GATE 2027 Sample Paper (Mechanical - ME)

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

GATE 2027 (Mechanical - ME)
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME

65 100 180 Min

GENERAL INSTRUCTIONS

1. This paper contains 65 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 1 or 2 marks (varies by question); for a multiple-choice question, one-third (1-mark
question) or two-thirds (2-mark question) of the allotted marks is deducted for a wrong answer; numerical-answer-type
questions carry no negative marking.

4. Total time allowed is 180 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

GATE 2027 (Mechanical - ME)
SAMPLE QUESTION PAPER

Questions 65 Max Marks 100 Time 180 Min

Attempt all questions. Choose the one correct option for each.

GENERAL APTITUDE

1. A retaining wall with measurements 30m x 12m x 6m
was constructed with bricks Of dimensions 8cm x 6cm x
6cm. If Of the wall consists Of bricks, the number Of
bricks used for the construction is __________ lakhs.

(A) 30

(B) 40

(C) 45

(D) 75

2. The nomenclature Of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles
were identified as baanis. Terms like gayaki and baaj were used to refer to vocal and instrumental styles, respectively.
With the institutionalization Of music education the term gharana became acceptable. Gharana originally referred to
hereditary musicians from a particular lineage, including disciples and grand disciples. Which one Of the following
pairings is NOT correct?

(A) dhrupad, baani

(B) gayaki, vocal

(C) baaj, institution

(D) gharana, lineage

3. Suresh wanted to lay a new carpet in his new mansion 4. If IMHO = JNIP; IDK = JEL; and SO TP, then IDC =
with an area Of 70 x 55 sq. mts. However an area Of 550 _______ .
sq. mts. had to be left out for flower pots. If the cost Of
(A) JOE
carpet is Rs. 50 per sq. mtS., how much money (in Rs.)
(B) JED
will be spent by Suresh for the carpet now?
(C) JDC
(A) Rs. 1,65,000
(D) JCD
(B) Rs. 1,92,500

(C) Rs. 2,75,000

(D) Rs. 1,27,500

5. X is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty
membership, X is almost forcing its customers towards its loyalty membership. If its loyalty membership continues to
grow at its current rate, within the next eight years more households will be watching X than cable television. Which
one Of the following statements can be inferred from the above paragraph?

(A) Most households that subscribe to X's loyalty membership discontinue watching cable television

(B) Non-members prefer to watch cable television

(C) Cable television operators don't subscribe to X's loyalty membership

(D) The X is cancelling accounts Of non-members

6. How many integers are there between 100 and 1000 7. One percent of the people of country X are taller than
all of whose digits are even? 6 ft. Two percent of the people of country Y are taller
than 6 ft. There are thrice as many people in country X as
(A) 60
in country Y. Taking both countries together, what is the
(B) 80
percentage of people taller than 6 ft?
(C) 100
(A) 3.0
(D) 90
(B) 2.5

(C) 1.5

(D) 1.25

8. The missing number in the given sequence 343, 1331, 9. It takes two hours for a person X to mow the lawn. Y
_______ 4913 is can mow the same lawn in four hours. How long (in
minutes) will it take X and Y, if they work together to
(A) 3375
mow the lawn?
(B) 2744
(A) 60
(C) 2197
(B) 80
(D) 4096
(C) 90

(D) 120

10. The boat arrived ______ dawn.

(A) in

(B) at

(C) on

(D) under

MECHANICAL ENGINEERING

11. Consider an ideal vapor compression refrigeration 12. If the characteristic curves of the partial differential
cycle. If the throttling process is replaced by an equation x u +2 x2 u =u -1 are μ(x, y) = c1 and ν(x, y)
xx xy x
isentropic expansion process, keeping all the other = c2, where c1 and c2 are constants, then
processes unchanged, which one of the following
(A) μ(x, y)=x2-y, ν(x, y)=y
statements is true for the modified cycle?
(B) μ(x, y)=x2+y, ν(x, y)=y
(A) Coefficient of performance is higher than that of the
(C) μ(x, y)=x2+y, ν(x, y)=x2
original cycle.
(D) μ(x, y)=x2-y, ν(x, y)=x2
(B) Coefficient of performance is lower than that of the
original cycle.

