GATE 2025 Question Paper Naval Architecture and Marine Engineering (NM)

GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude
Q.1 – Q.5 Carry ONE mark Each

Q.1 Despite his initial hesitation, Rehman’s _________ to contribute to the success of
the project never wavered.

Select the most appropriate option to complete the above sentence.

(A) ambivalence

(B) satisfaction

(C) resolve

(D) revolve

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Q.2 Bird : Nest :: Bee : _______

Select the correct option to complete the analogy.

(A) Kennel

(B) Hammock

(C) Hive

(D) Lair

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Q.3 If 𝑃𝑒 𝑥 = 𝑄𝑒 −𝑥 for all real values of 𝑥, which one of the following statements is
true?

(A) 𝑃=𝑄=0

(B) 𝑃=𝑄=1

(C) 𝑃 = 1; 𝑄 = −1

(D) 𝑃
=0
𝑄

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Q.4 The paper as shown in the figure is folded to make a cube where each square
corresponds to a particular face of the cube. Which one of the following options
correctly represents the cube?

Note: The figures shown are representative.

(A)

(B)

(C)

(D)

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Q.5 Let 𝑝1 and 𝑝2 denote two arbitrary prime numbers. Which one of the following
statements is correct for all values of 𝑝1 and 𝑝2 ?

(A) 𝑝1 + 𝑝2 is not a prime number.

(B) 𝑝1 𝑝2 is not a prime number.

(C) 𝑝1 + 𝑝2 + 1 is a prime number.

(D) 𝑝1 𝑝2 + 1 is a prime number.

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Q.6 – Q.10 Carry TWO marks Each

Q.6 Based only on the conversation below, identify the logically correct inference:

“Even if I had known that you were in the hospital, I would not have gone there to
see you”, Ramya told Josephine.

(A) Ramya knew that Josephine was in the hospital.

(B) Ramya did not know that Josephine was in the hospital.

(C) Ramya and Josephine were once close friends; but now, they are not.

(D) Josephine was in the hospital due to an injury to her leg.

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Q.7 If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which
one among the given options is the most appropriate code for BEACH ?

(A) CEADP

(B) IDBFC

(C) JGIBC

(D) IBCEC

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Q.8 Which one of the following options is correct for the given data in the table?

Iteration (i) 0 1 2 3

Input (I) 20 −4 10 15

Output (X) 20 16 26 41

Output (Y) 20 −80 −800 −12000

(A) 𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖>0

(B) 𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1) + 𝐼(𝑖); 𝑖>0

(C) 𝑋(𝑖) = 𝑋(𝑖 − 1)𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖); 𝑖>0

(D) 𝑋(𝑖) = 𝑋(𝑖 − 1) + 𝐼(𝑖); 𝑌(𝑖) = 𝑌(𝑖 − 1)𝐼(𝑖 − 1); 𝑖>0

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Q.9 In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The
corner L of the rectangle is on the side QR. Side MN of the rectangle passes through
the corner S of the square.

What is the area (in cm2) of the rectangle PLMN?

Note: The figure shown is representative.

N

P S

M

Q L R

(A) 2√2

(B) 2

(C) 8

(D) 4

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Q.10 The diagram below shows a river system consisting of 7 segments, marked P, Q, R,
S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We
need to connect these zones using the least number of bridges. Out of the following
options, which one is correct?

Note: The figure shown is representative.

Z2 Z3
R
V

P T
Q Z4

Z1 U
S Z5

(A) Bridges on P, Q, and T

(B) Bridges on P, Q, S, and T

(C) Bridges on Q, R, T, and V

(D) Bridges on P, Q, S, U, and V

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Q.11 – Q.35 Carry ONE mark Each

Q.11 ln 𝑡
The value of lim is ________.
𝑡→1 𝑡 2 −1

(A) 1
2

(B) 0

(C) 1

(D) ∞

Q.12 The Fourier series expansion of 𝑓(𝑥) = sin2 𝑥 in the interval (−𝜋, 𝜋) is ______.

