List of top Questions asked in GATE XE- 2025

A solid body of uniform specific gravity floats in a deep liquid pool. Take \( B \), \( G \), and \( M \) as the centre of buoyancy, centre of gravity, and metacentre of the body, respectively. Which one of the following options is correct for the stable floatation of the body in the pool when the body is given a small tilt angle?

Group-I shows different two-dimensional bodies and Group-II mentions their total drag coefficient \( C_d \) based on frontal area while facing parallel flow of fluid having Reynolds number \( Re \geq 10^4 \) along the direction of the arrow. The bodies are placed symmetrically with respect to the flow direction. Which one of the following options identifies the correct match between Group-I and Group-II, as per the concept of degree of streamlining? 

Figure shows two parallel plates (upper plate at \( x = b \) and lower one at \( x = -b \) of length L (aligned in \( z \)-direction and infinite width (in \( y \)-direction, normal to the plane of the figure)). Two immiscible, incompressible liquids are flowing steadily in the \( z \)-direction through the thin passage between the plates under the influence of a horizontal pressure gradient \( \left( \frac{P_0 - P_L}{L} \right) \). During the flow, the passage is always half-filled with denser fluid I (viscosity \( \mu_1 \)) at the bottom and rest is occupied by lighter fluid II (viscosity \( \mu_2 \)). Considering exactly in between the fluids and no instabilities in the flow, the shear stress \( \tau_{xz} \) is expressed as:
\[ \tau_{xz} = \frac{(P_0 - P_L) b}{L} \left( \frac{x}{b} - \frac{1}{2} \right) \left( \frac{\mu_1' - \mu_2'}{\mu_1' + \mu_2'} \right) \] Which one of the following options correctly identifies the location of the point having maximum velocity of the flow?

Group-I indicates different properties of fluid and Group-II defines their basic dimensions in terms of Force (F), Length (L), and Time (T).
Which one of the following options identifies the correct match between Group-I and Group-II?

Statement of Reynolds Transport Theorem is given below with three blanks.
The rate of change of ............. extensive property can be calculated by summing the rate of change of the amount of same property in the ............. and the rate at which the property is ............. the surface of the control volume.
Which one of the following options correctly fills the blanks by using its comma-separated phrases in sequence?

Consider the following Statements [1] and [2].
Statement [1]: The Eulerian study focuses attention on individual particle and its motion is observed as a function of time.
Statement [2]: The Lagrangian study focuses attention on the motion of the particles passing through an identified point.
Which one of the following options identifies the correctness of the given statements?
 

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?
Consider the function \[ f(x, y) = x^2y + 2xy^2 - 2x^2y^2. \] Then which one of the following statements is correct?
Let \( C \) be the positively oriented boundary of the domain bounded by the curves \( y = 2x^2 \) and \( y^2 = 4x \). Then the value of the line integral \[ \oint_C \left( 2y^2 + 2xy + 4y \right) dx + \left( x^2 + 4xy + 8x \right) dy \] is equal to:
One kg of dry air at 15°C is isothermally compressed to one tenth of its initial volume. The work done on the system is .......... kJ. (Round off to the nearest integer.) [Assume that the gas constant for dry air is \(287 \times 10^5 \, {J K}^{-1} \, {kg}^{-1}\).]
The sensible heat (SH) flux at the locations P and Q are SH\(_P\) and SH\(_Q\), respectively. The value of \( \frac{SH_P}{SH_Q} \) is .......... (in integer).
A column of air mass extending from surface to a height of 10 km moving eastward along 30°N strikes a north-south oriented mountain range. While crossing the mountain range, the air mass acquires a relative vorticity of \( -3.65 \times 10^{-5} \, {s}^{-1} \) at the top. If the air mass maintains the same latitude and conserves potential vorticity, the height of the mountain range is ........ km. (Round off to the nearest integer.) [Assume the angular velocity of the Earth is \( 7.3 \times 10^{-5} \, {s}^{-1} \) and initial relative vorticity is zero.]
A floating hot air balloon with volume 1000 m³ and gross mass (excluding the air in the balloon) 100 kg is in hydrostatic balance where the external air temperature is 10°C and density is 1 kg m³. The temperature of the air inside the balloon is ......... °C. (Round off to the nearest integer.) [Assume that the gas constant for dry air is 287 J K\(^{-1}\) kg\(^{-1}\).]
The solar constant for the Earth is 1368 W m\(^{-2}\). Consider the planet Jupiter whose mass is 320 times that of the Earth and distance from the Sun is 5.2 times that of the Earth. The solar constant for Jupiter is .......... W m\(^{-2}\). (Round off to the nearest integer.) [Assume the inverse square law for the solar radiation.]
In hot weather, a human body cools by the evaporation of sweat from its skin. The amount of water that must evaporate to cool the body by 1°C is .........% of the body mass. (Round off to two decimal places.) [Assume that latent heat of vaporization of water is \(2.25 \times 10^6 \, {J kg}^{-1}\) and specific heat capacities of both human body and liquid water are \(4.2 \times 10^3 \, {J K}^{-1} \, {kg}^{-1}\).]
The time period of the inertial oscillation at a location R is 1.5 times that of a particle moving at a speed of 0.5 m/s at a location S (87°E, 45°S). Which of the following is the latitude of location R? (Round off to the nearest integer)
Accumulated rainfall is often measured in mm. If the density of rain water is 1000 kg/m\(^3\) then, one mm of rain is equal to ......... kg/m\(^2\) of rain. (in integer).
The directions of the South Pacific Subtropical Gyre and the North Atlantic Subtropical Gyre are ........... and .........., respectively.
Which one of the following is the main cause of the land-sea temperature contrast that drives phenomena like sea breeze and the Indian summer monsoon?
A rotating weather system has a tangential velocity of 100 m/s, diameter of 1 km, and located at a latitude where the Coriolis parameter is \( 10^{-4} \, {s}^{-1} \). Which one of the following statements is true about this weather system?
Acceleration due to Coriolis force of a water parcel at a location P (67°E, 20°N) moving with a speed of 0.35 m/s is .......... \(\times 10^{-5}\) m/s\(^2\). (Round off to two decimal places)
[Assume the angular velocity of the Earth is \(7.3 \times 10^{-5}\) s\(^{-1}\))]
A unidirectional composite of a resin is prepared with continuous fibers, wherein the volume fraction of the fiber in the composite is 0.7. Assume that the resin has a modulus of 9 GPa and the fiber has a modulus of 90 GPa. A sample of this composite, possessing a breadth of 4 mm and a thickness of 1 mm, is subjected to a uniaxial tensile test along the direction of the fiber.
Corresponding to a strain of 0.5%, the force applied on the sample is ............ N. {(Round off to the nearest integer)}
A rubber contains 70 wt% butadiene (molar mass = 54 g/mol), 20 wt% isoprene (molar mass = 68 g/mol), 5 wt% sulfur and 5 wt% carbon black. Assume that all the sulfur is present in crosslinks. If each sulfide crosslink contains an average of two sulfur atoms, the percentage of possible crosslinks that are joined by vulcanization is ............%. {(Round off to one decimal place)}
At which of the following locations in the atmosphere is the anvil of a towering cumulonimbus cloud usually located?
During which of the following times of the day is the 2 m air temperature usually the lowest at a tropical location?