Mechanical Engineering (ME) 1991 GATE Paper without solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


GATE ME - 1991
1.1 An excitation is applied to a system at t = T and its response is zero for 
. t T -8 < < Such a system is 
(a) non-causal system 
(b) stable system 
(c) causal system 
(d) unstable system 
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency  
(b) greater than the resonant frequency  
(c) less than the resonant frequency  
(d) none of the above  
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function 
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = -
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two two-port networks are connected in cascade. The combination is to be 
represented as a single two-port network. The parameters of the network are 
obtained by multiplying the individual  
(a) z-parameter matrix (b) h-parameter matrix 
(c) y-parameter matrix (d) ABCD parameter matrix 
1.5 The pole-zero pattern of a certain filter is shown in the figure below. The filter 
must be of the following type. 
(a) low pass (b) high pass 
(c) all pass (d) band pass 
x(t) 
t=T 
t 
×
× 
×
jw 
-1 
+1 
-j1 
-j2 
+j1
+j2 
Page 2


GATE ME - 1991
1.1 An excitation is applied to a system at t = T and its response is zero for 
. t T -8 < < Such a system is 
(a) non-causal system 
(b) stable system 
(c) causal system 
(d) unstable system 
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency  
(b) greater than the resonant frequency  
(c) less than the resonant frequency  
(d) none of the above  
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function 
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = -
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two two-port networks are connected in cascade. The combination is to be 
represented as a single two-port network. The parameters of the network are 
obtained by multiplying the individual  
(a) z-parameter matrix (b) h-parameter matrix 
(c) y-parameter matrix (d) ABCD parameter matrix 
1.5 The pole-zero pattern of a certain filter is shown in the figure below. The filter 
must be of the following type. 
(a) low pass (b) high pass 
(c) all pass (d) band pass 
x(t) 
t=T 
t 
×
× 
×
jw 
-1 
+1 
-j1 
-j2 
+j1
+j2 
1.6 The necessary and sufficient condition for a rational function of s. T(s) to be 
driving point impedance of an RC network is that all poles and zeros should be 
(a) simple and lie on the negative axis in the s-plane 
(b) complex and lie in the left half of the s-plane 
(c) complex and lie in the right half of the s-plane 
(d) simple and lie on the positive real axis of the s-plane 
1.7 In the signal flow graph of Figure, the gain c/r will be 
(a) 
11
9
(b) 
22
15
(c) 
24
23
(d) 
44
23
1.8 A second order system has a transfer function given by 
( )
2
25
8 25
G s
s s
=
+ +
If the system, initially at rest is subjected to a unit step input at t = 0, the 
second peak in response will occur at 
(a) p sec (b) sec
3
p
(c) 
2
sec
3
p
(d) sec
2
p
1.9 The open loop transfer function of a feedback control system is: 
( ) ( )
( )
3
1
1
G s H s
s
=
+
The gain margin of the system is: 
(a) 2 (b) 4 (c) 8 (d) 16 
1.10 A unity feedback control system has the open loop transfer function 
( )
( )
( )
2
4 1 2
2
s
G s
s s
+
=
+
If the input to the system is a unit ramp, the steady state error will be 
(a) 0 (b) 0.5 (c) 2 (d) infinity 
-1 
-1 -1 
1 1 C 
5 
T 
2 3 4 
Page 3


GATE ME - 1991
1.1 An excitation is applied to a system at t = T and its response is zero for 
. t T -8 < < Such a system is 
(a) non-causal system 
(b) stable system 
(c) causal system 
(d) unstable system 
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency  
(b) greater than the resonant frequency  
(c) less than the resonant frequency  
(d) none of the above  
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function 
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = -
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two two-port networks are connected in cascade. The combination is to be 
represented as a single two-port network. The parameters of the network are 
obtained by multiplying the individual  
(a) z-parameter matrix (b) h-parameter matrix 
(c) y-parameter matrix (d) ABCD parameter matrix 
1.5 The pole-zero pattern of a certain filter is shown in the figure below. The filter 
must be of the following type. 