(A) 1 1
𝑓(𝑥) = − cos 2𝑥
2 2

∞
(B) cos 𝑛𝑥
𝑓(𝑥) = ∑(−1)𝑛−1
𝑛2
𝑛=1

∞
(C)
sin 2𝑛𝑥
𝑓(𝑥) = 2 ∑
𝑛
𝑛=1

∞
(D)
1 4 cos(2𝑛 − 1)𝜋𝑥
𝑓(𝑥) = − 2∑
2 𝜋 (2𝑛 − 1)2
𝑛=1

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Q.13 For all real values of 𝑥 and 𝑦, the partial differential equation in terms of 𝜓(𝑥, 𝑦)
𝜕2𝜓 𝜕2𝜓 𝜕2𝜓
given by 𝜕𝑥 2 + 2 𝜕𝑥𝜕𝑦 − 3 𝜕𝑦 2 = 0 is ________.

(A) hyperbolic

(B) parabolic

(C) elliptic

(D) elliptic within the region, 𝑥 2 − 𝑦 < 0

Q.14 The sum of the static pressure and dynamic pressure at a point in a fluid flow is
called the ________.

(A) kinematic pressure

(B) vacuum pressure

(C) stagnation pressure

(D) kinetic pressure

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Q.15 Identify the range of Reynolds number (Re) for a creeping flow.

(A) 2000 < Re < 20000

(B) 1000 < Re < 2000

(C) 10 < Re < 100

(D) Re << 1

Q.16 The ratio of the magnitudes of vorticity to rate of rotation in a fluid flow is _______.

(A) 2

(B) 3

(C) 1
2

(D) 1

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Q.17 In a laminar boundary layer, the ratio of boundary layer thickness (δ) to the
corresponding displacement thickness (δ*) lies between ______.

(A) 1.5 and 2.4

(B) 2.5 and 3.4

(C) 3.5 and 4.4

(D) 4.5 and 5.4

Q.18 For marine engine shafts subjected to high radial and axial thrust loads, which one
of the following types of bearings is the most suitable?

(A) Deep groove ball

(B) Sealed ball

(C) Tapered roller

(D) Needle

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Q.19 Which one of the following wave energy spectra is formulated for two peaks?

(A) Pierson-Moskowitz spectrum

(B) JONSWAP spectrum

(C) Ochi-Hubble spectrum

(D) Neumann spectrum

Q.20 According to linear water wave theory, at a point on the free surface of a regular
wave, the phase difference between the free surface elevation and the horizontal
water particle acceleration is ______.

(A) 0°

(B) 45°

(C) 90°

(D) 135°

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Q.21 The dynamic response amplitude |𝐻(𝜔)| of a single degree of freedom system
subjected to support motion is given by the following expression.

𝜔 2
1 + 4 𝜁 2 (𝜔 )
𝑛
|𝐻(𝜔)| = √
𝜔 2 2 𝜔 2
[1 − (𝜔 ) ] + 4 𝜁 2 (𝜔 )
𝑛 𝑛

|𝐻(𝜔)| increases with an increase in damping ratio (𝜁) if the excitation
frequency (𝜔) is _________ the natural frequency (𝜔𝑛 ) of the system.

(A) equal to

(B) 0.75 times

(C) √3
times
2

(D) greater than √2 times

Q.22 In the stress-strain curve of mild steel, plastic deformation starts at the ______.

(A) proportional limit

(B) elastic limit

(C) upper yield point

(D) lower yield point

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Q.23 In ships, a flash evaporator is used to obtain ______.

(A) distilled water

(B) low viscosity lubricating oil

(C) high-temperature heavy oil

(D) air for space heating

Q.24 Which one of the following is the most common type of gear assembly used for
coupling steam turbine and propeller shafts?

(A) Spur

(B) Single helical

(C) Double helical

(D) Worm

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Q.25 A ship of 5000 tonne displacement has two empty rectangular double bottom tanks
with dimensions:

Tank A: length 12 m, width 16 m, and height 2 m

Tank B: length 16 m, width 12 m, and height 2 m

The length of each tank is oriented along the length of the ship. It is required to
ballast the ship with 192 m3 of seawater of density 1025 kg/m3. Which one of the
following scenarios will minimize the free surface effect?

