Mechanical Engineering (ME) 2011 GATE Paper with solution - GATE Past Year Papers for Practice (All Branches)

 Page 1


?ME-Paper Code-A? GATE 2011
     1 
Q. No. 1 – 25 Carry One Mark Each 
1. A streamline and an equipotential line in a flow field
(A) Are parallel to each other (B) Are perpendicular to each other 
(C) Intersect at an acute angle (D) Are identical 
Answer: - (B) 
Explanation:-
dy dy
1
dx dx
f ?
? ? ? ?
× = -
? ? ? ?
? ? ? ?
 
Slope of equipotential Line × slope of stream function= -1
They are orthogonal to each line other. 
2. If a mass of moist air in an airtight vessel is heated to a higher temperature,
then
(A) Specific humidity of the air increases
(B) Specific humidity of the air decreases
(C) Relative humidity of the air increases
(D) Relative humidity of the air decreases
Answer: - (D) 
Explanation:- R.H. Decreases
3. In a condenser of a power plant, the steam condenses at a temperature of 
0
60 C . 
The cooling water enters at 
0
30 C and leaves at 
0
45 C . The logarithmic mean 
temperature difference (LMTD) of the condenser is
(A) 
0
16.2 C (B) 
0
21.6 C (C) 
0
30 C (D) 
0
37.5 C 
Answer: - (B) 
Explanation: - Flow configuration in condenser as shown below. 
O
1
T 30 C ? = ,
O
2
T 15 C ? = ,
O 1 2
1
2
T T 30 15
LMTD 21.6 C
30 T
ln
ln
15
T
? - ? -
= = =
? ? ? ? ?
? ? ? ?
? ? ?
? ?
O
60 C 
O
60 C 
O
45 C 
O
30 C
100% f = 
Heating 
? 
O
DBT C
Page 2


?ME-Paper Code-A? GATE 2011
     1 
Q. No. 1 – 25 Carry One Mark Each 
1. A streamline and an equipotential line in a flow field
(A) Are parallel to each other (B) Are perpendicular to each other 
(C) Intersect at an acute angle (D) Are identical 
Answer: - (B) 
Explanation:-
dy dy
1
dx dx
f ?
? ? ? ?
× = -
? ? ? ?
? ? ? ?
 
Slope of equipotential Line × slope of stream function= -1
They are orthogonal to each line other. 
2. If a mass of moist air in an airtight vessel is heated to a higher temperature,
then
(A) Specific humidity of the air increases
(B) Specific humidity of the air decreases
(C) Relative humidity of the air increases
(D) Relative humidity of the air decreases
Answer: - (D) 
Explanation:- R.H. Decreases
3. In a condenser of a power plant, the steam condenses at a temperature of 
0
60 C . 
The cooling water enters at 
0
30 C and leaves at 
0
45 C . The logarithmic mean 
temperature difference (LMTD) of the condenser is
(A) 
0
16.2 C (B) 
0
21.6 C (C) 
0
30 C (D) 
0
37.5 C 
Answer: - (B) 
Explanation: - Flow configuration in condenser as shown below. 
O
1
T 30 C ? = ,
O
2
T 15 C ? = ,
O 1 2
1
2
T T 30 15
LMTD 21.6 C
30 T
ln
ln
15
T
? - ? -
= = =
? ? ? ? ?
? ? ? ?
? ? ?
? ?
O
60 C 
O
60 C 
O
45 C 
O
30 C
100% f = 
Heating 
? 
O
DBT C
?ME-Paper Code-A? GATE 2011
     2 
4. A simply supported beam PQ is loaded by a moment of 1kN-m at the mid-span of
the beam as shown in the figure. The reaction forces 
P
R and 
Q
R at supports P
and Q respectively are
(A) 1kN downward, 1kN upward (B) 0.5kN upward, 0.5kN downward 
(C) 0.5kN downward, 0.5kNupward (D) 1kN upward, 1kN upward 
Answer: - (A) 
Explanation: - Take moments about ‘Q’ 
Q
R 1 1 0 × - = ? = ?
Q
R 1kN
But + = ? = - = - = ?
P Q P Q P
R R 0 R R lkN or R lkN
5. A double – parallelogram mechanism is shown in the figure. Note that PQ is a
single link. The mobility of the mechanism is
(A) -1 (B) 0 (C) 1 (D) 2 
Answer: - (C) 
6. The maximum possible draft in cold rolling of sheet increases with the
(A) Increase in coefficient of friction (B) Decrease in coefficient of friction 
(C) Decrease in roll radius (D) Increase in roll velocity 
Answer: - (A) 
7. The operation in which oil is permeated into the pores of a powder metallurgy
product is known as
(A) Mixing (B) Sintering (C) Impregnation (D) Infiltration
Answer: - (C) 
8. A hole is dimension
0.015
0
9
+
+
f mm. The corresponding shaft is of dimension 
0.010
0.001
9
+
+
f mm. The resulting assembly has 
(A) Loose running fit (B) Close running fit 
(C) Transition fit (D) Interference fit 
Answer: - (C) 
P Q
P Q
1 kN m -
1m
Page 3