(a) low pass (b) high pass 
(c) all pass (d) band pass 
x(t) 
t=T 
t 
×
× 
×
jw 
-1 
+1 
-j1 
-j2 
+j1
+j2 
1.6 The necessary and sufficient condition for a rational function of s. T(s) to be 
driving point impedance of an RC network is that all poles and zeros should be 
(a) simple and lie on the negative axis in the s-plane 
(b) complex and lie in the left half of the s-plane 
(c) complex and lie in the right half of the s-plane 
(d) simple and lie on the positive real axis of the s-plane 
1.7 In the signal flow graph of Figure, the gain c/r will be 
(a) 
11
9
(b) 
22
15
(c) 
24
23
(d) 
44
23
1.8 A second order system has a transfer function given by 
( )
2
25
8 25
G s
s s
=
+ +
If the system, initially at rest is subjected to a unit step input at t = 0, the 
second peak in response will occur at 
(a) p sec (b) sec
3
p
(c) 
2
sec
3
p
(d) sec
2
p
1.9 The open loop transfer function of a feedback control system is: 
( ) ( )
( )
3
1
1
G s H s
s
=
+
The gain margin of the system is: 
(a) 2 (b) 4 (c) 8 (d) 16 
1.10 A unity feedback control system has the open loop transfer function 
( )
( )
( )
2
4 1 2
2
s
G s
s s
+
=
+
If the input to the system is a unit ramp, the steady state error will be 
(a) 0 (b) 0.5 (c) 2 (d) infinity 
-1 
-1 -1 
1 1 C 
5 
T 
2 3 4 
1.11 The characteristic equation of a feedback control system is given by 
( )
3 2
5 6 0 s s K s K + + + + =
Where K > 0 is a scalar variable parameter. In the root loci diagram of the 
system the asymptotes of the root locus for large values of K meet at a point in 
the s-plane whose coordinates are 
(a) (-3,0) (b) (-2,0) (c) (-1,0) (d) (2,0) 
1.12  A linear second order single input continuous time system is described by the 
following set of differential equations  
( ) ( ) ( )
( ) ( ) ( ) ( )
1 1 2
2 1 2
2 4
2
x t x t x t
x t x t x t u t
= - +
= - +
Where ( ) ( )
1 2
 and x t x t are the state variables and ( ) u t is the control variable.
The system is:  
(a) controllable and stable (b) controllable but unstable  
(c) uncontrollable and unstable (d) uncontrollable and stable 
1.13 A linear time-invariant discrete-time system is described by the vector matrix 
difference equation 
( ) ( ) ( ) 1 x k FX k Gu k + = +
Where ( ) X k is the state vector, F is an n × n constant matrix, G is a
( ) n r × constant matrix and ( ) u k is the control vector. The state transition matrix
of the system is given by inverse Z-transform of 
(a) ZI - F (b) (ZI – F) Z (c) ( )
1
ZI F G
-
- (d) ( )
1
ZI F Z
-
-
1.14 A silicon sample is uniformly doped with 
16
10 phosphorous atoms/cm
3
 and 
16
2 10 × boron atoms/cm
3
. If all the dopants are fully ionized, the material is 
(a) n-type with carrier concentration of 
16 3
10 /cm
(b) p-type with carrier concentration of 
16 3
10 /cm
(c) p-type with carrier concentration of 
16 3
2 10 /cm ×
(d) 
2
T will get damaged and 
1
T will be safe 
1.15 An n-type silicon sample, having electron mobility 
n
µ = twice the hole mobility 
,
p
µ is subjected to a steady illumination such that the electron concentration 
doubles from its thermal equilibrium value. As a result, the conductivity of the 
sample increases by a factor of … 
Page 4


GATE ME - 1991
1.1 An excitation is applied to a system at t = T and its response is zero for 
. t T -8 < < Such a system is 
(a) non-causal system 
(b) stable system 
(c) causal system 
(d) unstable system 
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency  
(b) greater than the resonant frequency  
(c) less than the resonant frequency  
(d) none of the above  
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function 
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = -
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two two-port networks are connected in cascade. The combination is to be 
represented as a single two-port network. The parameters of the network are 
obtained by multiplying the individual  
(a) z-parameter matrix (b) h-parameter matrix 
(c) y-parameter matrix (d) ABCD parameter matrix 
1.5 The pole-zero pattern of a certain filter is shown in the figure below. The filter 
must be of the following type. 
