List of top Naval Architecture and Marine Engineering Questions asked in GATE NM

Let \(L = \begin{pmatrix} 3 & -1 & -1 & -1 \\ -1 & 2 & -1 & 0 \\ -1 & -1 & 3 & 0 \\ -1 & 0 & -1 & 1 \end{pmatrix}\). Which of the following are TRUE?

A simply supported beam with an overhang has experienced the bending moment as shown below. The corresponding concentrated load is 

 

The layout of a Tension Leg Platform (TLP) is shown in the following figure. It consists of four interconnected pontoons at the bottom and four cylindrical columns, which support the working platform at the top. The density of sea water is 1025 kg/m\(^3\). Neglect the weight and buoyancy of the tethers. During operation, the maximum mass (in metric tonnes) of the entire structure must lie between 

 

If the system of linear equations, \( x - ay - z = 0, ax - y - z = 0, x + y - z = 0 \), has infinite number of solutions, then the possible values of a are
If a random variable \( X \) has the probability density function \[ f(x) = \begin{cases} \frac{5}{32}x^4 & \text{if } 0 \le x \le 2 \\ 0 & \text{otherwise} \end{cases} \] and if \( Y = X^2 \), then the expected value of \( Y \) is .................... (round off to one decimal place)
A buoy of virtual mass 30 kg oscillates in a fluid medium as a single degree of freedom system. If the total damping in the system is set as 188.5 N-s/m, such that the oscillation just ceases to occur, then the natural period of the system is .................... s (round off to one decimal place)
The stress field, \(\sigma_x = 4x^3 + 3x^2y + 5xy^2\) \(\sigma_y = -x^3 + 6x^2y - 7xy^2\) \(\tau_{xy} = -5x^2y - 3xy^2\) would satisfy the strain compatibility condition if
If y(x) is the solution of the differential equation \[ (1+x^2)y'' - 2xy' = 0 \] satisfying y(0) = 0 and y'(0) = 3, then y(1) equals ....................
For a ship of length L = 100 m, the distance between the bow and stern pressure system is 0.942L. Assume g = 10 m/s². The ship velocity corresponding to the prismatic hump of the wave making resistance curve is .................... m/s (round off to one decimal place)
For a given time varying load applied on a single degree of freedom system, the dynamic response amplitude is always less than the static response amplitude if
The heave natural frequencies of a Jacket structure, FPSO and a semi-submersible are \(\omega_J\), \(\omega_F\) and \(\omega_S\) respectively. Each one of them has a pay load capacity of 10000 tonnes. Which of the following is TRUE?
A vertical frictionless piston-cylinder arrangement contains air of mass 1 kg. During a process, 50 J of heat is transferred from outside to the system such that the piston is raised slowly by 0.1 m from its initial equilibrium position. The mass of the piston is 1 kg, and the diameter is 0.1 m. Assume that g = 9.81 m/s², and Patm = 100 kPa. The change in internal energy of the air in J (round off to two decimal places) lies between
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A solid cantilever shaft of diameter 0.1 m and length 2 m is subjected to a torque of 10 kN-m at the free end (shear modulus is 82 GPa). The maximum induced shear stress is .................... N/mm\(^2\) (round off to the nearest integer).
The value of the surface integral \( \iint_S (x^2 \,dydz + y^2 \,dzdx + z^2 \,dxdy) \) over the surface of the cube given by \( 0 \le x \le 2, 0 \le y \le 2, 0 \le z \le 2 \), is
For a regular sinusoidal wave propagating in deep water having wave height of 3.5 m and wave period of 9 s, the wave steepness is .................... (round off to three decimal places)
The failure modes that may be observed in a riveted joint to fasten two plate members, subjected to shear load are
Let X be any random variable and \( Y = -2X + 3 \). If E[Y] = 1 and E[Y\(^2\)] = 9, then which of the following are TRUE?
Consider the contour integral \( \oint_C \frac{dz}{z^4 + z^3 - 2z^2} \), along the curve \( |z| = 3 \) oriented in the counterclockwise direction. If Res[f, z\(_0\)] denotes the residue of f(z) at the point z\(_0\), then which of the following are TRUE?
From the following, choose the offshore platform that can be used ONLY for offshore drilling purpose.
Which method among the following is based on the strain energy principle?
A horizontal cylinder of 1.0 m diameter is placed transversely at the aft of a ship and is completely immersed in water. The cylinder rotates at 100 RPM and inflow velocity is 10 m/s. Water density is 1000 kg/m\(^3\). Assuming an ideal planar flow, the lift force per unit length acting on the cylinder is ____________ kN/m (rounded off to one decimal place).
For a container ship, the propeller open water efficiency, thrust deduction fraction, and wake fraction are 0.60, 0.19, and 0.25, respectively. If the relative rotative efficiency of the propeller is 1.0, then the hull efficiency and quasi-propulsive efficiency of the propeller, respectively, are:
The diameter and rotating speed of a cargo ship propeller are 7.5 m and 120 RPM, respectively. An open water test is to be performed in a towing tank with a propeller model of 300 mm diameter. The corresponding propeller model speed is ________________ RPM.
A 10000 tonne displacement container ship’s main propulsion engine has a brake power equal to 46 MW and its service speed is 25 knots. Considering the engine brake power as double the effective power of the ship, then the ship resistance at the service speed lies in between ____________________ kN.