Mechanical Engineering (ME) 1998 GATE Paper without solution Notes | Study GATE Past Year Papers for Practice (All Branches) - GATE

 Page 1


GATE ME - 1998
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 For ,
6
x
p
= the sum of the series ( )
2
2 4
1
cos cos cos
n
x x x
8
= + +
?
Kis 
(a) p (b) 3 (c) 8 (d) 1 
1.2 ( )
2
1 s
-
+ is the Laplace transform of
(a) 
2
t (b) 
3
t (c) 
2t
e
-
(d) 
t
te
-
0?0 
1.3 ( )
2
0
If ,
x
x tdt F =
?
then
d
dx
F
is: 
(a) 
2
2x (b) x (c) 0 (d) 1 
1.4 The magnitude of the gradient of the function ( )
3
 at 1,0,2 f xyz = is:
(a) 0 (b) 3 (c) 8 (d) 8 
1.5 The probability that two friends share the same birth-month is: 
(a) 
1
6
(b) 
1
12
(c) 
1
144
(d) 
1
24
1.6 A car moving with uniform acceleration covers 450 m in a 5 second interval, and 
covers 700 m in the next 5 second interval. The acceleration of the car is: 
(a) 7 m/s
2
 (b) 50 m/s
2
 (c) 25 m/s
2
 (d) 10 m/s
2
 
1.7 The buckling load for a column pinned at both ends is 10 kN. If the ends are 
fixed, the buckling load changes to 
(a) 40 kN (b) 2.5 kN (c) 5 kN (d) 20 k N 
1.8 The normal stresses at a point are 10 MPa
x
s = and, 2 MPa;
y
s = the shear stress 
at this point is 4 MPa. The maximum principal stress at this point is: 
(a) 16 MPa (b) 14 MPa (c) 11 MPa (d) 10 MPa
Page 2


GATE ME - 1998
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 For ,
6
x
p
= the sum of the series ( )
2
2 4
1
cos cos cos
n
x x x
8
= + +
?
Kis 
(a) p (b) 3 (c) 8 (d) 1 
1.2 ( )
2
1 s
-
+ is the Laplace transform of
(a) 
2
t (b) 
3
t (c) 
2t
e
-
(d) 
t
te
-
0?0 
1.3 ( )
2
0
If ,
x
x tdt F =
?
then
d
dx
F
is: 
(a) 
2
2x (b) x (c) 0 (d) 1 
1.4 The magnitude of the gradient of the function ( )
3
 at 1,0,2 f xyz = is:
(a) 0 (b) 3 (c) 8 (d) 8 
1.5 The probability that two friends share the same birth-month is: 
(a) 
1
6
(b) 
1
12
(c) 
1
144
(d) 
1
24
1.6 A car moving with uniform acceleration covers 450 m in a 5 second interval, and 
covers 700 m in the next 5 second interval. The acceleration of the car is: 
(a) 7 m/s
2
 (b) 50 m/s
2
 (c) 25 m/s
2
 (d) 10 m/s
2
 
1.7 The buckling load for a column pinned at both ends is 10 kN. If the ends are 
fixed, the buckling load changes to 
(a) 40 kN (b) 2.5 kN (c) 5 kN (d) 20 k N 
1.8 The normal stresses at a point are 10 MPa
x
s = and, 2 MPa;
y
s = the shear stress 
at this point is 4 MPa. The maximum principal stress at this point is: 
(a) 16 MPa (b) 14 MPa (c) 11 MPa (d) 10 MPa
GATE ME - 1998
1.9 The ratio of average shear stress to the maximum shear stress in a beam with a 
square cross-section is: 
(a) 1 (b) 
2
3
(c) 
3
2
(d) 2 
1.10 Heat transfer coefficient for free convection in gases, forced convection in gases 
and vapours, and for boiling water lie, respectively in the ranges of 
(a) 5 – 15, 20 – 200 and 3000 – 50,000 W/m
2
K. 
