept at the ambient tempera-ture of C30c . The emf developed would be

(A) 700 V (B) 1000 V

(C) 3010 V (D) 5300 V

Q.78 A voltage generated using a AD 590 sensor is used to compensate for ambient tem-perature error for the iron-constantan thermocouple in the circuit shown in the figure suchthat the output voltage V0 is proportional to the measuring junction temperature Tm. Thevalues ofRL and E for exact compensation, assuming ideal components, are

7/27/2019 GATE- IN 2005

21/25

2005 IN

IN 21/25

www.gatehelp.com

(A) 1 k, 273 mV (B) 4.3 k, 1.174 V

(C) 5.3 k 1.447 V (D) 1 k, 303 mV

Common Data for Questions 79, 80

A bondel metal strain gauge has the following specifications :

Guauge factor = 2.0

Unstrained resistance = 120 at C0c

Maximum operation temperature = 150 Cc

Temperature coefficient of resistance = ( ) C2 10 5 1# c

Maximum tensile and compressive strain = 2 10

2#

Q.79 The temperature-induced resistance error at the maximum operating temperatureexpressed as the percentage of resistance change due to maximum tensile strain only, as-suming self-heating effects to be negligible,is

(A) 0.0625 (B) 0.625

(C) 6.26 (D) 7.5

Q.80 The strain gauges, with the specifications given above are mounted on a structural

member in a push-pull configuration, connected in a bridge along with two standard resis-tances, whose output is fed to an amplifier as shown in the figure. The output voltage V0per unit battery voltage, under maximum loading, is

7/27/2019 GATE- IN 2005

22/25

2005 IN

IN 22/25

www.gatehelp.com

(A) V04 (B) . V0 37

(C) 0.37 V (D) 0.4 V

Linked Answer Questions : Q.81a to Q.85b carry two marks each

Statement for Linked Answer Questions 81a & 81b

In the amplifier circuit shown in the figure, a 10 k resistance is connected in parallel to a

negative temperature coefficient thermistor to reduce non-linearity in the range 298-232K.

The thermistor specifications are :

R k10298 = , the characteristic constant K4000 = ,

10 expRT1

2981k298 = b l; E

Q.81a The magnitudes of the resistance change, between the temperatures 298 K and 323

K, when the thermistor is used alone and when it is used in parallel combination with the

resistance, are(A) 6.5 k, 2.4 k (B) 5.7 k, 1.6 k

(C) 6.1 k, 2.0 k (D) 5.3 k, 1.2 k

Q.81b In the given figure the potentiometer is adjusted so that the output voltage V0 is 0

at T K298= , the voltage output at 323 K is

(A) 500 mV (B) 400 mV

7/27/2019 GATE- IN 2005

23/25

2005 IN

IN 23/25

www.gatehelp.com

(C) 2.4 V (D) 2.6 V


In order to find the diameter of a cylinder, an optical flat is placed over a combination of

the cylinder and a gauge block which are in contact with each other as shown in the figure.

When the portion AB is examined with a coherent light source of wavelength 0.589 m

from above, 20 fringes are found in the field of view.

Q.82a The height BC is

(A) 2.945 m (B) 5.890 m

(C) 8.835 m (D) 11.78 m

Q.82b The length of the segment DG, which approximates the diameter of the cylinder, is

(A) 79.94 mm (B) 79.96 mm

(C) 79.98 mm (D) 80.20 mm

Statement for Linked Answer Question 83a & 83b

Given figure shows a transistor circuit with feedback

Q.83a In the circuit, in order to get V0 in the range of 0-30 V, the range ofVin is

(A) 0-30 V (B) 0.20 V

7/27/2019 GATE- IN 2005

24/25

2005 IN

IN 24/25

www.gatehelp.com

(C) 0-15 V (D) 1.10 V

Q.83b IfVin is generated using an n-bit DA converter, the minimum value ofn required,

so that the value ofV0 can be set with in an accuracy of less than 20 mV is,

(A) 9 (B) 10

(C) 11 (D) 12


Q.84a The transfer function G (s)c is

(A)s

1 0.1s+ (B)s

1 0.1s

+

(C)s 1

s

+(D)

s 1s

+

Q.84b The peak percentage overshoot of the closed loop system is

(A) 5.0 % (B) 10.0 %

(C) 16.3 % (D) 1.63 %


7/27/2019 GATE- IN 2005

25/25

2005 INwww.gatehelp.com

The thickness of a metal sheet from a rolling mill is manipulated by controlling the roll gap( )d t and measuring the sheet thickness ( )m t at a certain distance from the rolls as shown

in the figure. The thickness of the sheet at the roll out point is equal to the roll gap ( )d t

as shown and remains invariant during transit.

Q.85a Given the distance at which the thickness is measured is 0.5m from the roll gap and

the velocity of the sheet 0.2 m/s. the transfer function system, ( ) ( )/ ( )G s M s D s = , is

(A) exp( 2.5 )s (B) exp( 2.5 )s+

(C) exp( 0.4 )s+ (D) ( . )exp s0 4

Q.85b The gap ( )d t is controlled by a proportional controller along with a hydraulic

actuator of combined gain K and a unity feedback loop exists around K. ( )G s (Fig. b).

Increasing K beyond a certain value causes the system to become unstable.

The frequency of oscillations at the critical value ofK is

(A) = (B) .2 5 =

(C) .0 4 = (D).2 5

=

***********

Documents

GATE- IN 2005