GATE Sample Paper for Production and Industrial Engineering

Sample Paper aglase .co

PI: Production and Industrial Engineering

a b
Q.No. 1 The solution of ∫ is
dx dy
∫
1 1 xy

(A) ln( ab)

(B) ln( a/b)

(C) ln( a ) + ln( b )

(D) ln( a )ln( b )

Q.No. 2 In a sine bar, let h denote height of slip gauge and l be the distance between the rollers. The
relationship between error in angular measurement ( dθ ) and errors in the slip gauge combination ( dh ) and in
the spacing of the rollers ( dl ) is

(A) dθ = sin θ( dh

h
−
dl

l
)

(B) dθ = cos θ( dh

h
−
dl

l
)

(C) dθ = tan θ( dh

h
−
dl

l
)

(D) dθ = cot θ( dh

h
−
dl

l
)

Q.No. 3 The process capability ratio Cp is given by

(A) Upper Specification Limit - Lower Specification Limit/6 x Process Standard Deviation

(B) Upper Control Limit - Lower Control Limit/6 x Process Standard Deviation

(C) 6 x Process Standard Deviation/Upper Specification Limit - Lower Specification Limit

(D) 6 x Process Standard Deviation/Upper Control Limit - Lower Control Limit

Answer: (A)

Q.No. 4 Which one of the following instruments makes use of the principle of interference of light?

(A) Optical flat

(B) Auto-collimator

(C) Optical projector

(D) Coordinate measuring machine

Answer: (A)

∞
Q.No. 5 The improper integral $ ∫ 0
e
−2t
dt$ converges to

(A) 0

(B) 1.0

(C) 0.5

(D) 2.0

Q.No. 6 In Value Engineering approach, the value of the product is

(A) inversely proportional to its functions and directly proportional to its cost

(B) directly proportional to its functions and inversely proportional to its cost

(C) inversely proportional to its functions as well as its cost

(D) directly proportional to its functions as well as its cost

Q.No. 7 Which one of the following defects is NOT associated with the casting process?

(A) Hot tear

(B) Porosity

(C) Blister

(D) Central burst

Q.No. 8 The figure shows a beam of length L (in m) with a uniformly distributed transverse load of W (in
N/m) acting over it. The width and depth of the beam cross section are b (in m) and t (in m), respectively. The
magnitude of the maximum bending stress in the beam in N/m2 is

2

(A) 3WL

4bt
2

2

(B) 4WL

3bt
2

2

(C) 2WL

3bt
2

(D)
2
3WL
2
2bt

Answer: (A)

Q.No. 9 Schematic diagram of pouring basin and sprue of a gating system is shown in the Figure. Depth of
molten metal m the pouring basin is 100 mm and the height of the sprue is 1,500 mm.

Considering the cross-section of the sprue is circular, the
ratio d₁ : d₂ to avoid aspiration is

(A) 3:2

(B) 5:6

(C) 15:16

(D) 1:2

Q.No. 10 In a machine shop, four jobs need to be assigned to four different machines. Each of the jobs is to be
assigned to one machine only at a time. The time taken to complete the job in different machines is given in the

Table. In order to ensure that the total time
required to complete all the jobs is minimum, the optimal assignment of the job is

(A) J 1 ⇒ M4 , J2 ⇒ M2 , J3 ⇒ M3 , J4 ⇒ M1

(B) J1
⇒ M2 , J2 ⇒ M1 , J3 ⇒ M4 , J4 ⇒ M3

(C) J1
⇒ M2 , J2 ⇒ M1 , J3 ⇒ M3 , J4 ⇒ M4

(D) J 1 ⇒ M4 , J2 ⇒ M2 , J3 ⇒ M1 , J4 ⇒ M3

Q.No. 11 A rigid link PQ of length 1.0 m is pinned at P. It rotates about P in a vertical plane with a uniform
angular acceleration of 1.0 rad/s². At an instant when the angular velocity of the link is 1.0 rad/s, the magnitude
of total acceleration (in m/s²) of point Q relative to point P is

(A) 1.41

(B) 1.73

(C) 2

(D) 2.83

Answer: (A)
2

Q.No. 12 If roots of the auxiliary equation of are real and equal, the general solution of
d y dy
2
+ a + by = 0
dx dx

the differential equation is

(A) y = c e 1
−x /2
+ c2 e
ax /2

(B) y = (c + c x )e
1 2
−ax /2

(C) y = (c + c ln x )e
1 2
−x /2

(D) y = (c cos x + c sin x )e
1 2
−ax /2

Q.No. 13 In a gear manufacturing company, three orders P, Q and R are to be processed on a hobbing machine.
The orders were received in the sequence P — Q — R. The Table indicates the process time remaining and
production calendar due date for each order.