(b) 20 – 50, 200 – 500 and 50,000 – 10
5
 W/m
2
K. 
(c) 50 – 100, 500 – 1000 and 10
5
 – 10
6
 W/m
2
K. 
(d) 20 – 100, 200 – 1000, and a constant 10
6
 W/m
2
K. 
1.11 If 
N
V and a are the nozzle exit velocity and nozzle angle in an impulse turbine, 
the optimum blade velocity is given by 
(a) cos2
N
V a (b) sin2
N
V a (c) 
cos
2
N
V a
(d) 
2
2
N
V
1.12  A Curtis stage, Rateau stage and a 50% reaction stage in a steam turbine are 
examples of 
(a) different types of impulse stages 
(b) different types of reaction stages 
(c) a simple impulse stage, a velocity compounded impulse stage and reaction 
stage 
(d) a velocity compounded impulse stage, a simple impulse stage and a reaction 
stage 
1.13 The basic load rating of a ball bearing is 
(a) the maximum static radial load that can be applied without causing any 
plastic deformation of bearing component. 
(b) the radial load at which 90% of the group of apparently identical bearings 
run for one million revolutions before the first evidence of failure. 
(c) the maximum radial load that can be applied during operation without any 
plastic deformation of bearing components. 
(d) a combination of radial and axial loads that can be applied without any 
plastic deformation. 
1.14 Decreasing grain size in a polycrystalline material 
(a) increases yield strength and corrosion resistance 
(b) decreases yield strength and corrosion resistance 
(c) decreases yield strength but increases corrosion resistance  
(d) increases yield strength but decreases corrosion resistance. 
Page 3


GATE ME - 1998
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 For ,
6
x
p
= the sum of the series ( )
2
2 4
1
cos cos cos
n
x x x
8
= + +
?
Kis 
(a) p (b) 3 (c) 8 (d) 1 
1.2 ( )
2
1 s
-
+ is the Laplace transform of
(a) 
2
t (b) 
3
t (c) 
2t
e
-
(d) 
t
te
-
0?0 
1.3 ( )
2
0
If ,
x
x tdt F =
?
then
d
dx
F
is: 
(a) 
2
2x (b) x (c) 0 (d) 1 
1.4 The magnitude of the gradient of the function ( )
3
 at 1,0,2 f xyz = is:
(a) 0 (b) 3 (c) 8 (d) 8 
1.5 The probability that two friends share the same birth-month is: 
(a) 
1
6
(b) 
1
12
(c) 
1
144
(d) 
1
24
1.6 A car moving with uniform acceleration covers 450 m in a 5 second interval, and 
covers 700 m in the next 5 second interval. The acceleration of the car is: 
(a) 7 m/s
2
 (b) 50 m/s
2
 (c) 25 m/s
2
 (d) 10 m/s
2
 
1.7 The buckling load for a column pinned at both ends is 10 kN. If the ends are 
fixed, the buckling load changes to 
(a) 40 kN (b) 2.5 kN (c) 5 kN (d) 20 k N 
1.8 The normal stresses at a point are 10 MPa
x
s = and, 2 MPa;
y
s = the shear stress 
at this point is 4 MPa. The maximum principal stress at this point is: 
(a) 16 MPa (b) 14 MPa (c) 11 MPa (d) 10 MPa
GATE ME - 1998
1.9 The ratio of average shear stress to the maximum shear stress in a beam with a 
square cross-section is: 
(a) 1 (b) 
2
3
(c) 
3
2
(d) 2 
1.10 Heat transfer coefficient for free convection in gases, forced convection in gases 
and vapours, and for boiling water lie, respectively in the ranges of 
(a) 5 – 15, 20 – 200 and 3000 – 50,000 W/m
2
K. 
(b) 20 – 50, 200 – 500 and 50,000 – 10
5
 W/m
2
K. 
