GATE  >  Mechanical Engineering (ME) 1991 GATE Paper without solution

# 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=?
```

## GATE Past Year Papers for Practice (All Branches)

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

 1. What is the significance of the GATE exam for Mechanical Engineering (ME) in 1991? Ans. The GATE exam is an important national level examination for Mechanical Engineering (ME) conducted in India. It serves as a gateway for admission to postgraduate programs in prestigious institutes, recruitment in public sector undertakings (PSUs), and eligibility for scholarships. The 1991 GATE paper specifically refers to the question paper of that year, which can provide insights into the exam pattern and syllabus during that time.
 2. Can I find the solutions to the 1991 GATE Mechanical Engineering (ME) paper? Ans. Unfortunately, the provided article does not include the solutions to the 1991 GATE Mechanical Engineering (ME) paper. However, there are various online platforms and study materials available that may provide solutions or explanations for the questions from that year's paper.
 3. What are some important topics to focus on for the GATE Mechanical Engineering (ME) exam? Ans. The GATE Mechanical Engineering (ME) exam covers a wide range of topics. Some important areas to focus on include engineering mathematics, mechanics, strength of materials, thermodynamics, fluid mechanics, manufacturing processes, and machine design. It is recommended to refer to the official GATE syllabus and previous year question papers to understand the weightage of different topics.
 4. How can I prepare effectively for the GATE Mechanical Engineering (ME) exam? Ans. Effective preparation for the GATE Mechanical Engineering (ME) exam requires a structured approach. Start by understanding the syllabus and exam pattern. Create a study plan and allocate sufficient time for each topic. Utilize standard textbooks, reference materials, and online resources for study material. Solve previous year question papers and take mock tests to improve time management and identify weak areas. Regular practice, revision, and seeking guidance from experienced mentors or coaching institutes can significantly enhance your preparation.
 5. Does a good GATE score guarantee admission to top institutes for postgraduate programs in Mechanical Engineering (ME)? Ans. While a good GATE score is an essential requirement for admission to top institutes for postgraduate programs in Mechanical Engineering (ME), it does not guarantee admission solely. The admission process also considers factors like the number of available seats, the cutoff scores of the specific institute, and the candidate's performance in interviews or other selection rounds. It is advisable to research and apply to multiple institutes, considering their individual admission criteria and preferences.

## GATE Past Year Papers for Practice (All Branches)

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