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GATE–Sample Questions-Signals And System

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Forum Discription: GATE Model Test Papers: Share what you have with others and discuss the questions.
URL: http://forum.onestopgate.com/forum_posts.asp?TID=1839
Printed Date: 08Feb2025 at 2:05am


Topic: GATE–Sample Questions-Signals And System
Posted By: aparna
Subject: GATE–Sample Questions-Signals And System
Date Posted: 27Nov2007 at 2:48am
Que. 1      For a secound order system  with the close loop transfer function     
                T(s)= 9/[s^2+4s+9] the setting time for 2% band in secounds
is
A         1.5
B         2.0
C         3.0
D         4.0
Que. 2     The Nyquist sampling interval,for the signal sinc(700t)+sinc(500t) is
A         1/350 sec
B         (pi)/350 sec
C         1/700 sec
D         (pi)/175 sec
Que. 3     A video transmission system transmitts 625 picture frames/sec. Each frame
consist of a       (400*400) pixel grid with 64 intensity levals/pixal.The
data rate of the system is
A         16Mbps
B         100Mbps
C         600Mbps
D         6.4Mbps
Que. 4     Let x and y be two statistically independent random variables uniformly
distributed in the ranges (-1,1)and(-2,1) respectively let Z=x+y, then
the probality that is
A         0
B         1/6
C         1/3
D         1/12
Que. 5     The gain margin and the phase margin of a feedback system with G(s)H(s)=s/(s+100)^3
are
A         0db,0degree
B         infinite,infinite
C         infinite,0degree
D         88.5dB,infinite
Que. 6     For the polynomial P(s)=s^5+s^4+2s^3+2s^2+3s+15,the number of root which
is right halfe of the s-plane is
A         4
B         2
C         3
D         1
Que. 7     Laplace transform of tsin at is
A         2as/[(s^2)+(a^2)]^2
B         2a/[(s^2+a^2)]^2
C         2s/[(s^2)+(a^2)]^2
D         a/[(s^2+a^2)]^2
Que. 8     1Khz sinusoidal signal is ideally sampled at 1500 samples/sec and the
sasmpled signal is passed though an ideal low-pass filter with cutoff
freq. 800hz the output signal has freq.
A         0 hz
B         0.75Khz
C         0.5Khz
D         0.25Khz
Que. 9     A system function has a pole at s=0 and a zero at s=-1 the constant multiplier
is unity for an exitation cos t, the steady state response is given by
A         [(sqrt)2] cos(t+45degree)
B         [(sqrt)2] cos(t-45degree)
C         cos45degree
D         1/[(sqrt)2] cos(t+45degree)
Que. 10     For a liner transfer function of the variable, the transfer function of
the system
A         changes
B         does  not change
C         has no relation at all
D         depends on other fectors also
Que. 11     Asignal phase voltage source square wave inverter feeds pure inductive
load.The waveform of the load current will be
A         sinusodal
B         rectangular
C         trapezoidal
D         triangular
Que. 12     The unit ckt of the Nyquist plot transforms into 0dB line of the amplitude
plot the bode digram at
A         0 frequency
B         low frequency
C         high frequency
D         any frequency
Que. 13     An instruction used to set the carry flag in a computer can be classified
as
A         data transfer
B         arithmetic
C         logical
D         program control
Que. 14     a system function H(s)=V(s)/I(s)=s+2/2s+1         the system is at rest
for t<0.i(t)=unit step. the value of v(t) at t=0 and t=infinite respectively
are
A         2 and 1/2
B         1/2 and 2
C         0 and indetermined
D         2 and indetermined
Que. 15     H(s)=V(s)/I(s)=4s+6/s+2, i(t)=unit step function. v(t) as t->infinite
is given by
A         0
B         3
C         4
D         infinite
Que. 16     A driving point impedance Z(s)=V(s)/I(s)=s+1/s+2. the system is initally
at rest for a voltage a signal at unit step, the current i(t) through
Z is given by
A         1-e^-r
B         2-e^-r
C         2-2e^-r
D         1/2e^-r
Que. 17     For the random variable x following the probality density function p(x) shows in fig. the mean and the variance are respectively
                              ^
                              |  P(x)
                              |
     1/4     _____|___________
    |    |    |           |
                         |    |           |       
                      ___|____|___________|_______ x
                         -1   0           3   ---->    
A         1/2 and 2/3
B         1 and 4/3
C         1 and 2/3
D         2 and 4/3
Que. 18     If R is the source resistance the output resistance of an emittor follower
using the           s simplified hybrid model would be
A         h(ie)+R(s) /1+h(fe)
B         h(ie)  +R(s) /h(fe)
C         R(s) +1/h(fe)