(A) 100 % of the given ballast water is filled in Tank A.

(B) 100 % of the given ballast water is filled in Tank B.

(C) 50% of the given ballast water is filled in Tank A and the remaining in Tank B.

(D) 40% of the given ballast water is filled in Tank A and the remaining in Tank B.

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Q.26 The midship section of a barge of breadth W and depth H is shown in the figure.
All plate thicknesses are equal. The barge is subjected to a longitudinal bending
moment in the upright condition. Which one of the following statements is correct?

(A) Magnitude of longitudinal bending stress is maximum at point P and magnitude of
vertical shear stress is maximum at point Q.

(B) Magnitude of longitudinal bending stress is maximum at point S and magnitude of
vertical shear stress is maximum at point R.

(C) Magnitude of longitudinal bending stress is maximum at point Q and magnitude
of vertical shear stress is maximum at point S.

(D) Magnitude of longitudinal bending stress is maximum at point R and magnitude of
vertical shear stress is maximum at point P.

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Q.27 Consider a Planar Motion Mechanism (PMM) test of a ship model in a towing tank.
The transverse motion of the model from the centerline of the tank is described by
𝑦 = 𝑎0 cos(𝜔𝑡), where 𝜔 is the angular frequency. The carriage speed is 3 m/s,
√3
𝜔 = 2 rad/s and the maximum drift angle during the test is 30°. The amplitude of
oscillation 𝑎0 lies between ______.

(A) 0.2 m and 0.4 m

(B) 0.5 m and 0.7 m

(C) 1.0 m and 1.2 m

(D) 1.9 m and 2.1 m

Q.28 Consider the function 𝑓(𝑥) = |𝑥| − 1. Which of the following statements is/are
true in the interval [−10, 10]?

(A) The function is differentiable in the domain.

(B) The function is continuous in the domain.

(C) The function is not differentiable in the domain.

(D) The function is not continuous in the domain.

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Q.29 For a freely floating body in water, which of the following degrees of freedom
has/have inherent restoring force?

(A) Sway

(B) Surge

(C) Heave

(D) Pitch

Q.30 Which of the following boiler arrangements will ensure that there is NO
contamination of the primary feed system?

(A) Steam-to-steam generator

(B) Double evaporation boiler

(C) Water tube boiler

(D) Fire tube boiler

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Q.31 Which of the following components is/are NOT found in a two-stroke marine
diesel engine?

(A) Crankshaft

(B) Piston

(C) Spark plug

(D) Air-inlet valve

Q.32 Choose the correct statement(s) from the following with respect to a ship
generated Kelvin wave pattern in deep water.

(A) A system of transverse waves and divergent waves are observed behind the ship.

(B) A system of transverse waves and divergent waves are observed in front of the
ship.

(C) The waves are contained in a sector originating at the bow with a half angle
of 9 28′.

(D) The amplitude of wave components decrease as they propagate.

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Q.33 A box contains 12 red and 8 blue balls. Two balls are drawn randomly from the
box without replacement.

The probability of drawing a pair of balls having the same color is_________
(rounded off to three decimal places).

Q.34 The dynamics of a 90 m long ship are governed by the non-dimensional Nomoto
72
equation. The magnitude of Nomoto gain |𝐾 ′ | = 35𝜋 and that of Nomoto time
288
constant |𝑇′| = 35𝜋.

The steady turning radius of the ship for a 35 turning circle maneuver is
_________ m (answer in integer).

Q.35 A ship of length 200 m has a beam of 25 m. She floats in seawater with an even
keel draught of 5 m. The prismatic coefficient of the ship is 0.9; the mass
displacement is 20500 tonne and the density of seawater is 1025 kg/m3.

The midship section coefficient is _______ (rounded off to two decimal places).

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Q.36 – Q.65 Carry TWO marks Each

Q.36 Consider 𝑓(𝑡) = cos(𝑎𝑡), where a is a real constant. The Laplace transform of
𝑓(𝑡) is _________.