(C) Coefficient of performance is the same as that of the
original cycle.

(D) Refrigerating effect is lower than that of the original
cycle.

13. The natural frequencies corresponding to the spring- 14. In the following table, x is a discrete random variable
mass systems I and II are ���� and ������, respectively. The ratio
and����
p(x)
/ ������
is the probability density. The standard
is deviation of x is

(A) 1/4 x 1 2 3

p(x) 0.3 0.6 0.1
(B) 1/2

(C) 2 (A) 0.18

(D) 4 (B) 0.36

(C) 0.54

(D) 0.6

15.  The principal value of (-1)(-2 i / π) is 16. Two rollers Of diameters D₁ (in mm) and D₂ (in mm)
are used to measure the internal taper angle in the V-
(A) e²
groove of a machined component. The heights H₁ (in mm)
(B) e²ⁱ
and H₂ (in mm) are measured by using a height gauge
(C) e⁻²ⁱ after inserting the rollers into the same V-groove as
(D) e⁻² shown in the figure.
Which one of the following is the correct relationship to
evaluate the angle �� as shown in the figure?

(A) α=(D -D )2(H -H )-(D -D )
1 2 1 2 1 2
(B) α=(D -D )2(H -H )-2(D -D )
1 2 1 2 1 2
(C) α=(H -H )-(D -D )2(D -D )
1 2 1 2 1 2
(D) α=(H -H )(D -D )
1 2 1 2

17. For a single server with Poisson arrival and
exponential service time. the arrival rate is 12 per hour.
Which one of the following service rates will provide a
steady state finite queue length?

(A) 6 per hour

(B) 10 per hour

(C) 12 per hour

(D) 24 per hour

18. The length, width and thickness of a steel sample are 400 mm, 40 mm and 20 mm, respectively. Its thickness
needs to be uniformly reduced by 2 mm in a single pass by using horizontal slab milling. The milling cutter (diameter:
100 mm, width: 50 mm) has 20 teeth and rotates at 1200 rpm. The feed per tooth is 0.05 mm. The feed direction is
along the length of the sample. If the over-travel distance is the same as the approach distance, the approach
distance and time taken to complete the required machining task are

(A) 14 mm, 18.4 s

(B) 21 mm, 28.9 s

(C) 21 mm, 39.4 s

(D) 14 mm, 21.4 s

19.  The Fourier cosine series for an even function f(x) is 20. A mass m is attached to two identical springs having
given by f(x)=a +Σ ∞a (n x) The value of the spring constant k as shown in the figure. The natural
0 n=1 n
coefficient a₂ for the function f(x) = cos²(x) in [0,π] is frequency ⍵ of this single degree of freedom system is

(A) -0.5 (A) √((2 k)/(m))

(B) 0.0 (B) √((k)/(m))

(C) 0.5 (C) √((k)/(2 m))

(D) 0 (D) √((4 k)/(m))

21. The table presents the demand of a product. By
simple three-months moving average method, the
demand-forecast of the product for the month of
September is

(A) 490

(B) 510

(C) 530

(D) 536.67

22. A car having weight W is moving in the direction as shown in the figure. The center of gravity (CG) of the car is
located at height h from the ground, midway between the front and rear wheels. The distance between the front and
rear wheels is l. The acceleration of the car is a, and acceleration due to gravity is g. The reactions on the front wheels
R and rear wheels R are given by
f r

(A) R =R =(W)/(2)-(W)/(g)((h)/(l)) a
f r
(B) R =(W)/(2)+(W)/(g)((h)/(l)) a ; R =(W)/(2)-(W)/(g)((h)/(l)) a
f r
(C) R =(W)/(2)-(W)/(g)((h)/(l)) a ; R =(W)/(2)+(W)/(g)((h)/(l)) a
f r
(D) R =R =(W)/(2)+(W)/(g)((h)/(l)) a
f r