?ME-Paper Code-A? GATE 2011
     1 
Q. No. 1 – 25 Carry One Mark Each 
1. A streamline and an equipotential line in a flow field
(A) Are parallel to each other (B) Are perpendicular to each other 
(C) Intersect at an acute angle (D) Are identical 
Answer: - (B) 
Explanation:-
dy dy
1
dx dx
f ?
? ? ? ?
× = -
? ? ? ?
? ? ? ?
 
Slope of equipotential Line × slope of stream function= -1
They are orthogonal to each line other. 
2. If a mass of moist air in an airtight vessel is heated to a higher temperature,
then
(A) Specific humidity of the air increases
(B) Specific humidity of the air decreases
(C) Relative humidity of the air increases
(D) Relative humidity of the air decreases
Answer: - (D) 
Explanation:- R.H. Decreases
3. In a condenser of a power plant, the steam condenses at a temperature of 
0
60 C . 
The cooling water enters at 
0
30 C and leaves at 
0
45 C . The logarithmic mean 
temperature difference (LMTD) of the condenser is
(A) 
0
16.2 C (B) 
0
21.6 C (C) 
0
30 C (D) 
0
37.5 C 
Answer: - (B) 
Explanation: - Flow configuration in condenser as shown below. 
O
1
T 30 C ? = ,
O
2
T 15 C ? = ,
O 1 2
1
2
T T 30 15
LMTD 21.6 C
30 T
ln
ln
15
T
? - ? -
= = =
? ? ? ? ?
? ? ? ?
? ? ?
? ?
O
60 C 
O
60 C 
O
45 C 
O
30 C
100% f = 
Heating 
? 
O
DBT C
?ME-Paper Code-A? GATE 2011
     2 
4. A simply supported beam PQ is loaded by a moment of 1kN-m at the mid-span of
the beam as shown in the figure. The reaction forces 
P
R and 
Q
R at supports P
and Q respectively are
(A) 1kN downward, 1kN upward (B) 0.5kN upward, 0.5kN downward 
(C) 0.5kN downward, 0.5kNupward (D) 1kN upward, 1kN upward 
Answer: - (A) 
Explanation: - Take moments about ‘Q’ 
Q
R 1 1 0 × - = ? = ?
Q
R 1kN
But + = ? = - = - = ?
P Q P Q P
R R 0 R R lkN or R lkN
5. A double – parallelogram mechanism is shown in the figure. Note that PQ is a
single link. The mobility of the mechanism is
(A) -1 (B) 0 (C) 1 (D) 2 
Answer: - (C) 
6. The maximum possible draft in cold rolling of sheet increases with the
(A) Increase in coefficient of friction (B) Decrease in coefficient of friction 
(C) Decrease in roll radius (D) Increase in roll velocity 
Answer: - (A) 
7. The operation in which oil is permeated into the pores of a powder metallurgy
product is known as
(A) Mixing (B) Sintering (C) Impregnation (D) Infiltration
Answer: - (C) 
8. A hole is dimension
0.015
0
9
+
+
f mm. The corresponding shaft is of dimension 
0.010
0.001
9
+
+
f mm. The resulting assembly has 
(A) Loose running fit (B) Close running fit 
(C) Transition fit (D) Interference fit 
Answer: - (C) 
P Q
P Q
1 kN m -
1m
?ME-Paper Code-A? GATE 2011
     3 
9. Heat and work are
(A) Intensive properties (B) Extensive properties 
(C) Point functions (D) Path functions 
Answer: - (D) 
Explanation: - Heat and work are path functions. 
Since dQ and dW are dependent on path followed between two given end states
of a thermodynamic process undergone by system. 
10. A column has a rectangular cross-section of 10mm x 20mm and a length of 1m.
The slenderness ratio of the column is close to
(A) 200 (B) 346 (C) 477 (D) 1000
Answer: - (B) 
Explanation:- 
= =
=
min
min xx yy
lengthof column L
Slenderness ratio
least radiusof gyration K
I
But K
A
WhereI is minimum area moment of inertia i.e. I or I , whicever is less.
For the given section 
×
= =
3
3
min
20 10
I 1667mm
12
? = =
×
1667
K 2.89
20 10
and  = =
1000
ratio 346
2.89
11. A series expansion for the function sin? is
(A) 
2 4
1 ....
2! 4!
? ?
- + - (B) 
3 5
....
3! 5!
? ?
?- + - 
(C) 
2 3
1 ....
2! 3!
? ?
+ ?+ + + (D) 
3 5
....
3! 5!
? ?
?+ + + 
Answer:- (B) 
Explanation:- 
3 5
x x
Sinx=x ....
3! 5!
- + - 
12. Green sand mould indicates that
(A) Polymeric mould has been cured (B) Mould has been totally dried
(C) Mould is green in colour (D) Mould contains moisture
Answer: - (D) 
13. What is 
0
sin
lim
??
?
?
 equal to? 
(A) ? (B) sin? (C) 0 (D) 1 
Answer: - (D) 
Explanation: - Applying L’ Hospitals rule, we have 
0
Cos
lim Cos0 1
1
??
?
= = 
Page 4