D         1/h(fe)
Que. 19     A unit feedback system has an open-loop transfer function of          
            G(s)=1000/s(s+10)^2               the magnitude of G(jw) in
the DB at an angular frequency at w= 20 red/sec
A         0dB
B         10dB
C         20dB
D         none of the above
Que. 20     A linear discreate time system has the characteristic equation Z^3-0.81Z=0.the
system
A         is stable
B         is marginally stable
C         is unstable
D         stability can not be assessed from the given information
Que. 21     H(s)=V(s)/I(s) = s+3/(s+3)^2  .i(t) is unit step.V(t)
is steady state is given by
A         3/2
B         3/4
C         1
D         0
Que. 22     In case of synchro error dector,the electrical zreo position of control
transformer is obtained when angular displacement between rotors is
A         0
B         45degree
C         90degree
D         180degree
Que. 23     A second order differential equation is given by                      
 d^2x/dt^2+5dx/dt+7x=7y The undamped natural freq. and damping ratio are
A         1,5
B         5,7
C         1,[(sqrt)7]
D         [(sqrt)7],0.94
Que. 24     An amplifier has a bandwidth of 20khz and a midband gain of 50 without
feedback.If a -ve feedback of 1% is applied.then bandwidth with feedback
is
A         13.3khz
B         30khz
C         10khz
D         40khz
Que. 25     A unity feedback system has the plan transfer function              Gp
(s)=1/[(s+1)(2s+1) ] an integral controller with transfer function G  
(s)=k/s is placed in the feedforward path the of the feedback system.
the value of k such that the compensated system has an open loop gain
margin of 2.5
A         3/5
B         5/3
C         2
D         none of the above
Que. 26     The fourier transform of the unit step function is
A         f(jw)=j/w
B         f(jw)=jw
C         f(jw)=1/jw
D         f(jw)=1/w
Que. 27     The fourier transform of function f(at) is given by
A         f(at)=aF(w)
B         f(at)=2/a F(w)
C         f(at)=1/a F(w/a)
D         none
Que. 28     The eigen value of the matrix A= |0  1|  are
                                      |1  0|
A         1,1
B         -1,-1
C         j,-j
D         1,-1
Que. 29     the trigonometric fourier series ofa perodic function can have only
A         cosine term
B         sine term
C         cosine and sine term
D         none of these
Que. 30     inverse Laplace transform of 10/(s^2)+2s+5  is
A         10 (e^-t) sin2t
B         5 (e^-t) sin2t
C         10 (e^-t) cos2t
D         5 (e^-t) cos2t
Que. 31     Laplace transform of (e^-at) f(t) is
A         F(s) (e^-at)
B         F(s-a)
C         F(s+a)
D         F(s)/(s +a)
Que. 32     |Adj A| is equal to
A                  |A|^n
B                  |A|^(n-1)
C                  |A|^(n+1)
D                  |A^-1|
Que. 33     About the fourier series expansion ofa perodic function it can be said
that
A         Even function have only a constant and cosine terms in there
FS expansion
B         odd function have only sine terms in there FS expansion
C         functions with half wave symmetry contain only odd harmonics
D         all above the three
Que. 34     the final value of [(L^-1)(2s+1)]/[(s^4)+8(s^3)+16(s^2)+s] is
A         infinity
B         2
C         1
D         0
Que. 35     The fourier transform of a Gaussian time pulse is
A         uniform
B         A pair of impulses
C         Gaussian
D         Rayleigh
Que. 36     The discrete time system described by y(n)=x(n)^2 is
A         causal,linear and time varying
B         causal,non-linear and time varying
C         non-causal,linear and time invarying
D         non-causal,non-linear and time variant
Que. 37     Which one of the following transfer functions does correspond to a non-minimum
phase system?
A         s/[(s^2)+2s+1]
B         (s+1)/[(s^2)+2s+1]
C         (s+1)/[(s^2)+2s-1
D         (s-1)/[(s^2)+2s+1]
Que. 38     The electromechanical closed loop control system has the following characteristic
equation:       [(s^3)+6K(s^2)+(K+2)s+8]=0  where K is the forward gain
of the system.the condition for closed loop stability is
A         K=0.528
B         K=2
C         K=0
D         K=-2528
Que. 39     Which of the following signal is/are periodic?
A         S(t)=cos2t+cos3t+cos5t
B         S(t)=exp[j8(pi)t]
C         S(t)=exp(-7t)sin10(pi)t
D         S(t)=cos2tcos4t
Que. 40     A secound-order system has a transfer function given by     G(s)=25/[(s^2)+8s+25]
If the system,initally at rest is subjected to a unit step input at t=0,the
secound peak in response will occur at
A         (pi) sec
B         (pi) /3 sec
C         2(pi)/3 sec
D         (pi)/2 sec



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