23. During a non-flow thermodynamic process (1-2) 24. The peak wavelength of radiation emitted by a black
executed by a perfect gas, the heat interaction is equal body at a temperature of 2000 K is 1 .45 µm. If the peak
to the work interaction (Q₁-₂ = W₁-₂) when the process is wavelength of emitted radiation changes to 2.90 µm,
then the temperature (in K) of the black body is
(A) Isentropic

(B) Polytropic (A) 500

(C) Isothermal (B) 1000

(D) Adiabatic (C) 4000

(D) 8000

26. A bar of uniform cross section and weighing 100 N is
held horizontally using two massless and inextensible
strings S1 and S2 as shown in the figure. The tensions in
25.
the strings are

(A) a (A) T₁ = 100 N and T₂ = 0 N

(B) b (B) T₁ = 0 N and T₂ = 100 N

(C) 2c (C) T₁ = 75 N and T₂ = 25 N

(D) (b + 2c) (D) T₁ = 25 N and T₂ = 75 N

27. Interpolator in a CNC machine 28. A frictionless gear train is shown in the figure. The
leftmost 12-teeth gear is given a torque of 100 N-m. The
(A) controls spindle speed
output torque from the 60-teeth gear on the right in N-m
(B) coordinates axes movements
is
(C) operates tool changer
(A) 5
(D) commands canned cycle
(B) 20

(C) 500

(D) 2000

29. A slender rod of length ,L diameter d ( L >>d ) and 30. A matrix P is decomposed into its symmetric part S
thermal conductivity 1k is joined with another rod of and skew symmetric part V. If S=(arrayccc -4 & 4 & 2 \\ 4
identical dimensions, but of thermal conductivity k₂ , to & 3 & 7 / 2 \\ 2 & 7 / 2 & 2 array), V=(arrayccc 0 & -2 & 3 \\
form a composite cylindrical rod of length 2L . The heat 2 & 0 & 7 / 2 \\ -3 & -7 / 2 & 0 array) Then matrix P is
transfer in radial direction and contact resistance are
(A) (arrayccc -4 & 6 & -1 \\ 2 & 3 & 0 \\ 5 & 7 & 2 array)
negligible. The effective thermal conductivity of the
(B) (arrayccc -4 & 2 & 5 \\ 6 & 3 & 7 \\ -1 & 0 & 2 array)
composite rod is
(C) (arrayccc 4 & -6 & 1 \\ -2 & -3 & 0 \\ -5 & -7 & -2 array)
(A) k₁+ k₂
(D) (arrayccc -2 & 9 / 2 & -1 \\ -1 & 81 / 4 & 11 \\ -2 & 45 / 2
(B) √k k
1 2 & 73 / 4 array)
(C) k k k +k
1 2 1 2
(D) 2 k k k +k
1 2 1 2

31. An initially stress-free massless elastic beam of 32. In a four bar planar mechanism shown in the figure,
length L and circular cross-section with diameter d (d L) AB = 5 cm, AD = 4 cm and DC = 2 cm. In the configuration
is held fixed between two walls as shown. The beam shown, both AB and DC are perpendicular to AD. The bar
material has Young's modulus E and coefficient of AB rotates with an angular velocity of 10 rad/s. The
thennal expansion α. If the beam is slowly and uniformly magnitude of angular velocity (in rad/s) of bar DC at this
heated. the temperature rise required to cause the beam instant is
to buckle is proportional to
(A) 0
(A) d (B) 10
(B) d2 (C) 15
(C) d3 (D) 25
(D) d4