(A) 𝑎
𝑠 2 + 𝑎2

(B) 𝑠
𝑠 2 + 𝑎2

(C) 𝑎
𝑠 2 − 𝑎2

(D) 𝑠
𝑠 2 − 𝑎2

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Q.37 A square shaped body is subjected to only direct tensile stresses 𝜎𝑥 and 𝜎𝑦 as shown
in the figure. If 𝜎𝑥 > 𝜎𝑦 , then the value of normal stress (𝜎𝜃 ) and shear stress (𝜏𝜃 )
respectively are ______.

𝜎𝑥 −𝜎𝑦 𝜎𝑥 +𝜎𝑦
(A) and
2 2

𝜎𝑥 +𝜎𝑦 𝜎𝑥 −𝜎𝑦
(B) and
2 2

𝜎𝑥 +𝜎𝑦 𝜎𝑥 +𝜎𝑦
(C) and
2 2

𝜎𝑥 −𝜎𝑦 𝜎𝑥 −𝜎𝑦
(D) and
2 2

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Q.38 The beam PQRS is subjected to a vertical point load of 10 kN at point S as shown
in the figure.

The magnitude of fixed end moment at P is _______ kN-m.

(A) 50

(B) 10

(C) 30

(D) 40

Q.39 For a butt weld joint of two plates, which one of the following loading scenarios
has the least permissible stress?

(A) Tensile

(B) Bending

(C) Bearing

(D) Shear

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Q.40 Match the non-dimensional numbers in Column 1 with the corresponding
definitions in Column 2

Column 1 Column 2

I. Froude number P. Ratio of inertial force to surface
tension force

II. Reynolds number Q. Ratio of inertial force to
gravitational force

III. Euler number R. Ratio of inertial force to viscous
force

IV. Weber number S. Ratio of pressure force to inertial
force

(A) I – S; II – R; III – P; IV - Q

(B) I – Q; II – R; III – S; IV – P

(C) I – Q; II – R; III – P; IV – S

(D) I – S; II – Q; III – R; IV – P

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Q.41 A closed system is undergoing a reversible process 1-P-2 from state 1 to 2, as shown
in the figure, where X and Y are thermodynamic properties. An irreversible process
2-Q-1 brings the system back from 2 to 1.

The net change in entropy of the system and surroundings during the above-
mentioned cycle are ________ respectively.

(A) positive and negative

(B) negative and positive

(C) zero and negative

(D) zero and positive

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Q.42 An ideal Brayton cycle (1-2-3-4) consisting of two isentropic and two isobaric
processes is shown in the T-s plot, where T is the temperature and s is the specific
entropy of the system. Which one of the following plots represents the
corresponding actual cycle 1-2′-3-4′ (denoted by dashed lines) between the same
two pressures p1 and p2 ?

(A)

(B)

(C)

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(D)

Q.43 Consider a rectangular barge of length (𝐿) 100 m, breadth 25 m and draught 10 m.
The barge has the following non-dimensional hydrodynamic derivatives with
respect to a coordinate system whose origin is at the center of gravity.

𝑌𝑣′ = −1000 × 10−5 , 𝑁𝑟′ = −800 × 10−5 ,

𝑁𝑣′ = −200 × 10−5, 𝑌𝑟′ = 100 × 10−5

The stability criterion 𝐶 ′ is given by

𝐶 ′ = 𝑌𝑣′ (𝑁𝑟′ − 𝑚′ 𝑥𝐺′ ) − (𝑌𝑟′ − 𝑚′ )𝑁𝑣′
𝑚
where 𝑚′ = 1 , 𝑚 is the mass of the barge, 𝜌 is the density of seawater, and 𝑥𝐺
𝜌 𝐿3
2
is the distance of the center of gravity from the origin.

Which one of the following is correct regarding the controls-fixed straight-line
stability?

(A) Unstable with 𝐶′ = −1.8 × 10−5

(B) Stable with 𝐶′ = 3.2 × 10−5

(C) Stable with 𝐶′ = −1.8 × 10−5

(D) Unstable with 𝐶′ = 3.2 × 10−5

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Q.44 A ship has a propeller of 5 m pitch rotating at 120 rpm. The ship travels at 8 m/s
and the wake fraction is 0.25. The apparent slip ratio and real slip ratio
are ______ respectively.