(a) low pass (b) high pass 
(c) all pass (d) band pass 
x(t) 
t=T 
t 
×
× 
×
jw 
-1 
+1 
-j1 
-j2 
+j1
+j2 
1.6 The necessary and sufficient condition for a rational function of s. T(s) to be 
driving point impedance of an RC network is that all poles and zeros should be 
(a) simple and lie on the negative axis in the s-plane 
(b) complex and lie in the left half of the s-plane 
(c) complex and lie in the right half of the s-plane 
(d) simple and lie on the positive real axis of the s-plane 
1.7 In the signal flow graph of Figure, the gain c/r will be 
(a) 
11
9
(b) 
22
15
(c) 
24
23
(d) 
44
23
1.8 A second order system has a transfer function given by 
( )
2
25
8 25
G s
s s
=
+ +
If the system, initially at rest is subjected to a unit step input at t = 0, the 
second peak in response will occur at 
(a) p sec (b) sec
3
p
(c) 
2
sec
3
p
(d) sec
2
p
1.9 The open loop transfer function of a feedback control system is: 
( ) ( )
( )
3
1
1
G s H s
s
=
+
The gain margin of the system is: 
(a) 2 (b) 4 (c) 8 (d) 16 
1.10 A unity feedback control system has the open loop transfer function 
( )
( )
( )
2
4 1 2
2
s
G s
s s
+
=
+
If the input to the system is a unit ramp, the steady state error will be 
(a) 0 (b) 0.5 (c) 2 (d) infinity 
-1 
-1 -1 
1 1 C 
5 
T 
2 3 4 
1.11 The characteristic equation of a feedback control system is given by 
( )
3 2
5 6 0 s s K s K + + + + =
Where K > 0 is a scalar variable parameter. In the root loci diagram of the 
system the asymptotes of the root locus for large values of K meet at a point in 
the s-plane whose coordinates are 
(a) (-3,0) (b) (-2,0) (c) (-1,0) (d) (2,0) 
1.12  A linear second order single input continuous time system is described by the 
following set of differential equations  
( ) ( ) ( )
( ) ( ) ( ) ( )
1 1 2
2 1 2
2 4
2
x t x t x t
x t x t x t u t
= - +
= - +
Where ( ) ( )
1 2
 and x t x t are the state variables and ( ) u t is the control variable.
The system is:  
(a) controllable and stable (b) controllable but unstable  
(c) uncontrollable and unstable (d) uncontrollable and stable 
1.13 A linear time-invariant discrete-time system is described by the vector matrix 
difference equation 
( ) ( ) ( ) 1 x k FX k Gu k + = +
Where ( ) X k is the state vector, F is an n × n constant matrix, G is a
( ) n r × constant matrix and ( ) u k is the control vector. The state transition matrix
of the system is given by inverse Z-transform of 
(a) ZI - F (b) (ZI – F) Z (c) ( )
1
ZI F G
-
- (d) ( )
1
ZI F Z
-
-
1.14 A silicon sample is uniformly doped with 
16
10 phosphorous atoms/cm
3
 and 
16
2 10 × boron atoms/cm
3
. If all the dopants are fully ionized, the material is 
(a) n-type with carrier concentration of 
16 3
10 /cm
(b) p-type with carrier concentration of 
16 3
10 /cm
(c) p-type with carrier concentration of 
16 3
2 10 /cm ×
(d) 
2
T will get damaged and 
1
T will be safe 
1.15 An n-type silicon sample, having electron mobility 
n
µ = twice the hole mobility 
,
p
µ is subjected to a steady illumination such that the electron concentration 
doubles from its thermal equilibrium value. As a result, the conductivity of the 
sample increases by a factor of … 
1.16 The small signal capacitances of an abrupt 
1
P n - junction is 
2
1 / nF Cm at zero 
bias. If the built in voltage is 1 volt, the capacitance at a reverse bias voltage of 
99 volts is equal to … 
1.17 Referring to the figure. The switch S is in position 1 initially and steady state 
conditions exist from time t = 0 to 
0
. t t = The switch is suddenly thrown into 
position 2. The current 1 through the 10K resistor as a function of time t from t = 
0, is …. (Give the sketch showing the magnitudes of the current at t = 0, 
0
 and t t t = = 8 ) 
1.18 Discrete transistors 
1 2
