List of top Questions asked in GATE NM

Assume that a ship has length \(L = 200 \, \text{m}\) and operates at a design speed \(U = 12 \, \text{m/s}\). If in a turning circle maneuver the ship exhibits a steady turning diameter of \(6L\), then the yaw rate of the ship is ________________ rad/s (correct to two decimal places).

If the maximum static deflection of a shaft is 5 mm, then the estimated critical speed using Rayleigh–Ritz method is ____________ RPM (rounded off to nearest integer).

Which of the following flows are represented by the velocity field, \[ \mathbf{V} = (x^2 - y^2) \hat{i} - 2xy \hat{j}? \]

If a ship enters shallow water from deep water, maintaining the same speed, then which of the following are TRUE?

For a rigid vessel at sea, which of the following statements are TRUE?

Which of the following are TRUE for pressure, temperature and density of a thermodynamic system?

Let \( f(x,y,z)=xy+yz+xz \). If a point \( (0,0,\lambda) \) lies on the tangent plane to the surface \( f(x,y,z)=3 \) at the point \( (1,1,1) \), then the value of \( \lambda \) is __________.

In an internal combustion engine, supercharging is the process of supplying intake air at a pressure

The most desirable property amongst the following for a lubricating oil is:

If $\dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n \cos(nx)$ is the Fourier cosine series of the function $f(x)=\sin x,\; 0<x<\pi$, then which of the following are TRUE?

A simply supported beam is loaded with a uniformly distributed load (UDL). Which statements about strain energy are TRUE?

In a diesel engine, the ignition is initiated by the:

A truck loaded with a half-filled water tank is moving at a constant horizontal acceleration $a$. The acceleration due to gravity is $g$. At steady state, the angle $\theta$ made by the free surface with the horizontal plane is

Which one of the following combinations of elementary flows will lead to an ideal flow past a deeply submerged circular cylinder with circulation?

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.

The margin line used for the floodable length calculation of a ship is:

Consider a rectangular box barge of length 80 m, breadth 20 m and depth 15 m floating at an even draught of 10 m. Assume that the heave added mass of the vessel is equal to its mass displacement and the acceleration due to gravity is 9.81 m/s\(^2\). The heave natural period of the vessel lies in between ________________ s.

A 1:20 scaled model of a surface ship is tested in a towing tank. The model is towed at 3 m/s and drag force measured is 10 N. The velocity of the prototype and the drag force acting on the prototype, respectively, are ________________ m/s and ________________ kN.

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.
Let X, Y, and Z represent the following operations:
X: rotation of the square by 180 degree with respect to the S-Q axis.
Y: rotation of the square by 180 degree with respect to the P-R axis.
Z: rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.
Consider the following three distinct sequences of operation (which are applied in the left to right order).
(1) XYZ
(2) XY
(3) ZZZZ
Which one of the following statements is correct as per the information provided above?

Let \( A \) be a real non-zero square matrix of order \( n \). If the homogeneous system of linear equations \( Ax = 0 \) has only the trivial solution, then:

Let \( z = x + iy \), where \( x \) and \( y \) are real numbers. Consider the complex functions: \[ f(z) = (x^2 - y^2) + i 2xy \] and \[ g(z) = 2xy + i(x^2 - y^2) \] Then on the complex plane,

If a population has exponential distribution with mean 1, then its median is:

Let \( \omega_f \) be the excitation frequency of a sinusoidal load and \( \omega_n \) be the natural frequency of a single degree of freedom system. Then the dynamic response of the system is highly affected by the stiffness of the system when:

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.
If the security guard does not move around the posted location and has a 360° view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery?

Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.
Which one of the following is the correct logical inference based on the information in the above passage?