(A) 0.20 and 0.40

(B) 0.40 and 0.20

(C) 0.20 and 0.25

(D) 0.25 and 0.20

Q.45 A ship of length 100 m and displacement 5000 tonne floats even-keel at 6.5 m in
fresh water of density 1000 kg/m3. The ship’s hydrostatic properties are:

MCT per cm is 10 tonne-m,
TPC in seawater is 6.25,
LCB is 2 m forward of amidship,
LCF is 2 m forward of amidship.

The ship has moved to seawater of density 1025 kg/m3 without change in the
displacement. The new forward and aft draughts are ______ respectively.

(A) 6.04 m and 6.54 m

(B) 6.30 m and 6.64 m

(C) 6.64 m and 6.30 m

(D) 6.30 m and 6.30 m

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Q.46 Consider a case where the load 𝑄 for a ship structure has only statistical
uncertainties. The probability density function of the load 𝑝𝑄 (𝑥) is shown in the
figure. The characteristic limit value of the load (𝑄𝐿𝑐 ) is 1.5 and factor of safety is
1. Which of the following probability of exceedance value(s) of the load will lead
to a safe design?

(A) 0.05

(B) 0.10

(C) 0.15

(D) 0.20

Q.47 3 5
The value of ∫1 𝑑𝑦 ∫2 𝑥 2 𝑦 𝑑𝑥 is __________ (answer in integer).

Q.48 1 0 2 −1
Let 𝑀 = [ ] and 𝐾 = [ ] satisfy the eigenvalue problem given by
0 2 −1 1
[𝑀 − 𝛼𝐾]𝜑 = 0.

The lowest eigenvalue 𝛼 is ________ (rounded off to two decimal places).

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Q.49 The gradient of 𝑦 = 3𝑥 2 sin(2𝑥) at (0.2, 1) is ________ (rounded off to three
decimal places).

Q.50 A simply supported solid beam is subjected to a vertical point load of 10 N at the
middle. The length of the beam is 4 m, and the cross section is 0.5 m × 0.5 m.

The magnitude of maximum tensile stress in the beam is ________ N/m2
(answer in integer).

Q.51 ⃗ = 𝑦𝑥𝑖̂ + 𝑦𝑧𝑗̂ + (𝑧 + 𝑥 2 )𝑘̂.
The displacement field of a body is given by 𝑢

The shear strain 𝛾𝑥𝑦 at (2, 1, 5) is ________(answer in integer).

Q.52 A freely-floating rectangular barge of length 200 m is divided into five equal
compartments. In light-weight condition, the weight and buoyancy are uniformly
distributed along the length of the barge. Assume g = 9.81 m/s2.

If 500 tonne of liquid cargo is added to each of the two end compartments as shown
in the figure, then the maximum bending moment is ________ MN-m (rounded off
to two decimal places).

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Q.53 The stream function of a two-dimensional flow field is given as
𝜓 = 2𝑥𝑦 + 2𝑦 + 2𝑥. The coordinates of two points P and Q in the flow field are
(1, 2) and (2, 5) respectively.

The magnitude of flow discharge between the streamlines passing through P and Q
is __________(answer in integer).

Q.54 A tank with a constant water level of 4 m above the centreline of an opening of
diameter 100 mm is shown in the figure. Neglect all losses and assume
g = 9.81 m/s2.

The discharge through the opening is _____________ litre/s (answer in integer).

Q.55 Air flows with a velocity of 2 m/s over a flat stationary surface parallel to its length
of 0.5 m. Kinematic viscosity of air 𝜐 is 1.5×10-5 m2/s.

Using Blasius solution, the boundary layer thickness at the trailing edge of the
surface is ________ mm (rounded off to two decimal places).