?ME-Paper Code-A? GATE 2011
     1 
Q. No. 1 – 25 Carry One Mark Each 
1. A streamline and an equipotential line in a flow field
(A) Are parallel to each other (B) Are perpendicular to each other 
(C) Intersect at an acute angle (D) Are identical 
Answer: - (B) 
Explanation:-
dy dy
1
dx dx
f ?
? ? ? ?
× = -
? ? ? ?
? ? ? ?
 
Slope of equipotential Line × slope of stream function= -1
They are orthogonal to each line other. 
2. If a mass of moist air in an airtight vessel is heated to a higher temperature,
then
(A) Specific humidity of the air increases
(B) Specific humidity of the air decreases
(C) Relative humidity of the air increases
(D) Relative humidity of the air decreases
Answer: - (D) 
Explanation:- R.H. Decreases
3. In a condenser of a power plant, the steam condenses at a temperature of 
0
60 C . 
The cooling water enters at 
0
30 C and leaves at 
0
45 C . The logarithmic mean 
temperature difference (LMTD) of the condenser is
(A) 
0
16.2 C (B) 
0
21.6 C (C) 
0
30 C (D) 
0
37.5 C 
Answer: - (B) 
Explanation: - Flow configuration in condenser as shown below. 
O
1
T 30 C ? = ,
O
2
T 15 C ? = ,
O 1 2
1
2
T T 30 15
LMTD 21.6 C
30 T
ln
ln
15
T
? - ? -
= = =
? ? ? ? ?
? ? ? ?
? ? ?
? ?
O
60 C 
O
60 C 
O
45 C 
O
30 C
100% f = 
Heating 
? 
O
DBT C
?ME-Paper Code-A? GATE 2011
     2 
4. A simply supported beam PQ is loaded by a moment of 1kN-m at the mid-span of
the beam as shown in the figure. The reaction forces 
P
R and 
Q
R at supports P
and Q respectively are
(A) 1kN downward, 1kN upward (B) 0.5kN upward, 0.5kN downward 
(C) 0.5kN downward, 0.5kNupward (D) 1kN upward, 1kN upward 
Answer: - (A) 
Explanation: - Take moments about ‘Q’ 
Q
R 1 1 0 × - = ? = ?
Q
R 1kN
But + = ? = - = - = ?
P Q P Q P
R R 0 R R lkN or R lkN
5. A double – parallelogram mechanism is shown in the figure. Note that PQ is a
single link. The mobility of the mechanism is
(A) -1 (B) 0 (C) 1 (D) 2 
Answer: - (C) 
6. The maximum possible draft in cold rolling of sheet increases with the
(A) Increase in coefficient of friction (B) Decrease in coefficient of friction 
(C) Decrease in roll radius (D) Increase in roll velocity 
Answer: - (A) 
7. The operation in which oil is permeated into the pores of a powder metallurgy
product is known as
(A) Mixing (B) Sintering (C) Impregnation (D) Infiltration
Answer: - (C) 
8. A hole is dimension
0.015
0
9
+
+
f mm. The corresponding shaft is of dimension 
0.010
0.001
9
+
+
f mm. The resulting assembly has 
(A) Loose running fit (B) Close running fit 
(C) Transition fit (D) Interference fit 
Answer: - (C) 
P Q
P Q
1 kN m -
1m
?ME-Paper Code-A? GATE 2011
     3 
9. Heat and work are
(A) Intensive properties (B) Extensive properties 
(C) Point functions (D) Path functions 
Answer: - (D) 
Explanation: - Heat and work are path functions. 
Since dQ and dW are dependent on path followed between two given end states
of a thermodynamic process undergone by system. 
