The GATE 2025 NM Question Paper PDF is available as the exam is over. The IIT Roorkee is conducting the GATE 2025 Naval Architecture & Marine Engineering exam. February 1st in Shift 2 took place from 2:30 PM to 5:30 PM. As per the updated exam pattern, the exam consists of 65 questions carrying a total of 100 marks, with 10 from the General Aptitude section and 55 questions from Engineering Mathematics and Core Mathematics topics.
The difficulty level of GATE 2025 NM was moderate.
GATE 2025 NM Question Paper with Solutions PDF
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GATE 2025 NM Question Paper with Solutions
Despite his initial hesitation, Rehman’s ________ to contribute to the success of the project never wavered.
Bird : Nest :: Bee : _______
Select the correct option to complete the analogy.
If \( P e^x = Q e^{-x} \) for all real values of \( x \), which one of the following statements is true?
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.
Let \( p_1 \) and \( p_2 \) denote two arbitrary prime numbers. Which one of the following statements is correct for all values of \( p_1 \) and \( p_2 \)?
Based only on the conversation below, identify the logically correct inference:
\textit{“Even if I had known that you were in the hospital, I would not have gone there to see you”, Ramya told Josephine.
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?
Which one of the following options is correct for the given data in the table?
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 cm\(^2\)) of the rectangle PLMN?
Note: The figure shown is representative.
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.
The value of \( \lim_{t \to 1} \frac{\ln t}{t^2 - 1} \) is ________.
The Fourier series expansion of \( f(x) = \sin^2 x \) in the interval \((- \pi, \pi)\) is ______.
For all real values of \( x \) and \( y \), the partial differential equation in terms of \( \psi(x, y) \) given by \[ \frac{\partial^2 \psi}{\partial x^2} + 2 \frac{\partial^2 \psi}{\partial x \partial y} - 3 \frac{\partial^2 \psi}{\partial y^2} = 0 \]
is ______\.
The sum of the static pressure and dynamic pressure at a point in a fluid flow is called the ________.
Identify the range of Reynolds number (Re) for a creeping flow.
The ratio of the magnitudes of vorticity to rate of rotation in a fluid flow is _______.
In a laminar boundary layer, the ratio of boundary layer thickness (\( \delta \)) to the corresponding displacement thickness (\( \delta^ \)) lies between ______.
For marine engine shafts subjected to high radial and axial thrust loads, which one of the following types of bearings is the most suitable?
Which one of the following wave energy spectra is formulated for two peaks?
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 ______.
The dynamic response amplitude \( |H(\omega)| \) of a single degree of freedom system subjected to support motion is given by the following expression: \[ |H(\omega)| = \sqrt{\frac{1 + 4 \zeta^2 \left( \frac{\omega}{\omega_n} \right)^2 }{\left[ 1 - \left( \frac{\omega}{\omega_n} \right)^2 \right]^2 + 4 \zeta^2 \left( \frac{\omega}{\omega_n} \right)^2} } \]
Where the damping ratio is \( \zeta \), the excitation frequency is \( \omega \), and the natural frequency of the system is \( \omega_n \). The amplitude \( |H(\omega)| \) increases with an increase in damping ratio (\( \zeta \)) if the excitation frequency (\( \omega \)) is _______ the natural frequency (\( \omega_n \)) of the system.
In the stress-strain curve of mild steel, plastic deformation starts at the ______.
In ships, a flash evaporator is used to obtain ______.
Which one of the following is the most common type of gear assembly used for coupling steam turbine and propeller shafts?
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 m\(^3\) of seawater of density 1025 kg/m\(^3\). Which one of the following scenarios will minimize the free surface effect?
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?
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 \( y = a_0 \cos(\omega t) \), where \( \omega \) is the angular frequency.
The carriage speed is 3 m/s, \( \omega = \frac{\sqrt{3}}{2} \) rad/s,
and the maximum drift angle during the test is \( 30^\circ \).
The amplitude of oscillation \( a_0 \) lies between ______.
Consider the function \( f(x) = |x| - 1 \). Which of the following statements is/are true in the interval \([-10, 10]\)?
For a freely floating body in water, which of the following degrees of freedom has/have inherent restoring force?
Which of the following boiler arrangements will ensure that there is NO contamination of the primary feed system?
Which of the following components is/are NOT found in a two-stroke marine diesel engine?
Choose the correct statement(s) from the following with respect to a ship-generated Kelvin wave pattern in deep water.
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 ______\
The dynamics of a 90 m long ship are governed by the non-dimensional Nomoto equation. The magnitude of Nomoto gain \( |K'| = \frac{72}{35\pi} \) and that of Nomoto time constant \( |T'| = \frac{288}{35\pi} \). The steady turning radius of the ship for a 35° turning circle maneuver is _____ m (answer in integer).
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).
Consider \( f(t) = \cos(at) \), where \( a \) is a real constant. The Laplace transform of \( f(t) \) is _________.
A square‑shaped body is subjected to only direct tensile stresses \(\sigma_x\) and \(\sigma_y\) as shown. If \(\sigma_x>\sigma_y\), then the value of normal stress (\(\sigma_{\theta}\)) and shear stress (\(\tau_{\theta}\)) respectively are \rule{3cm{0.4pt.