Considering today as the Day 10 in the production calendar of the Hobbing Shop, the sequence of the orders
scheduled using the 'Critical Ratio' rule is

(A) P-Q-R

(B) P-R-Q

(C) Q-P-R

(D) Q-R-P

Q.No. 14 Vector triple product a x ( b x c ) of three vectors a, b and c is given by

(A) ( a · c ) b - ( a · b ) c

(B) ( b · c ) a - ( a · c ) b

(C) ( a · b ) c - ( a · c ) b

(D) ( b · c ) a - ( a · b ) c

Answer: (A)

Q.No. 15 For the complex numbers z and z , the value of (z is
2
1 = 2 + 3i 2 = 4 − 5i 1 + z2)

(A) 32 - 24i

(B) -32 - 24i

(C) 32 + 24i

(D) -32 + 24i

Answer: (A)

Q.No. 16 An acceptance sampling plan is selected with sample size n = 80, acceptance number c = 2 for a lot
size of 10,000 units. The probability of accepting the lot is based on Poisson distribution. Assuming
rectification inspection, if incoming lot quality p is 0.03 and mean (λ) is 2.4, the average outgoing quality
(AOQ) is closest to

(A) 0.0011

(B) 0.0087

(C) 0.0170

(D) 0.0338

Q.No. 17 A pair of spur gears with 20° full-depth involute teeth is used to transmit 3.5 kW of power. The
pinion rotates at 700 rpm and has a pitch circle diameter of 100 mm. Assuming a single pair of teeth in contact,
the total force acting on a gear tooth (in kN) is

(A) 0.347

(B) 0.954

(C) 1.016

(D) 1.302

Q.No. 18 An LPP is defined as Maximize z=15x +12x Subject to x +2x ≤ 3 x ,x ≥ 0 The objective
1 2 1 2 1 2

function of the dual of this LPP is

(A) Maximize w= y +y 1 1

(B) Maximize w= y +2y 1 1

(C) Maximize w= 2y -4y 1 2

(D) Maximize w= 3y +5y 1 2

Q.No. 19 In a shaft-hole system, the dimensions with tolerances (in mm) are as follows:
Shaf t: ϕ20
+x
−x
Hole: ϕ20 where both x and y are positive real numbers. Which one of the following
−0.01
−y

will provide an interference fit?

(A) x = 0.05, y = 0.040

(B) x = 0.04, y = 0.035

(C) x = 0.04, y = 0.032

(D) x = 0.02, y = 0.035

Q.No. 20 In a service centre, cars arrive according to Poisson distribution with a mean of 2 cars per hour. The
time for servicing a car is exponential with a mean of 15 minutes. The expected waiting time (in minute) in the
queue is

(A) 10

(B) 15

(C) 25

(D) 30

Q.No. 21 A 100 mm long cylindrical workpiece of diameter 50 mm is reduced to 25 mm diameter using
extrusion process. The flow curve for the metal has strength coefficient as K = 750 MPa and the strain
hardening co-efficient is 0.15. Assuming no friction and no redundant work, the required ram pressure (in
MPa) is closest to

(A) 164

(B) 364

(C) 428

(D) 950

Q.No. 22 For a classical (Wilson) model of determining economic order quantity (EOQ), the carrying and
ordering costs are Cr and Co, respectively. For an annual demand D, the minimum yearly total inventory cost is

(A) √D C Ce r

(B) √1.5D C C o

(C) √2D C C o r

(D) √3D C C o r

Q.No. 23 The capacity of a passenger airline is expressed in terms of

(A) available seats

(B) available miles

(C) available sectors

(D) available seat miles

Q.No. 24 True centrifugal casting process in horizontal configuration is to be used for casting a metallic
cylinder with outside diameter 0.275 m and inside diameter 0.250 m. If G-factor (ratio of centrifugal force
experienced by the rotating cast metal to its weight) is 65 and acceleration due to gravity is 9.8 m/s², the
minimum rotational speed (in rpm) required is closest to

(A) 325

(B) 650

(C) 975

(D) 1300

Q.No. 25 To make holes of 0.5 mm diameter and 30 mm depth in a mild steel component, the most suitable
process is

