List of top Questions asked in GATE NM- 2022

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.

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?

Consider the following inequalities.
\text{(i) } 2x - 1 \(>\) 7
\text{(ii) } 2x - 9 \(<\)1
Which one of the following expressions below satisfies the above two inequalities?

Four points \( P(0, 1), Q(0, -3), R(-2, -1), \) and \( S(2, -1) \) represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?

In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below. Statement of P: R has copied in the exam.
Statement of Q: S has copied in the exam.
Statement of R: P did not copy in the exam.
Statement of S: Only one of us is telling the truth.
Statement of T: R is telling the truth.
The investigating team had authentic information that S never lies. Based on the information given above, the person who has copied in the exam is:

A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets ₹1000 more than S, what is the share of Q (in ₹)?

A trapezium has vertices marked as P, Q, R, and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm, and SP = 3 cm. What is the shortest distance between PQ and SR (in cm)?

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a "hole in the interior" that can be formed within the 4 $\times$ 4 grid using the unit squares as building blocks?

Mr. X speaks __________ Japanese __________ Chinese.