 and T T having maximum collector current rating of 0.75 
amps are connected in parallel as shown in the figure. This combination is treated 
as a single transistor to carry a total current of 1 ampere, when biased with self 
bias circuit. When the circuit is switched on, 
1
T draws 0.55 amps and 
2
T draws 
0.45 amps. If the supply is kept on continuously, ultimately it is very likely that 
(a) both 
1 2
 and T T get damaged (b) both 
1 2
 and T T will be safe 
(c) 
1
T will get damaged and 
2
T will be safe 
(d) 
2
T will get damaged and 
1
T will be safe 
20V 
20V 
10K 
1 
S 
2 
T 1 T 2
Page 5


GATE ME - 1991
1.1 An excitation is applied to a system at t = T and its response is zero for 
. t T -8 < < Such a system is 
(a) non-causal system 
(b) stable system 
(c) causal system 
(d) unstable system 
1.2 In a series RLC high Q circuit, the current peaks at a frequency
(a) equal to the resonant frequency  
(b) greater than the resonant frequency  
(c) less than the resonant frequency  
(d) none of the above  
1.3 The voltage across an impedance in a network is ( ) ( ) ( ), V s z s I s = where V(s) ,
Z(s) are the Laplace transforms of the corresponding time function 
( ) ( ) ( ) , and . v t z t i t The voltage ( ) v t is:
(a) ( ) ( ) ( ) . t z t t ? ? = (b) ( ) ( ) ( )
1
0
. t i t z t d ? t t = -
?
(c) ( ) ( ) ( )
1
0
. t i t z t d ? t t = +
?
(d) ( ) ( ) ( ) t z t i t ? = +
1.4 Two two-port networks are connected in cascade. The combination is to be 
represented as a single two-port network. The parameters of the network are 
obtained by multiplying the individual  
(a) z-parameter matrix (b) h-parameter matrix 
(c) y-parameter matrix (d) ABCD parameter matrix 
1.5 The pole-zero pattern of a certain filter is shown in the figure below. The filter 
must be of the following type. 
(a) low pass (b) high pass 
(c) all pass (d) band pass 
x(t) 
t=T 
t 
×
× 
×
jw 
-1 
+1 
-j1 
-j2 
+j1
+j2 
1.6 The necessary and sufficient condition for a rational function of s. T(s) to be 
driving point impedance of an RC network is that all poles and zeros should be 
(a) simple and lie on the negative axis in the s-plane 
(b) complex and lie in the left half of the s-plane 
(c) complex and lie in the right half of the s-plane 
(d) simple and lie on the positive real axis of the s-plane 
1.7 In the signal flow graph of Figure, the gain c/r will be 
(a) 
11
9
(b) 
22
15
(c) 
24
23
(d) 
44
23
1.8 A second order system has a transfer function given by 
( )
2
25
8 25
G s
s s
=
+ +
If the system, initially at rest is subjected to a unit step input at t = 0, the 
second peak in response will occur at 
(a) p sec (b) sec
3
p
(c) 
2
sec
3
p
(d) sec
2
p
1.9 The open loop transfer function of a feedback control system is: 
( ) ( )
( )
3
1
1
G s H s
s
=
+
The gain margin of the system is: 
(a) 2 (b) 4 (c) 8 (d) 16 
1.10 A unity feedback control system has the open loop transfer function 
( )
( )
( )
2
4 1 2
2
s
G s
s s
+
=
+
If the input to the system is a unit ramp, the steady state error will be 
(a) 0 (b) 0.5 (c) 2 (d) infinity 
-1 
-1 -1 
1 1 C 
5 
T 
2 3 4 
1.11 The characteristic equation of a feedback control system is given by 
( )
3 2
5 6 0 s s K s K + + + + =
Where K > 0 is a scalar variable parameter. In the root loci diagram of the 
system the asymptotes of the root locus for large values of K meet at a point in 
the s-plane whose coordinates are 
(a) (-3,0) (b) (-2,0) (c) (-1,0) (d) (2,0) 
1.12  A linear second order single input continuous time system is described by the 
following set of differential equations  
( ) ( ) ( )
( ) ( ) ( ) ( )
1 1 2
2 1 2
2 4
2
x t x t x t
x t x t x t u t
= - +
= - +
Where ( ) ( )
1 2
 and x t x t are the state variables and ( ) u t is the control variable.
