List of top Questions asked in GATE NM

'When it is raining, peacocks dance.'
Based only on this sentence, which one of the following options is necessarily true?

A ship floating in seawater has a TPC (Tonne Per Centimeter immersion) of 20.

If bilge keel of total mass 65.1 tonne and volume 44 \(\text{m}^3\) is added to the ship, then the change in the mean draft is ______ cm.

Assume that after bilge keel fitment, the TPC remains constant, and the ship undergoes parallel sinkage. Density of seawater is 1025 \(\text{kg/m}^3\).

A differentiable function \(f(x)\) is such that \(f(-0.1) = 2\), \(f(0) = 1\), and \(f(0.1) = 2\).

Then, \(\dfrac{d^2f}{dx^2}\) at \(x = 0\) is ______ (answer in integer).

The RAO (Response Amplitude Operator) of a floating body with no forward speed is denoted by \(H(\omega)\).

If it encounters a wave spectrum \(S(\omega)\), then its response spectrum is ______.

Consider the function \(f(x,y) = x^3 + y^2\).

If \(\vec{F} = \nabla f\), then \(\displaystyle\int \vec{F} \cdot d\vec{r}\) evaluated from \((0,0)\) to \((1,2)\) is ______ (answer in integer).

Choose the CORRECT bending moment diagram for the simply supported beam shown in the figure with a concentric moment \(M\) at mid span.

Consider hogging as positive and sagging as negative.

Figures not to scale

The Fourier series expansion of the function \( f(x) = |\cos(x)| \) in the interval \( (-\pi, \pi) \) is \( \alpha + \beta \left[ \dfrac{1}{3}\cos(2x) - \dfrac{1}{15}\cos(4x) + \cdots \right] \).
The values of \( \alpha \) and \( \beta \) respectively are ______.

A ship is moving at 10 m/s in head sea condition. A person on board counts the time period between two successive wave crests as \(\pi\) seconds.
The frequency of the incoming wave is ______ rad/s (answer in integer).
Assume g = 10 m/s\(^2\).

Which of the following statements is/are TRUE regarding matrices?

Adverse pressure gradient implies that ______.

A day can only be cloudy or sunny. The probability of a day being cloudy is 0.5, independent of the condition on other days. What is the probability that in any given four days, there will be three cloudy days and one sunny day?

A static system consisting of air, water, oil and mercury is shown in the figure. If Q is open to the atmosphere, the gauge pressure at P is ______ kPa (rounded off to one decimal place).
Consider \(g = 10 \text{ m/s}^2\), \(h_1 = 0.5\) m, \(h_2 = 0.7\) m, \(h_3 = 0.8\) m, density of water \(= 1000 \text{ kg/m}^3\), \(SG_{oil} = 0.9\) and \(SG_{mercury} = 13.6\) (where SG is specific gravity).

The potential flow theory assumes that the flow is ______.

The drag force on a non-lifting smooth body immersed in an incompressible, irrotational, uniform flow is ______.

Two tiles are missing in Panel I. Which one of the options in Panel II is the appropriate choice for the missing tiles?

Which of the following structures is/are mainly used for harbor berthing?

A solid beam with a rectangular cross-section of breadth 0.5 m and depth 0.12 m, experiences a vertical shear force of 50 kN at a section.
The maximum shear stress in that section is ______ MPa (answer in two decimal places).

The values of Stock A and Stock B on a particular day are Rs. 50 and Rs. 80, respectively. An investor invests Rs. 100 in Stock A and Rs. 80 in Stock B. He sells all the stocks the next day when the value of Stock A is Rs. 55 and Stock B is Rs. 70. The profit made by the investor is Rs. ________

The sway-yaw coupled maneuvering equation of motion for a ship is
\[ \begin{bmatrix} M - Y_{\dot{v}} & -Y_{\dot{r}} \\ -N_{\dot{v}} & I_z - N_{\dot{r}} \end{bmatrix} \begin{bmatrix} \dot{v} \\ \dot{r} \end{bmatrix} = \begin{bmatrix} Y_v & Y_r \\ N_v & N_r \end{bmatrix} \begin{bmatrix} v \\ r \end{bmatrix} + \begin{bmatrix} Y_{\delta} \\ N_{\delta} \end{bmatrix} \delta_R \]For a control-fixed straight-line stability, the eigenvalues of the function should be ______.

A propeller of 4 m pitch is rotating at 120 rpm. It has a behind-hull propeller efficiency of 60% and a real slip of 25%.
If the power delivered to the propeller is 2800 kW, then the thrust produced by it is ______ kN (answer in integer).

A ship is undergoing a steady starboard turn. Assume that the total hydrodynamic forces \(Y\) including the rudder forces act at the centre of buoyancy \(B\).
If \(W\) is the weight of the ship, \(G\) is the centre of gravity and \(M\) is the transverse metacentre, then the magnitude of the heel angle \(\phi\) is given by ______.
Assume that \(\phi\) is small.

The virtual work principle states that ______.

The weight of a ship is uniformly distributed along its length.
Under which ONE or MORE of the following conditions will the ship be subjected to hogging moment?
Note: The weight is equal to buoyancy in all of the following conditions.