(c) 50 – 100, 500 – 1000 and 10
5
 – 10
6
 W/m
2
K. 
(d) 20 – 100, 200 – 1000, and a constant 10
6
 W/m
2
K. 
1.11 If 
N
V and a are the nozzle exit velocity and nozzle angle in an impulse turbine, 
the optimum blade velocity is given by 
(a) cos2
N
V a (b) sin2
N
V a (c) 
cos
2
N
V a
(d) 
2
2
N
V
1.12  A Curtis stage, Rateau stage and a 50% reaction stage in a steam turbine are 
examples of 
(a) different types of impulse stages 
(b) different types of reaction stages 
(c) a simple impulse stage, a velocity compounded impulse stage and reaction 
stage 
(d) a velocity compounded impulse stage, a simple impulse stage and a reaction 
stage 
1.13 The basic load rating of a ball bearing is 
(a) the maximum static radial load that can be applied without causing any 
plastic deformation of bearing component. 
(b) the radial load at which 90% of the group of apparently identical bearings 
run for one million revolutions before the first evidence of failure. 
(c) the maximum radial load that can be applied during operation without any 
plastic deformation of bearing components. 
(d) a combination of radial and axial loads that can be applied without any 
plastic deformation. 
1.14 Decreasing grain size in a polycrystalline material 
(a) increases yield strength and corrosion resistance 
(b) decreases yield strength and corrosion resistance 
(c) decreases yield strength but increases corrosion resistance  
(d) increases yield strength but decreases corrosion resistance. 
GATE ME - 1998
1.15 Auto collimator is used to check 
(a) roughness (b) flatness 
(c) angle (d) automobile balance 
1.16 Failure of a bead weld between a heavy steel section and a thin section is mainly 
due to the formation of  
(a) spheroidite   (b) bainite 
(c) carbon free zone due to burning of carbon at high temperature 
(d) martensite. 
1.17 Ideal surface roughness, as measured by the maximum height of unevenness, is 
best achieved when the material is removed by 
(a) an end mill   (b) a grinding wheel 
(c) a tool with zero nose radius (d) a ball mill 
1.18 In the specification of dimensions and fits, 
(a) allowance is equal to bilateral tolerance  
(b) allowance is equal to unilateral tolerance 
(c) allowance is independent of tolerance  
(d) allowance is equal to the difference between maximum and minimum 
dimension specified by the tolerance. 
1.19. In machining using abrasive material, increasing abrasive grain size 
(a) increases the material removal rate 
(b) decreases the material removal rate 
(c) first decreases and then increases the material removal rate 
(d) first increases and then decreases the material removal rate 
1.20. With increasing temperature of intake air, IC engine efficiency 
(a) decreases (b) increases 
(c) remains same (d) depends on other factors 
1.21. Chills are used in moulds to 
(a) achieve directional solidification  
(b) reduce the possibility of blowholes 
(c) reduce freezing time  
(d) smoothen metal flow for reducing splatter. 
Page 4


GATE ME - 1998
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 For ,
6
x
p
= the sum of the series ( )
2
2 4
1
cos cos cos
n
x x x
8
= + +
?
Kis 
(a) p (b) 3 (c) 8 (d) 1 
1.2 ( )
2
1 s
-
+ is the Laplace transform of
(a) 
2
t (b) 
3
t (c) 
2t
e
-
(d) 
t
te
-
0?0 
1.3 ( )
2
0
If ,
x
x tdt F =
?