33. In a casting process, a vertical channel through 34. A 200 mm long, stress free rod at room temperature
which molten metal flows downward from pouring basin is held between two immovable rigid walls. The
to runner for reaching the mold cavity is called temperature of the rod is uniformly raised by 250°C. If
the Young’s modulus and coefficient of thermal
(A) blister
expansion are 200 GPa and 1×10−5 /°C, respectively, the
(B) sprue
magnitude of the longitudinal stress (in MPa) developed
(C) riser in the rod is
(D) pin hole
(A) 450 to 500

(B) 461 to 471

(C) 499 to 601

(D) 499 to 501

35. Let Xi be a sequence of independent Poisson(λ) 36. The value of the integral r · n d S over the closed
S
variables and let t W =(1)/(n) Σ n X . Thenthe limiting surface S bounding a volume V, where r=x i+y j+z k is the
n i=1 i
distribution of √(n)(W -λ) is the normal distribution with position vector and n is the normal to the surface S, is
n
zero mean and variance given by
(A) V
(A) 1 (B) 2V
(B) √λ (C) 3V
(C) λ (D) 4V
(D) λ2

37. A harmonic function is analytic if it satisfies the 38. An ideal water jet with volume flow rate of 0.05 m3/s
Laplace equation. If ��(��, ��) = 2��² − 2��² + 4���� is a harmonic
strikes a flat plate placed normal to its path and exerts a
function, then its conjugate harmonic function ��(��, ��) is force of 1000 N. Considering the density of water as 1000
kg/m3, the diameter (in mm) of the water jet is
(A) 4���� − 2��² + 2��² + constant

(B) 4��² − 4���� + constant (A) 56 to 58

(C) 2��² − 2��² + ���� + constant (B) 56 to 60

(D) −4���� + 2��² − 2��² + constant (C) 54 to 56

(D) 56 to 57

39. A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of θ = 30° as shown in
the figure. The glue used at the interface fails if Criterion 1: the maximum normal stress exceeds 2.5 MPa. Criterion 2:
the maximum shear stress exceeds 1.5 MPa. Assume that the interface fails before the logs fail. When a uniform
tensile stress of 4 MPa is applied, the interface

(A) fails only because of criterion 1

(B) fails only because of criterion 2

(C) fails because of both criteria 1 and 2

(D) does not fail

40. An aluminium alloy (density 2600 kg/m3) casting is to 41. Consider the following partial differential equation
be produced. A cylindrical hole of 100 mm diameter and for u(x, y) with the constant c > I : (∂ u)/(∂ y)+c (∂ u)/(∂
100 mm length is made in the casting using sand core x)=0 Solution of this equation is
(density 1600 kg/m3). The net buoyancy force (in newton)
(A) u(x, y) = f(x+ cy)
acting on the core is
(B) u(x, y) = f(x- cy)
(A) 6 to 8
(C) u(x, y) = f(cx+ y)
(B) 5 to 9
(D) u(x, y) = f(x- cy)
(C) 3 to 6

(D) 7 to 8

42. Select the correct statement for 50% reaction stage 43. In the space above the mercury column in a
in a steam turbine. barometer tube, the gauge pressure of the vapour is

(A) The rotor blade is symmetric. (A) positive, but more than one atmosphere

(B) The stator blade is symmetric. (B) Negative

(C) The absolute inlet flow angle is equal to absolute exit (C) Zero
flow angle. (D) positive, but less than one atmosphere
(D) The absolute exit flow angle is equal to inlet angle of
rotor blade.

44. A pair of spur gears with module 5 mm and a center 45. The volume and temperature of air (assumed to be
distance of 450 mm is used for a speed reduction of 5:1. an ideal gas) in a closed vessel is 2.87 m³ and 300 K,
The number of teeth on pinion is respectively. The gauge pressure indicated by a
manometer fitted to the wall of the vessel is 0.5 bar. If
(A) 28 to 30
the gas constant of air IS R = 287 J/kg.K and the
(B) 29 to 31
atmospheric pressure is 1 bar, the mass of air (in kg) in
(C) 29 to 30 the vessel is
(D) 29 to 32
(A) 1.67