(A) chemical machining

(B) electrochemical machining

(C) abrasive jet machining

(D) plasma arc machining

Q.No. 26 In Glass Fiber Reinforced Plastic (GFRP) composites with long fibers, the role of matrix is to (P)
support and transfer the stresses to the fibers (Q) reduce propagation of cracks (R) cany the entire load (S)
protect the fibers against damage The correct statements are

(A) P, Q and R

(B) Q, R and S

(C) P, Q and S

(D) P, R and S

Q.No. 27 The figure shows two bodies connected through a riveted joint with one rivet. The diameter of the
rivet is d (in m). The joint transmits a load of F (in N) whose line of action is perpendicular to and intersects
the vertical axis of the rivet. Neglect any effect of bending of the rivet. If the allowable shear stress for the
material of the rivet is τ N/m2, the diameter of the rivet required to prevent failure in shear is

(A) √ F

πτ

(B) √ 2F

πτ

(C) √ 4F

πτ

(D) √ 8F

πτ

Q.No. 28 In a NC milling operation, the tool path is generated using absolute programing for the trajectory

shown in the figure The corresponding block of the NC program is

(A) G02 X 120.0 Y 60.0 R 60.0;

(B) G02 X 60.0 Y 120.0 R 60.0;

(C) G03 X 60.0 Y 120.0 R 60.0;

(D) G03 X 120.0 Y 60.0 R 60.0;

Answer: (A)

Q.No. 29 A uniform cantilever beam ABC of length L is subjected to a point load P at point B and a
concentrated moment M at point C (as shown in figure). Let E be the Young’s modulus of the beam material
and l be the area moment of inertia of the beam’s cross-section. Assuming the validity of the Euler-Bernoulli

theory of slender beams, the downward deflection at point C is
3 2

(A) PL

3E I
+
ML

2E I

3 2

(B) PL

24E I
+
ML

EI

(C)
3 2
PL ML
+
48E I 2E I

3 2

(D) 5P L

48E I
+
ML

2E I

2

Q.No. 30 General solution of x 2 d y
is
dy
2
+ x − y = 0
dx dx

(A) y =
C1 C2
+ 3
x x

(B) y = C x 1
2
+
C2

x
2

(C) y = C x +1
C2

x

(D) y = C x + C x
1 2
3

Q.No. 31 Consider the analytic function f(z) = x² - y² + i2xy of the complex variable z = x + iy, where i = √-1
The derivative f’(z) is

(A) 2x + i2y

(B) x² + iy²

(C) x + iy

(D) 2x - i2y

Answer: (A)

Q.No. 32 The ideal stress-strain behavior for a completely brittle material during tensile testing up to failure is
described by

(A)

(B)

(C)

(D)

Q.No. 33 The divergence of the vector v→ = y ^ı + z ^ȷ + x k^ is
2 2 2

(A) 2x

(B) 2y

(C) 2z

(D) 0

Q.No. 34 The preparatorY and miscellaneous codes used in CNC part programming and the functions are
given in the Table.

The correct combination of code and the respective function is

(A) P-4, Q-1, R-3, S-2

(B) P-4, Q-1, R-2, S-3

(C) P-1, Q-4, R-3, S-2

(D) P-2, Q-1, R-3, S-4

Answer: (A)

Q.No. 35 The statement that best describes the function of a GO gauge in the context of Taylor's principle of
gauging is

(A) GO gauge checks the Maximum Material Condition and is designed to check as many dimensions as
possible

(B) GO gauge checks the Least Material Condition and is designed to check as many dimensions as possible

(C) GO gauge checks the Maximum Material Condition and is designed to cheek only one dimension

(D) GO gauge checks the Least Material Condition and is designed to check only one dimension

Answer: (A)

Q.No. 36 An approach used In product development which combines the efforts of design, manufacturing, and
other functions to reduce the total time in introducing a new product in the market is

(A) Concurrent engineering

(B) Lean manufacturing

(C) Value engineering

(D) Break-even analysis

Answer: (A)

Q.No. 37 Accuracy of a measuring instrument is expressed as

(A) true value — measured value

(B) measured value — true value

(C) $1 − true value − measured value

true value
$

(D) $1 + true value − measured value

true value
$

Q.No. 38 With reference to Iron-Carbon equilibrium phase diagram, the Crystal structure of 0.3% plain carbon
steel at 1,100℃ is

(A) HCP

(B) BCT

(C) BCC

(D) FCC

Q.No. 39 A non-traditional machining process which utilizes mechanical energy as the principal energy source
for removing the material is

(A) Electric discharge machining

(B) Laser beam machining

(C) Ultrasonic machining

(D) Plasma arc machining

Q.No. 40 Which of the following is a causal forecasting method?