then
d
dx
F
is: 
(a) 
2
2x (b) x (c) 0 (d) 1 
1.4 The magnitude of the gradient of the function ( )
3
 at 1,0,2 f xyz = is:
(a) 0 (b) 3 (c) 8 (d) 8 
1.5 The probability that two friends share the same birth-month is: 
(a) 
1
6
(b) 
1
12
(c) 
1
144
(d) 
1
24
1.6 A car moving with uniform acceleration covers 450 m in a 5 second interval, and 
covers 700 m in the next 5 second interval. The acceleration of the car is: 
(a) 7 m/s
2
 (b) 50 m/s
2
 (c) 25 m/s
2
 (d) 10 m/s
2
 
1.7 The buckling load for a column pinned at both ends is 10 kN. If the ends are 
fixed, the buckling load changes to 
(a) 40 kN (b) 2.5 kN (c) 5 kN (d) 20 k N 
1.8 The normal stresses at a point are 10 MPa
x
s = and, 2 MPa;
y
s = the shear stress 
at this point is 4 MPa. The maximum principal stress at this point is: 
(a) 16 MPa (b) 14 MPa (c) 11 MPa (d) 10 MPa
GATE ME - 1998
1.9 The ratio of average shear stress to the maximum shear stress in a beam with a 
square cross-section is: 
(a) 1 (b) 
2
3
(c) 
3
2
(d) 2 
1.10 Heat transfer coefficient for free convection in gases, forced convection in gases 
and vapours, and for boiling water lie, respectively in the ranges of 
(a) 5 – 15, 20 – 200 and 3000 – 50,000 W/m
2
K. 
(b) 20 – 50, 200 – 500 and 50,000 – 10
5
 W/m
2
K. 
(c) 50 – 100, 500 – 1000 and 10
5
 – 10
6
 W/m
2
K. 
(d) 20 – 100, 200 – 1000, and a constant 10
6
 W/m
2
K. 
1.11 If 
N
V and a are the nozzle exit velocity and nozzle angle in an impulse turbine, 
the optimum blade velocity is given by 
(a) cos2
N
V a (b) sin2
N
V a (c) 
cos
2
N
V a
(d) 
2
2
N
V
1.12  A Curtis stage, Rateau stage and a 50% reaction stage in a steam turbine are 
examples of 
(a) different types of impulse stages 
(b) different types of reaction stages 
(c) a simple impulse stage, a velocity compounded impulse stage and reaction 
stage 
(d) a velocity compounded impulse stage, a simple impulse stage and a reaction 
stage 
1.13 The basic load rating of a ball bearing is 
(a) the maximum static radial load that can be applied without causing any 
plastic deformation of bearing component. 
(b) the radial load at which 90% of the group of apparently identical bearings 
run for one million revolutions before the first evidence of failure. 
(c) the maximum radial load that can be applied during operation without any 
plastic deformation of bearing components. 
(d) a combination of radial and axial loads that can be applied without any 
plastic deformation. 
1.14 Decreasing grain size in a polycrystalline material 
(a) increases yield strength and corrosion resistance 
(b) decreases yield strength and corrosion resistance 
(c) decreases yield strength but increases corrosion resistance  
(d) increases yield strength but decreases corrosion resistance. 
GATE ME - 1998
1.15 Auto collimator is used to check 
(a) roughness (b) flatness 
(c) angle (d) automobile balance 
1.16 Failure of a bead weld between a heavy steel section and a thin section is mainly 
due to the formation of  
(a) spheroidite   (b) bainite 
(c) carbon free zone due to burning of carbon at high temperature 
(d) martensite. 
1.17 Ideal surface roughness, as measured by the maximum height of unevenness, is 
best achieved when the material is removed by 
(a) an end mill   (b) a grinding wheel 
(c) a tool with zero nose radius (d) a ball mill 
1.18 In the specification of dimensions and fits, 
(a) allowance is equal to bilateral tolerance  
(b) allowance is equal to unilateral tolerance 
(c) allowance is independent of tolerance  
(d) allowance is equal to the difference between maximum and minimum 
dimension specified by the tolerance. 