10. A column has a rectangular cross-section of 10mm x 20mm and a length of 1m.
The slenderness ratio of the column is close to
(A) 200 (B) 346 (C) 477 (D) 1000
Answer: - (B) 
Explanation:- 
= =
=
min
min xx yy
lengthof column L
Slenderness ratio
least radiusof gyration K
I
But K
A
WhereI is minimum area moment of inertia i.e. I or I , whicever is less.
For the given section 
×
= =
3
3
min
20 10
I 1667mm
12
? = =
×
1667
K 2.89
20 10
and  = =
1000
ratio 346
2.89
11. A series expansion for the function sin? is
(A) 
2 4
1 ....
2! 4!
? ?
- + - (B) 
3 5
....
3! 5!
? ?
?- + - 
(C) 
2 3
1 ....
2! 3!
? ?
+ ?+ + + (D) 
3 5
....
3! 5!
? ?
?+ + + 
Answer:- (B) 
Explanation:- 
3 5
x x
Sinx=x ....
3! 5!
- + - 
12. Green sand mould indicates that
(A) Polymeric mould has been cured (B) Mould has been totally dried
(C) Mould is green in colour (D) Mould contains moisture
Answer: - (D) 
13. What is 
0
sin
lim
??
?
?
 equal to? 
(A) ? (B) sin? (C) 0 (D) 1 
Answer: - (D) 
Explanation: - Applying L’ Hospitals rule, we have 
0
Cos
lim Cos0 1
1
??
?
= = 
?ME-Paper Code-A? GATE 2011
     4 
14. Eigen values of a real symmetric matrix are always
(A) Positive  (B) Negative (C) Real (D) Complex 
Answer: - (C) 
Explanation: - Eigen values of a real symmetric matrix are always real 
15. A pipe of 25mm outer diameter carries steam. The heat transfer coefficient
between the cylinder and surroundings is 
2
5W /m K . It is proposed to reduce the 
heat loss from the pipe by adding insulation having a thermal conductivity of
0.05W/mK. Which one of the following statements is TRUE?
(A) The outer radius of the pipe is equal to the critical radius
(B) The outer radius of the pipe is less than the critical radius
(C) Adding the insulation will reduce the heat loss
(D) Adding the insulation will increase the heat loss
Answer: - (C) 
Explanation: -Critical Radius of Insulation = 
k
h
? ?
? ?
? ?
O.05
m 10mm
5
? ?
= =
? ?
? ?
 
( ) >
outer critical
r r ? Adding insulation shall decrease H.T. Rate.
16. The contents of a well-insulated tank are heated by a resistor of 23O in which
10A current is flowing. Consider the tank along with its contents as a
thermodynamic system. The work done by the system and the heat transfer to
the system are positive. The rates of heat (Q), work (W) and change in internal
energy ( ) U ? during the process in kW are
(A) Q 0,W 2.3, U 2.3 = = - ? = + (B) Q 2.3,W 0, U 2.3 = + = ? = +
(C) Q 2.3,W 0, U 2.3 = - = ? = - (D) Q 0,W 2.3, U 2.3 = = + ? = -
Answer: - (A) 
Explanation: - 
( ) ( )
2 2
electric
W i R 10 20 watts 2.3kw on system = = × = -
Ilaw :- w U f- = ?
( )
elect
O W u - - = ?
i 10A =
23O
V
= Q 0 adiabatic 
Page 5


?ME-Paper Code-A? GATE 2011
     1 
Q. No. 1 – 25 Carry One Mark Each 
1. A streamline and an equipotential line in a flow field
(A) Are parallel to each other (B) Are perpendicular to each other 
(C) Intersect at an acute angle (D) Are identical 
Answer: - (B) 
Explanation:-
dy dy
1
dx dx
f ?
? ? ? ?
× = -
? ? ? ?
? ? ? ?
 
