List of top Questions asked in GATE Engineering Sciences- 2025

The vertical (depth) profiles for three parameters P1, P2, and P3 in the northern Indian Ocean are given in the figure. The values along the x-axis are the normalized values of the parameters and the y-axis is the depth (m). Identify the parameters P1, P2, and P3 from the options given below.

The sea surface height concentric isolines (\(L1\) and \(L2\) in cm) and the distance between them (\(dx\) in km) for three different eddies at the same latitude are given in the figure. Which one of the following orders is correct about the magnitudes of the geostrophic currents within the isolines?

A rotating weather system has a tangential velocity of \(100~\mathrm{m/s}\), diameter of \(1~\mathrm{km}\), and located at a latitude where the Coriolis parameter is \(10^{-4}~\mathrm{s^{-1}}\). Which one of the following statements is true about this weather system?

The directions of the South Pacific Subtropical Gyre and the North Atlantic Subtropical Gyre are ________________ and ________________, respectively.

In canning and retorting of foods, which of the following is the correct expression of Ball process time (B)? Assume: \(t_p = \) processor’s process time; \(t_c = \) come-up time.

In a set of copolymerization reactions, the following monomer reactivity ratios (\(r_1\) and \(r_2\)) were found for different cases: \[ \begin{array}{|c|c|c|} \hline \text{Case} & r_1 & r_2 \\ \hline I & 0.1 & 10 \\ II & 0.003 & 0.02 \\ III & 3.4 & 5.6 \\ IV & 51 & 0.01\\ \hline \end{array} \] Which option(s) correctly identify/identifies the type of copolymerization corresponding to each Case?

During material testing, stress is applied from time \(t_i\) to \(t_f\).

The corresponding strain responses for three different materials are shown in plots P, Q, and R.

Choose the option(s) where the strain response is correctly mapped to its material class.

Injection molding is typically used to make plastic parts. If the pressure at the gate is monitored as a function of time during the injection of a thermoplastic polymer, identify the profile that best describes this event.

Air enters a hair dryer at 22 °C and 100 kPa with a velocity of 3.7 m/s, and leaves the dryer at 83 °C and 100 kPa with a velocity of 9.1 m/s. The exit area of the dryer is 18.7 cm\(^2\), and the ambient temperature is 22 °C. The air is an ideal gas with gas constant \(R = 0.287 \, kJ/kg\!-\!K\) and isobaric specific heat \(c_p = 1.005 \, kJ/kg\!-\!K\). If the change in potential energy is neglected, the second law efficiency (in %) of the dryer is ..................... (rounded off to one decimal place).

Consider a gas obeying the relation \[ P(v - b) = RT \] where \(b\) and \(R\) are constants. Which of the following statement(s) is/are CORRECT about the specific heat capacity at constant pressure?

A rigid tank of 300 litre capacity contains 3 kg of oxygen (molar mass = 32 kg/kmol) at \(25^\circ C\). If oxygen behaves as an ideal gas, the pressure (in kPa) inside the tank is ............... (rounded off to two decimal places). Use: \(R_u = 8.314 \, kJ/kmol-K\)

Let \(T_H\) and \(T_L\) denote the absolute temperatures of high and low temperature reservoirs, respectively. The coefficient of performance (COP) of a reversible refrigerator operating between these two reservoirs is

A closed system undergoes a process 1–2 in which it absorbs 150 kJ of energy as heat and does 90 kJ of work. Then it follows another process 2–3 in which 80 kJ of work is done on it while it rejects 60 kJ as heat. If it is desired to restore the system to the initial state (state 1) by an adiabatic path, the work interaction (in kJ) in this process will be

A cylinder of volume \(0.1 \, m^3\) is filled with nitrogen at \(10 \, MPa\) and \(300 \, K\). Consider nitrogen to be an ideal gas. The cylinder develops a leak and nitrogen escapes to the atmosphere which is at \(0.1 \, MPa\). After some time, the pressure in the cylinder reduces to \(5 \, MPa\). Assuming the cylinder and the leaked gas temperature remains constant at \(300 \, K\), the work done (in MJ) by nitrogen gas is:

An electric motor’s rotor is spinning at 1500 rpm when its load and power are cut off. The rotor, which has a mass of 50 kg and a radius of gyration of 200 mm, then coasts down to rest. Due to kinetic friction, a constant torque of 10 Nm acts on the rotor as it coasts down. The number of revolutions executed by the rotor before it comes to rest is .......... (in integer).