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Q.56 A negligibly thin horizontal plate PQ has a length 3 m and width 1 m. It is being
pulled along its length at a speed of 1 m/s in between two static parallel plates as
shown in the figure. The gap of 6 cm between the plates is filled with a Newtonian
fluid of dynamic viscosity µ = 0.2 N-s/m2. The thin plate is located at 3 cm from
the top surface. The velocity distribution between the thin plate and the static plates
is linear.

The steady force required to pull the plate is ________N (answer in integer).

Q.57 Water of density 𝜌 = 1000 kg/m3 flows with a velocity V = 50 m/s through a 180°
curved tube of uniform cross-section as shown in the figure. If the flow rate is
0.06 m3/s, the magnitude of reaction force Fx required to keep it stationary
is __________ kN (rounded off to one decimal place).

Q.58 An ocean wave is propagating from deep to shallow water. The wave is approaching
the coast at 45o counterclockwise from the shore normal with an initial phase speed
of 12.5 m/s. After entering the shallow water, the wave direction becomes 30o
counterclockwise from the shore normal.

The phase speed of the wave at the shallow water is __________ m/s (rounded off
to one decimal place).

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Q.59 Consider the psychrometric process denoted by the straight line from state 1 to 2 in
the figure. The specific humidity, Dry Bulb Temperature (DBT) and Wet Bulb
Temperature (WBT) at the two states are shown in the table. The latent heat of
vaporization of water (hfg ) is 2440 kJ/kg.

If the flow rate of air is 1 kg/s, the rate of heat transfer from the air is ________kW
(rounded off to two decimal places).

Property State 1 State 2

Specific humidity (kg of water 0.020 0.015
vapour/kg of dry air)

DBT (℃) 25 25

WBT (℃) 25 22

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Q.60 Consider a weightless, frictionless piston with a 2 kg mass placed on it as shown in
the figure. At equilibrium in position 1, the cylinder contains 0.1 kg of air. The
piston cross-sectional area is 0.01 m2. The ambient pressure in the surroundings
outside the piston-cylinder arrangement is 0 bar (absolute). When the mass above
the piston is removed instantaneously, it moves up and hits the stop at position 2
which is 0.1 m above the initial position.

Assuming g = 9.81 m/s2, the thermodynamic work done by the system during this
process is _______ J (answer in integer).

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Q.61 A two-stroke four-cylinder large marine diesel engine has a cylinder bore of
600 mm and stroke length of 2400 mm. The brake thermal efficiency (𝜂𝑏𝑡ℎ ) is 45%
and fuel consumption rate (𝑚̇𝑓 ) is 0.265 kg/s at an engine speed (N) of 100 rpm.
Assuming the calorific value of fuel is 42 MJ/kg, the brake mean effective pressure
(bmep) is ______ bar (rounded off to one decimal place).

Q.62 A multi-cell midship section of a ship with B = 40 m and D = 20 m is shown in the
figure. The shear-flows are given as 𝑞1 = 𝑞2 = 𝑞3 = 0.9376 MN/m.

The applied twisting moment on the midship section is ___________MN-m
(rounded off to two decimal places).

Organizing Institute: IIT Roorkee Page 38 of 39

Q.63 A ship of 3300 tonne displacement is undergoing an inclining experiment in
seawater of density 1025 kg/m3. A mass of 6 tonne is displaced transversely by
12 m as shown in the figure. This results in 0.12 m deflection of a 11 m long
pendulum suspended from the centerline. The transverse metacenter of the ship is
located at 7.25 m above the keel.

The distance of the center of gravity from the keel is _______ m (rounded off to two
decimal places).

Q.64 A ship moving at a steady forward speed of 10 m/s experiences a total resistance of
140 kN. The Quasi Propulsive Coefficient (QPC) is 0.70; the propeller shaft losses
are 5% and the mechanical efficiency of the main engine is 80%.

The indicated power of the main engine is_______ kW (rounded off to two decimal
places).

Q.65 A single degree of freedom system is undergoing free oscillation. The natural
frequency and damping ratio of the system are 1 rad/sec and 0.01 respectively.

The reduction in peak amplitude over three cycles is __________ % (rounded off
to one decimal place).

Organizing Institute: IIT Roorkee Page 39 of 39

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