(A) Naive approach

(B) Moving average

(C) Exponential smoothing

(D) Linear regression

Q.No. 41 The Merchant circle diagram showing various forces associated with a cutting process using a

wedge-shaped tool is given in the Figure. The
coefficient of friction can be estimated from the ratio

(A)
f1

f2

(B) f3

f4

(C) f5

f6

(D)
f6

f5

Q.No. 42 The operating characteristic curves of three single sampling plans X, Y and Z with same lot size and
acceptance number are shown in the Figure.

Considering the above
operating characteristic curves, the correct relationship of the plans with respect to sample size is

(A) sample size of X < sample size of Y < sample size of Z

(B) sample size of X = sample size of Y = sample size of Z

(C) sample size of X > sample size of Y > sample size of Z

(D) sample size of X > sample size of Y < sample size of Z

Q.No. 43 For any real, square and non-singular matrix B , the det B −1
is

(A) zero

(B) det B −1

(C) -(det B)

(D) det B

Q.No. 44 A 20 mm HSS drill with a point angle of 118˚ is used for drilling a through hole on a metallic plate
of thickness 100 mm with a cutting speed of 333.33 mm/s and feed of 0.22 mm/rev. Assuming that the drill is
touching the surface of the plate at the start, the drilling time (in s) is closest to

(A) 85

(B) 90

(C) 96

(D) 100

Q.No. 45 The process used for producing long bars of fiber reinforced plastics (FRP) with uniform cross-
section is

(A) Extrusion

(B) Pultrusion

(C) Injection Molding

(D) Thermoforming

Q.No. 46 A firm, with a production target of 50,000 units/year, has the following data for the selection of a

new location for its plant The most economical
location for the firm is

(A) P

(B) Q

(C) R

(D) S

Answer: (A)

Q.No. 47 If the Laplace transform of e ρt
is
1

s −ω
is the Laplace transform of t cosht t is
2

(A) 1+s

2
2
(s −1)

(B) 2
st

(s −1)

2

(C) 1−s

2 2
(s −1)

2

(D) 1+s

1−s
2

Answer: (A)

Q.No. 48 In ASME process chart, the symbol represents

(A) operation

(B) inspection

(C) delay

(D) transport

Q.No. 49 The purpose of the ratchet in a micrometer is to

(A) impart smooth movement to the spindle

(B) compensate for the wear of the screw thread

(C) prevent rotation of the spindle while reading the scale

(D) maintain sufficient and uniform measuring pressure

Q.No. 50 An electrical appliances showroom sells 2,400 ceiling fans in one year (52 weeks). The holding cost
is 10 % of the cost of the ceiling fan. The cost of one ceiling fan is Rs. 600. The cost incurred for placing an
order is Rs. 201. There is a lead time of 5 weeks. The economic order quantity (EOQ) and the reorder level,
respectively (rounded to the next higher integer) are

(A) 231, 127

(B) 38, 231

(C) 127, 231

(D) 127, 13

Q.No. 51 The man-hours required T to manufacture the nth unit in a plant is given by 1 where b=0.322 at the
n

80% learning rate. If the manufacturing time for the first unit T is 80 man-hours, the total time (in man-hours)
1

required to manufacture the first 4 units, at 80% learning rate, is

(A) 322.11

(B) 251.35

(C) 103.76

(D) 51.19

Q.No. 52 An integrating factor for the differential equation dy

dx
+ my = e
−m x
is

(A) em

(B) e-m

(C) e-mx

(D) emx

Q.No. 53 Self-sharpening tendency of a conventional grinding wheel depends upon

(A) wheel structure

(B) wheel grade

(C) grit hardness

(D) grit size

Q.No. 54 Three Carnot engines E , E , E operate as shown in the figure (T > T > T )
1 2 3 1 2 3

The efficiency of the engine 𝔼3 in terms of the efficiencies η1 and η2 of the
engines E and E , respectively, is
1 2

(A) η + η
1 2

(B) η + η − η η
1 2 1 2

(C) 1 − η − η
1 2

(D) 1 − η η
1 2

Q.No. 55 REL chart is used in

(A) Quality management

(B) Inventory management

(C) Facility management

(D) Human resource management