A massless cantilever beam, with a tip mass \(m = 10 \, kg\), is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length \(L = 1 \, m\), with a circular cross-section of diameter \(d = 20 \, mm\). The Young’s modulus of the beam material is \(E = 200 \, GPa\).

The natural frequency of the spring-mass system is .......... Hz (rounded off to two decimal places).

A simply-supported beam has a circular cross-section with diameter \(20 \, mm\), area \(A = 314.2 \, mm^2\), area moment of inertia \(I = 7854 \, mm^4\), and length \(L = 4 \, m\). A point load \(P = 100 \, N\) acts at the center and an axial load \(Q = 20 \, kN\) acts through the centroidal axis.

The magnitude of the offset between the neutral axis and the centroidal axis, at \(L/2\) from the left, is ............ mm (rounded off to one decimal place).

A simply-supported beam, with a point load \(P = 150 \, kN\) at a distance of \(L/3\) from the left end, is shown in the figure. The elastic-strain energy (U) of the beam is given by: \[ U = \frac{2}{243} \cdot \frac{P^2 L^3}{EI} \] where the section modulus, \(EI = 16.66 \times 10^5 \, Nm^2\), and the length of the beam \(L = 1 \, m\).

The deflection at the loading point is .......... mm (rounded off to two decimal places).

A closed thin cylindrical tank with mean diameter \(d = 300 \, mm\) and thickness \(t = 2 \, mm\), is subjected to a uniform internal gas pressure \(p\). The allowable shear stress on the curved wall of the tank is 70 MPa. Based on the Tresca criteria, which one of the following options for the maximum safe value of \(p\) (in MPa) is CORRECT?

Consider two blocks, P of mass 100 kg and Q of mass 150 kg, resting as shown in the figure. The angle of the wedge is \(\theta = 30^\circ\). The coefficient of friction between the two blocks is \(\mu = 0.2\). Assume no friction exists at all other interfaces.
The minimum force required to move block P upward is \(W\).

Which one of the following options is closest to the correct magnitude of \(W\) (in N)?

In an FCC crystal with lattice parameter \(a\), consider the reaction of two leading partial dislocations, AB and CD, at the line of intersection of their slip planes \((111)\) and \((\bar{1}11)\), respectively. Dislocations AB and CD have Burgers vectors \(\vec{b}_1\) and \(\vec{b}_2\), respectively, as given in the figure. Which one of the following options for the slip plane and the Burgers vector of the resulting dislocation is correct?

Let \(X\) and \(Y\) be two random variables with mean \(0\), variance \(1\), and correlation coefficient \(\tfrac{1}{3}\). Then the value of \(\mathrm{Var}(X+3Y)\) is equal to:

Let $f(z)$ be an analytic function such that \[ Re(f'(z)) = 3x^2 - 4y - 3y^2, f(i)=0, f'(0)=0, \] where $i = \sqrt{-1}$. Then the value of $f(1)$ is:

For $a,b \in \mathbb{R}$, consider the system of linear equations: \[ x + y + az = 2, \] \[ 2y + 2z = 1, \] \[ ax + 2z = b \] If the system has infinitely many solutions, then which of the following statements is/are correct?

For a steady and incompressible flow, the velocity field $\vec{V}$ in Cartesian $(x,y,z)$ coordinate system is given as: \[ \vec{V} = 5x \, \mathbf{i} - P y \, \mathbf{j} + 3 \mathbf{k}. \] Here, $\mathbf{i}, \mathbf{j}, \mathbf{k}$ are unit vectors along $x, y, z$ directions, respectively, and $P$ is a constant. Which one of the following options is the correct value of $P$ that satisfies the conservation of mass for the given velocity field?