Slope of equipotential Line × slope of stream function= -1
They are orthogonal to each line other. 
2. If a mass of moist air in an airtight vessel is heated to a higher temperature,
then
(A) Specific humidity of the air increases
(B) Specific humidity of the air decreases
(C) Relative humidity of the air increases
(D) Relative humidity of the air decreases
Answer: - (D) 
Explanation:- R.H. Decreases
3. In a condenser of a power plant, the steam condenses at a temperature of 
0
60 C . 
The cooling water enters at 
0
30 C and leaves at 
0
45 C . The logarithmic mean 
temperature difference (LMTD) of the condenser is
(A) 
0
16.2 C (B) 
0
21.6 C (C) 
0
30 C (D) 
0
37.5 C 
Answer: - (B) 
Explanation: - Flow configuration in condenser as shown below. 
O
1
T 30 C ? = ,
O
2
T 15 C ? = ,
O 1 2
1
2
T T 30 15
LMTD 21.6 C
30 T
ln
ln
15
T
? - ? -
= = =
? ? ? ? ?
? ? ? ?
? ? ?
? ?
O
60 C 
O
60 C 
O
45 C 
O
30 C
100% f = 
Heating 
? 
O
DBT C
?ME-Paper Code-A? GATE 2011
     2 
4. A simply supported beam PQ is loaded by a moment of 1kN-m at the mid-span of
the beam as shown in the figure. The reaction forces 
P
R and 
Q
R at supports P
and Q respectively are
(A) 1kN downward, 1kN upward (B) 0.5kN upward, 0.5kN downward 
(C) 0.5kN downward, 0.5kNupward (D) 1kN upward, 1kN upward 
Answer: - (A) 
Explanation: - Take moments about ‘Q’ 
Q
R 1 1 0 × - = ? = ?
Q
R 1kN
But + = ? = - = - = ?
P Q P Q P
R R 0 R R lkN or R lkN
5. A double – parallelogram mechanism is shown in the figure. Note that PQ is a
single link. The mobility of the mechanism is
(A) -1 (B) 0 (C) 1 (D) 2 
Answer: - (C) 
6. The maximum possible draft in cold rolling of sheet increases with the
(A) Increase in coefficient of friction (B) Decrease in coefficient of friction 
(C) Decrease in roll radius (D) Increase in roll velocity 
Answer: - (A) 
7. The operation in which oil is permeated into the pores of a powder metallurgy
product is known as
(A) Mixing (B) Sintering (C) Impregnation (D) Infiltration
Answer: - (C) 
8. A hole is dimension
0.015
0
9
+
+
f mm. The corresponding shaft is of dimension 
0.010
0.001
9
+
+
f mm. The resulting assembly has 
(A) Loose running fit (B) Close running fit 
(C) Transition fit (D) Interference fit 
Answer: - (C) 
P Q
P Q
1 kN m -
1m
?ME-Paper Code-A? GATE 2011
     3 
9. Heat and work are
(A) Intensive properties (B) Extensive properties 
(C) Point functions (D) Path functions 
Answer: - (D) 
Explanation: - Heat and work are path functions. 
Since dQ and dW are dependent on path followed between two given end states
of a thermodynamic process undergone by system. 
10. A column has a rectangular cross-section of 10mm x 20mm and a length of 1m.
The slenderness ratio of the column is close to
(A) 200 (B) 346 (C) 477 (D) 1000
Answer: - (B) 
Explanation:- 
= =
=
min
min xx yy
lengthof column L
Slenderness ratio
least radiusof gyration K
I
But K
A
WhereI is minimum area moment of inertia i.e. I or I , whicever is less.
For the given section 
×
= =
3
3
min
20 10
I 1667mm
12
? = =
×
1667
K 2.89
20 10
and  = =
1000
ratio 346
2.89
11. A series expansion for the function sin? is
(A) 
2 4
1 ....
2! 4!
? ?
- + - (B) 
3 5
....
3! 5!
? ?
?- + - 
(C) 
2 3
1 ....
2! 3!
? ?
+ ?+ + + (D) 
3 5
....
3! 5!
? ?
?+ + + 
Answer:- (B) 
Explanation:- 
3 5
x x
Sinx=x ....
3! 5!
- + - 
12. Green sand mould indicates that
(A) Polymeric mould has been cured (B) Mould has been totally dried
(C) Mould is green in colour (D) Mould contains moisture
Answer: - (D) 
13. What is 
0
sin
lim
??
?
?
 equal to? 
(A) ? (B) sin? (C) 0 (D) 1 
Answer: - (D) 
Explanation: - Applying L’ Hospitals rule, we have 
0
Cos
lim Cos0 1
1
??
?
= = 
?ME-Paper Code-A? GATE 2011
     4 
14. Eigen values of a real symmetric matrix are always
(A) Positive  (B) Negative (C) Real (D) Complex 
Answer: - (C) 
Explanation: - Eigen values of a real symmetric matrix are always real 
15. A pipe of 25mm outer diameter carries steam. The heat transfer coefficient
between the cylinder and surroundings is 
2
5W /m K . It is proposed to reduce the 
heat loss from the pipe by adding insulation having a thermal conductivity of
0.05W/mK. Which one of the following statements is TRUE?
(A) The outer radius of the pipe is equal to the critical radius
(B) The outer radius of the pipe is less than the critical radius
(C) Adding the insulation will reduce the heat loss
(D) Adding the insulation will increase the heat loss
Answer: - (C) 
Explanation: -Critical Radius of Insulation = 
k
h
? ?
? ?
? ?
O.05
m 10mm
5
? ?
= =
? ?
? ?
 