1.19. In machining using abrasive material, increasing abrasive grain size 
(a) increases the material removal rate 
(b) decreases the material removal rate 
(c) first decreases and then increases the material removal rate 
(d) first increases and then decreases the material removal rate 
1.20. With increasing temperature of intake air, IC engine efficiency 
(a) decreases (b) increases 
(c) remains same (d) depends on other factors 
1.21. Chills are used in moulds to 
(a) achieve directional solidification  
(b) reduce the possibility of blowholes 
(c) reduce freezing time  
(d) smoothen metal flow for reducing splatter. 
GATE ME - 1998
1.22. One of the following statements about PRS (Periodic Reordering System) is not 
true. Identify, 
(a) PRS requires continuous monitoring of inventory levels 
(b) PRS is useful in control of perishable items 
(c) PRS provides basis for adjustments to account for variations in demand 
(d) In PRS, inventory holding costs are higher than in Fixed Recorder Quantity 
System 
1.23. In inventory planning, extra inventory is unnecessarily carried to the end of the 
planning period when using one of the following lot size decision policies: 
(a) Lot – for – lot production 
(b) Economic Order Quantity (EOQ) lot size  
(c) Period Order Quantity (POQ) lot size 
(d) Part Period total cost balancing 
1.24. In a weaving operation, the parameter to be controlled is the number of defects 
per 10 square yards of material. Control chart appropriate for this task is 
(a) P - chart (b) C - chart (c) R - chart (d) X -Chart 
1.25 Which one of the following forecasting techniques is not suited for making 
forecasts for planning production schedules in the short range? 
(a) Moving average   (b) Exponential moving average 
(c) Regression analysis  (d) Delphi 
2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct.
2.1 The general solution of the differential equation 
2
2
2
0
d y dy
x x y
dx
dx
- + = is: 
(a) 
2
Ax Bx + (A,B are constants) 
(b) log Ax B x + (A,B are constants) 
(c) 
2
log Ax Bx x + (A,B are constants) 
(d) log Ax Bx x + (A,B are constants) 
2.2. The best fit line using least squares for the data (0,0), (10, 24), (20, 36) and 
(30,60) is: 
(a) 2x – y = 0   (b) 2x – y + 4 = 0 
(c) 2x – y – 4 = 0   (d) None of these 
Page 5


GATE ME - 1998
SECTION - A 
1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct. Indicate the correct answer by
darkening the appropriate bubble against the question number on the left hand
side of the Objective Response Sheet (ORS). You may use the answer book
provided for any rough work, if needed.
1.1 For ,
6
x
p
= the sum of the series ( )
2
2 4
1
cos cos cos
n
x x x
8
= + +
?
Kis 
(a) p (b) 3 (c) 8 (d) 1 
1.2 ( )
2
1 s
-
+ is the Laplace transform of
(a) 
2
t (b) 
3
t (c) 
2t
e
-
(d) 
t
te
-
0?0 
1.3 ( )
2
0
If ,
x
x tdt F =
?
then
d
dx
F
is: 
(a) 
2
2x (b) x (c) 0 (d) 1 
1.4 The magnitude of the gradient of the function ( )
3
 at 1,0,2 f xyz = is:
(a) 0 (b) 3 (c) 8 (d) 8 
1.5 The probability that two friends share the same birth-month is: 
(a) 
1
6
(b) 
1
12
(c) 
1
144
(d) 
1
24
1.6 A car moving with uniform acceleration covers 450 m in a 5 second interval, and 
covers 700 m in the next 5 second interval. The acceleration of the car is: 
(a) 7 m/s
2
 (b) 50 m/s
2
 (c) 25 m/s
2
 (d) 10 m/s
2
 
1.7 The buckling load for a column pinned at both ends is 10 kN. If the ends are 
fixed, the buckling load changes to 
(a) 40 kN (b) 2.5 kN (c) 5 kN (d) 20 k N 
1.8 The normal stresses at a point are 10 MPa
x
s = and, 2 MPa;
y
s = the shear stress 
at this point is 4 MPa. The maximum principal stress at this point is: 
(a) 16 MPa (b) 14 MPa (c) 11 MPa (d) 10 MPa
GATE ME - 1998
1.9 The ratio of average shear stress to the maximum shear stress in a beam with a 
square cross-section is: 
(a) 1 (b) 
2
3
(c) 
3
2
(d) 2 
1.10 Heat transfer coefficient for free convection in gases, forced convection in gases 
and vapours, and for boiling water lie, respectively in the ranges of 
(a) 5 – 15, 20 – 200 and 3000 – 50,000 W/m
2
K. 