(B) 3.33

(C) 5.00

(D) 6.66

46. 500 students are taking one or more courses out of 47. Which of the following conditions is used to
chemistry, physics and Mathematics. Registration records determine the stable equilibrium of all partially
indicate course enrolment as follows: chemistry ( 329 ) , submerged floating bodies?
physics ( 186 ) , Mathematics ( 295 ) , chemistry and
(A) Centre of buoyancy must be above the centre of gravity
physics ( 83 ) , chemistry and Mathematics ( 217 ) , and
(B) Centre of buoyancy must be below the centre of gravity
physic and Mathematics ( 63 ) , How many students are
taking all 3 subjects? (C) Metacentre must be at a higher level than the centre of
gravity
(A) 12
(D) Metacentre must be at a lower level than the centre of
(B) 53
gravity
(C) 67

(D) 87

48. A six-faced fair dice is rolled five times. The 49. Which one of the following instruments is widely used
probability (in %) of obtaining “ONE” at least four times to check and calibrate geometric features of machine
is tools during their assembly?

(A) 33.3 (A) Ultrasonic probe

(B) 3.33 (B) Coordinate Measuring Machine (CMM)

(C) 0.33 (C) Laser interferometer

(D) 0.0033 (D) Vernier calipers

50. A rod of length 20 mm is stretched to make a rod of 51. Match the following products with the suitable
length 40 mm. Subsequently, it is compressed to make a manufacturing process
rod of final length 10 mm. Consider the longitudinal
(A) P-4, Q-3, R-1, S-2
tensile strain as positive and compressive strain as
(B) P-2, Q-1, R-3, S-4
negative. The total true longitudinal strain in the rod is
(C) P-4, Q-1, R-2, S-3
(A) -0.5
(D) P-1, Q-3, R-4, S-2
(B) -0.69

(C) -0.75

(D) -1.0

52. In orthogonal turning of a cylindrical tube of wall 53. The values of enthalpies at the stator inlet and rotor
thickness 5 mm, the axial and the tangential cutting outlet of a hydraulic The turbomachine stages are h₁ and
forces were measured as 1259 N and 1601 N, h₃ respectively. The enthalpy at the stator outlet (or,
respectively. The measured chip thickness after rotor inlet) is The condition (h₂ — h₁ ) (h₃ — h₂) indicates
machining was found to be 0.3 mm. The rake angle was that the degree Of reaction Of this Stage is
10° and the axial feed was 100 mm/min. The rotational
(A) zero
speed of the spindle was 1000 rpm. Assuming the
(B) 50%
material to be perfectly plastic and Merchant’s first
solution, the shear strength of the material is closest to (C) 75%

(D) 100%
(A) 722 MPa

(B) 920 MPa

(C) 200 MPa

(D) 875 MPa

54. The divergence of the vector field u=ex( y i+ y j) is

(A) 0

(B) ex y+ex y

(C) 2 ex y

(D) 2 ex y

55. The wall of a constant diameter pipe of length 1 m is heated uniformly with flux ��” by wrapping a heater coil
around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the
flow is assumed to be laminar and steady all through the pipe. The bulk temperature of the fluid is equal to 0 ºC at the
inlet and 50 ºC at the exit. The wall temperatures are measured at three locations, P, Q and R, as shown in the figure.
The flow thermally develops after some distance from the inlet. The following measurements are made: Among the
locations P, Q and R, the flow is thermally developed at

(A) P, Q and R

(B) P and Q only

(C) Q and R only

(D) R only

56. Biot number signifies the ratio of 57. In a power plant, water (density = 1000 kg/m3) is
pumped from 80 kPa to 3 MPa. The pump has an
(A) convective resistance in the fluid to conductive
isentropic efficiency of 0.85. Assuming that the
resistance in the solid
temperature of the water remains the same, the specific
(B) conductive resistance in the solid to convective
work (in kJ/kg) supplied to the pump is
resistance in the fluid
(A) 0.34
(C) inertia force to viscous force in the fluid
(B) 2.48
(D) buoyancy force to viscous force in the fluid
(C) 2.92