The system is:  
(a) controllable and stable (b) controllable but unstable  
(c) uncontrollable and unstable (d) uncontrollable and stable 
1.13 A linear time-invariant discrete-time system is described by the vector matrix 
difference equation 
( ) ( ) ( ) 1 x k FX k Gu k + = +
Where ( ) X k is the state vector, F is an n × n constant matrix, G is a
( ) n r × constant matrix and ( ) u k is the control vector. The state transition matrix
of the system is given by inverse Z-transform of 
(a) ZI - F (b) (ZI – F) Z (c) ( )
1
ZI F G
-
- (d) ( )
1
ZI F Z
-
-
1.14 A silicon sample is uniformly doped with 
16
10 phosphorous atoms/cm
3
 and 
16
2 10 × boron atoms/cm
3
. If all the dopants are fully ionized, the material is 
(a) n-type with carrier concentration of 
16 3
10 /cm
(b) p-type with carrier concentration of 
16 3
10 /cm
(c) p-type with carrier concentration of 
16 3
2 10 /cm ×
(d) 
2
T will get damaged and 
1
T will be safe 
1.15 An n-type silicon sample, having electron mobility 
n
µ = twice the hole mobility 
,
p
µ is subjected to a steady illumination such that the electron concentration 
doubles from its thermal equilibrium value. As a result, the conductivity of the 
sample increases by a factor of … 
1.16 The small signal capacitances of an abrupt 
1
P n - junction is 
2
1 / nF Cm at zero 
bias. If the built in voltage is 1 volt, the capacitance at a reverse bias voltage of 
99 volts is equal to … 
1.17 Referring to the figure. The switch S is in position 1 initially and steady state 
conditions exist from time t = 0 to 
0
. t t = The switch is suddenly thrown into 
position 2. The current 1 through the 10K resistor as a function of time t from t = 
0, is …. (Give the sketch showing the magnitudes of the current at t = 0, 
0
 and t t t = = 8 ) 
1.18 Discrete transistors 
1 2
 and T T having maximum collector current rating of 0.75 
amps are connected in parallel as shown in the figure. This combination is treated 
as a single transistor to carry a total current of 1 ampere, when biased with self 
bias circuit. When the circuit is switched on, 
1
T draws 0.55 amps and 
2
T draws 
0.45 amps. If the supply is kept on continuously, ultimately it is very likely that 
(a) both 
1 2
 and T T get damaged (b) both 
1 2
 and T T will be safe 
(c) 
1
T will get damaged and 
2
T will be safe 
(d) 
2
T will get damaged and 
1
T will be safe 
20V 
20V 
10K 
1 
S 
2 
T 1 T 2
GATE ME - 1991
1.19. The built-in potential of the gate junction of a n-channel JFET is 0.5 volts. The 
drain current saturates at 4.0
DS
V = volts when 0.
GS
V = The pinch off voltage is 
________. 
1.20. In figure, all transistors are identical and have a high value of beta. The voltage 
DC
V is equal to ______. 
1.21. In figure, both transistors are identical and have a high value of beta. Take the 
dc base-emitter voltage drop as 0.7 volt and KT/q = 25 mV. The small signal low 
frequency voltage gain ( )
o i
V V is equal to _______
Q 1 
Q 2 Q 3 
Q 4 
5mA 1kO 
10 volts 
V DC=? 
V i 
~ 
1kO 
1.2kO
10 volts 
-5.7 volts 
V O/V=?