(b) 20 – 50, 200 – 500 and 50,000 – 10
5
 W/m
2
K. 
(c) 50 – 100, 500 – 1000 and 10
5
 – 10
6
 W/m
2
K. 
(d) 20 – 100, 200 – 1000, and a constant 10
6
 W/m
2
K. 
1.11 If 
N
V and a are the nozzle exit velocity and nozzle angle in an impulse turbine, 
the optimum blade velocity is given by 
(a) cos2
N
V a (b) sin2
N
V a (c) 
cos
2
N
V a
(d) 
2
2
N
V
1.12  A Curtis stage, Rateau stage and a 50% reaction stage in a steam turbine are 
examples of 
(a) different types of impulse stages 
(b) different types of reaction stages 
(c) a simple impulse stage, a velocity compounded impulse stage and reaction 
stage 
(d) a velocity compounded impulse stage, a simple impulse stage and a reaction 
stage 
1.13 The basic load rating of a ball bearing is 
(a) the maximum static radial load that can be applied without causing any 
plastic deformation of bearing component. 
(b) the radial load at which 90% of the group of apparently identical bearings 
run for one million revolutions before the first evidence of failure. 
(c) the maximum radial load that can be applied during operation without any 
plastic deformation of bearing components. 
(d) a combination of radial and axial loads that can be applied without any 
plastic deformation. 
1.14 Decreasing grain size in a polycrystalline material 
(a) increases yield strength and corrosion resistance 
(b) decreases yield strength and corrosion resistance 
(c) decreases yield strength but increases corrosion resistance  
(d) increases yield strength but decreases corrosion resistance. 
GATE ME - 1998
1.15 Auto collimator is used to check 
(a) roughness (b) flatness 
(c) angle (d) automobile balance 
1.16 Failure of a bead weld between a heavy steel section and a thin section is mainly 
due to the formation of  
(a) spheroidite   (b) bainite 
(c) carbon free zone due to burning of carbon at high temperature 
(d) martensite. 
1.17 Ideal surface roughness, as measured by the maximum height of unevenness, is 
best achieved when the material is removed by 
(a) an end mill   (b) a grinding wheel 
(c) a tool with zero nose radius (d) a ball mill 
1.18 In the specification of dimensions and fits, 
(a) allowance is equal to bilateral tolerance  
(b) allowance is equal to unilateral tolerance 
(c) allowance is independent of tolerance  
(d) allowance is equal to the difference between maximum and minimum 
dimension specified by the tolerance. 
1.19. In machining using abrasive material, increasing abrasive grain size 
(a) increases the material removal rate 
(b) decreases the material removal rate 
(c) first decreases and then increases the material removal rate 
(d) first increases and then decreases the material removal rate 
1.20. With increasing temperature of intake air, IC engine efficiency 
(a) decreases (b) increases 
(c) remains same (d) depends on other factors 
1.21. Chills are used in moulds to 
(a) achieve directional solidification  
(b) reduce the possibility of blowholes 
(c) reduce freezing time  
(d) smoothen metal flow for reducing splatter. 