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 \rule{2cm{0.4pt kN‑m.
For a butt weld joint of two plates, which one of the following loading scenarios has the least permissible stress?
Match the non-dimensional numbers in Column 1 with the corresponding definitions in Column 2:
\begin{tabular{ll
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
\end{tabular
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 \rule{3cm}{0.4pt} respectively.
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 \(p_1\) and \(p_2\)?
- (A)
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- (B)
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- (C)
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- (D)
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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: \[ Y_v' = -1000 \times 10^{-5}, \quad N_r' = -800 \times 10^{-5}, \quad N_v' = -200 \times 10^{-5}, \quad Y_r' = 100 \times 10^{-5} \]
The stability criterion \( C' \) is given by: \[ C' = Y_v'(N_r' - m' x_G') - (Y_r' - m') N_v' \]
where \( m' = \frac{m}{\frac{1}{2} \rho L^3} \), \( m \) is the mass of the barge, \( \rho \) is the density of seawater, and \( x_G \) 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 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 ship of length 100 m and displacement 5000 tonne floats even-keel at 6.5 m in fresh water of density 1000 kg/m\(^3\). 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/m\(^3\) without change in the displacement. The new forward and aft draughts are ______ respectively.
Consider a case where the load \( Q \) for a ship structure has only statistical uncertainties. The probability density function of the load \( p_Q(x) \) is shown in the figure. The characteristic limit value of the load \( Q_L \) is 1.5 and the factor of safety is 1. Which of the following probability of exceedance value(s) of the load will lead to a safe design?
The value of \( \int_1^3 \int_2^5 x^2 y \, dx \, dy \) is ______\ (answer in integer).
Let \( M = \begin{bmatrix} 1 & 0
0 & 2 \end{bmatrix} \) and \( K = \begin{bmatrix} 2 & -1
-1 & 1 \end{bmatrix} \) satisfy the eigenvalue problem given by: \[ (M - \alpha K)\phi = 0. \]
The lowest eigenvalue \( \alpha \) is ________ (rounded off to two decimal places).
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The gradient of \( y = 3x^2 \sin(2x) \) at \( (0.2, 1) \) is:
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 \(\times\) 0.5 m. The magnitude of maximum tensile stress in the beam is ________ N/m\(^2\) (answer in integer).
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The displacement field of a body is given by \( \vec{u} = yx \hat{i} + yz \hat{j} + (z + x^2) \hat{k} \). The shear strain \( \gamma_{xy} \) at \( (2, 1, 5) \) is:
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 \( g = 9.81 \, m/s^2 \). 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 98.10 MN·m (rounded off to two decimal places).
The stream function of a two-dimensional flow field is given as \( \psi = 2xy + 2y + 2x \). 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 \underline{\hspace{1cm (answer in integer).
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 \( g = 9.81 \, m/s^2 \). The discharge through the opening is \rule{3cm{0.4pt litres/s (answer in integer).
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 \( \nu \) is \( 1.5 \times 10^{-5} \, m^2/s \).
Using Blasius solution, the boundary layer thickness at the trailing edge of the surface is \underline{\hspace{1cm mm (rounded off to two decimal places).
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 \( \mu = 0.2 \, N-s/m^2 \). 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 \rule{3cm{0.4pt N (answer in integer).
Water of density \( \rho = 1000 \, kg/m^3 \) 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 \( 0.06 \, m^3/s \), the magnitude of the reaction force \( F_x \) required to keep it stationary is \rule{3cm{0.4pt kN (rounded off to one decimal place).
An ocean wave is propagating from deep to shallow water. The wave is approaching the coast at \( 45^\circ \) counterclockwise from the shore normal with an initial phase speed of \( 12.5 \, m/s \). After entering the shallow water, the wave direction becomes \( 30^\circ \) counterclockwise from the shore normal.
The phase speed of the wave at the shallow water is \underline{\hspace{1cm m/s (rounded off to one decimal place).
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 \( h_{fg} = 2440 \, kJ/kg \).
If the flow rate of air is 1 kg/s, the rate of heat transfer from the air is \rule{3cm{0.4pt kW (rounded off to two decimal places).
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 m\(^2\). 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 \( g = 9.81 \, m/s^2 \), the thermodynamic work done by the system during this process is \rule{3cm{0.4pt J (answer in integer).
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 (\( \eta_{bth} \)) is 45%, and fuel consumption rate (\( \dot{m}_f \)) 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 \underline{\hspace{1cm bar (rounded off to one decimal place).
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 \( q_1 = q_2 = q_3 = 0.9376 \, MN/m \).
The applied twisting moment on the midship section is \rule{3cm{0.4pt MN·m (rounded off to two decimal places).
A ship of 3300 tonne displacement is undergoing an inclining experiment in seawater of density 1025 kg/m\(^3\). A mass of 6 tonne is displaced transversely by 12 m as shown in the figure. This results in a 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 \rule{3cm}{0.4pt} m (rounded off to two decimal places).
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 \underline{\hspace{1cm kW (rounded off to two decimal places).
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 \underline{\hspace{1cm % (rounded off to one decimal place).
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