(D) 3.43

58. The lengths of a large stock of titanium rods follow a 59. Match the processes with their characteristics.
normal distribution with a mean (��) of 440 mm and a
(A) P-2,Q-3,R-1,S-4
standard deviation (��) of 1 mm. What is the percentage of
(B) P-3,Q-2,R-1,S-4
rods whose lengths lie between 438 mm and 441 mm?
(C) P-3,Q-2,R-4,S-1
(A) 81.85%
(D) P-2,Q-4,R-3,S-1
(B) 68.4%

(C) 99.75%

(D) 86.64%

60. Consider the polynomial p(X)=X4+4 in the ring Q[X] 61. A gas is heated in a duct as it flows over a resistance
of polynomials in the variable X with coefficients in the heater. Consider a 101 kW electric heating system. The
field Q of rational numbers. Then gas enters the heating section of the duct at 100 kPa and
27 ºC with a volume flow rate of 15 m3/s. If heat is lost
(A) the set of zeros of p(X) in C forms a group under
from the gas in the duct to the surroundings at a rate of
multiplication
51 kW, the exit temperature of the gas is (Assume
(B) p(X) is reducible in the ring Q[X]
constant pressure, ideal gas, negligible change in kinetic
(C) the splitting field of p(X) has degree 3 over Q and potential energies and constant specific heat; Cp = 1
(D) the splitting field of p(X) has degree 4 over Q kJ/kg·K; R = 0.5 kJ/kg·K.)

(A) 32 ºC

(B) 37 ºC

(C) 53 ºC

(D) 76 ºC

62. A plane-strain compression (forging) of a block is 63. A four bar mechanism is shown below. For the
shown in the figure. The strain in the z-direction is zero. mechanism to be a crank-rocker mechanism, the length
The yield strength (Sy) in uniaxial tension/compression of of the link PQ can be
the material of the block is 300 MPa and it follows the
(A) 80 mm
Tresca (maximum shear stress) criterion. Assume that
(B) 200 mm
the entire block has started yielding. At a point where
��z=40 MPa (compressive) and ��xy the stress component ��y (C) 300 mm

is (D) 350 mm

(A) 340 MPa (compressive)

(B) 340 MPa (tensile)

(C) 260 MPa (compressive)

(D) 260 MPa (tensile)

64. Consider a beam with circular cross-section of 65. In a four bar planar mechanism shown in the figure,
diameter d The ratio of the second moment of area about AB = 5 cm, AD = 4 cm and DC = 2 cm. In the configuration
the neutral axis to the section modulus of the area is shown, both AB and DC are perpendicular to AD. The bar
AB rotates with an angular velocity of 10 rad/s. The
(A) d/2
magnitude of angular velocity (in rad/s) of bar DC at this
(B) πd/2
instant is
(C) d
(A) 0
(D) πd
(B) 10

(C) 15

(D) 25

ANSWER KEY

1. (C) 2. (C) 3. (A) 4. (B) 5. (A) 6. (C) 7. (D)

8. (C) 9. (B) 10. (B) 11. (A) 12. (A) 13. (B) 14. (D)

15. (A) 16. (A) 17. (D) 18. (D) 19. (C) 20. (A) 21. (B)

22. (C) 23. (C) 24. (B) 25. (B) 26. (B) 27. (B) 28. (D)

29. (D) 30. (B) 31. (B) 32. (D) 33. (B) 34. (D) 35. (C)

36. (C) 37. (A) 38. (D) 39. (C) 40. (D) 41. (B) 42. (D)

43. (B) 44. (B) 45. (B) 46. (B) 47. (C) 48. (C) 49. (C)

50. (B) 51. (C) 52. (A) 53. (B) 54. (C) 55. (C) 56. (B)

57. (D) 58. (A) 59. (A) 60. (B) 61. (A) 62. (A) 63. (A)

64. (A) 65. (D)