GATE ME - 1998
1.22. One of the following statements about PRS (Periodic Reordering System) is not 
true. Identify, 
(a) PRS requires continuous monitoring of inventory levels 
(b) PRS is useful in control of perishable items 
(c) PRS provides basis for adjustments to account for variations in demand 
(d) In PRS, inventory holding costs are higher than in Fixed Recorder Quantity 
System 
1.23. In inventory planning, extra inventory is unnecessarily carried to the end of the 
planning period when using one of the following lot size decision policies: 
(a) Lot – for – lot production 
(b) Economic Order Quantity (EOQ) lot size  
(c) Period Order Quantity (POQ) lot size 
(d) Part Period total cost balancing 
1.24. In a weaving operation, the parameter to be controlled is the number of defects 
per 10 square yards of material. Control chart appropriate for this task is 
(a) P - chart (b) C - chart (c) R - chart (d) X -Chart 
1.25 Which one of the following forecasting techniques is not suited for making 
forecasts for planning production schedules in the short range? 
(a) Moving average   (b) Exponential moving average 
(c) Regression analysis  (d) Delphi 
2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks
each.  For each of these sub-questions, four possible alternatives (A, B, C and D)
are given, out of which ONLY ONE is correct.
2.1 The general solution of the differential equation 
2
2
2
0
d y dy
x x y
dx
dx
- + = is: 
(a) 
2
Ax Bx + (A,B are constants) 
(b) log Ax B x + (A,B are constants) 
(c) 
2
log Ax Bx x + (A,B are constants) 
(d) log Ax Bx x + (A,B are constants) 
2.2. The best fit line using least squares for the data (0,0), (10, 24), (20, 36) and 
(30,60) is: 
(a) 2x – y = 0   (b) 2x – y + 4 = 0 
(c) 2x – y – 4 = 0   (d) None of these 
GATE ME - 1998
2.3. The maximum principal strain in a thin cylindrical tank, having a radius of 25 cm 
and wall thickness of 5 mm when subjected to an internal pressure of 1 MPa, is 
(taking Young’s modulus as 200 GPa and Poisson’s ratio as 0.2)  
(a) 
4
2.25 10
-
× (b) 2.25 (c) 
6
2.25 10
-
× (d) 22.5 
2.4. A square bar of side 4 cm and length 100 cm is subjected to an axial load P. the 
same bar is then used as a cantilever beam and subjected to an end load P. the 
ratio of the strain energies, stored in the bar is the second case to that stored in 
the first case, is: 
(a) 16 (b) 400 (c) 1000 (d) 2500 
2.5. An IC engine has a bore and stroke of 2 units each. The area to calculate heat 
loss can be taken as  
(a) 4p (b) 5p (c) 6p (d) 8p 
2.6. An air breathing aircraft is flying at an altitude where the air density is half the 
value at ground level. With reference to the ground level, the air-fuel ratio at this 
altitude will be  
(a) 
3
2 (b) 2 (c) 2 (d) 4 
2.7. For the data listed below for two journal bearings A and B, predict the flow 
conditions in the bearings 
Bearing 
Diameter 
(m) 
Radial 
clearance 
(m) 
Surface 
speed of 
shaft (m/s) 
Viscosity of 
lubricant 
(Pa – s) 
Density of 
lubricant 
(kg/m
3
) 
A 0.01 10
-5
210 0.001 1000 
B 0.05 10
-4
10 0.01 850 
(a) laminar in both A and B (b) turbulent in both A and B 
(c) Laminar in A and turbulent in B (d) turbulent in A and laminar B 
2.8. The isentropic heat drop in the nozzle of an impulse steam turbine with a nozzle 
efficiency 0.9, blade velocity ratio 0.5, and mean blade velocity 150 m/s in kJ/kg 
is 
(a) 50 (b) 40 (c) 60 (d) 75 
2.9. Air ( )
P
C 1 / , 1.4 kJ kg ? = = enters a compressor at a temperature of 27°C. the
compressor pressure ratio is 4. Assuming an efficiency of 80%, the compressor 
work required in kJ/kg is 
(a) 160 (b) 172 (c) 182 (d) 225