( ) >
outer critical
r r ? Adding insulation shall decrease H.T. Rate.
16. The contents of a well-insulated tank are heated by a resistor of 23O in which
10A current is flowing. Consider the tank along with its contents as a
thermodynamic system. The work done by the system and the heat transfer to
the system are positive. The rates of heat (Q), work (W) and change in internal
energy ( ) U ? during the process in kW are
(A) Q 0,W 2.3, U 2.3 = = - ? = + (B) Q 2.3,W 0, U 2.3 = + = ? = +
(C) Q 2.3,W 0, U 2.3 = - = ? = - (D) Q 0,W 2.3, U 2.3 = = + ? = -
Answer: - (A) 
Explanation: - 
( ) ( )
2 2
electric
W i R 10 20 watts 2.3kw on system = = × = -
Ilaw :- w U f- = ?
( )
elect
O W u - - = ?
i 10A =
23O
V
= Q 0 adiabatic 
?ME-Paper Code-A? GATE 2011
     5 
17. Match the following criteria of material failure, under biaxial stresses
1
s and
2
s
and yield stress 
y
s , with their corresponding graphic representations :
P.  Maximum-normal-stress criterion L. 
Q. Maximum-distortion-energy criterion M. 
R. Maximum-shear–stress criterion N. 
(A) P-M, Q-L, R-N (B) P-N, Q-M, R-L (C) P-M, Q-N, R-L (D) P-N, Q-L,R-M 
Answer: - (C) 
18. The product of two complex numbers 1 i + and 2-5i is
(A) 7-3i (B) 3-4i (C) -3-4i (D) 7+3i 
Answer: - (A) 
Explanation: - ( )( ) 1 i 2 5i 2 5i 2i 5 + - = - + + 7 3i = -
19. Cars arrive at a service station according to Poisson’s distribution with a mean
rate of 5 per hour. The service time per car is exponential with a mean of
10minutes. At steady state, the average waiting time in the queue is
(A) 10 minutes (B) 20 minutes (C) 25 minutes (D) 50 minutes 
Answer: - (D) 
? ?
= ? = µ = ? = = ? = = =
µ- ? µ -
5
5 5
6
Wq ; Where 5/hr, 6/hr, ; Wq hr 50min
6 6 5 6
 
20. The word kanban is most appropriately associated with
(A) Economic order quantity (B) Just–in–time production 
(C) Capacity planning (D) Product design 
Answer: - (B) 
y
s
2
s
1
s
y
s
y
-s
y
-s
y
s
2
s
1
s
y
s
y
-s
y
-s
y
s
2
s
1
s
y
s
y
-s
y
-s