List of top Questions asked in GATE Engineering Sciences

The triple point \( (T_t, P_t) \) is shown in a schematic phase diagram (pressure (P) – temperature (T) plot) for one component system. \( G_S, G_L, G_V \) are the free energies of solid, liquid, and vapor, respectively. At a constant pressure, \( P_t \), the correct free energy \( G \) versus temperature \( T \) plot is:

Match the detector for a scanning electron microscope (SEM) in Column I with the resulting output in Column II. 

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 \( (111) \), respectively, as shown in the figure below. Dislocations AB and CD, have Burgers vectors \( \mathbf{b_1} \) and \( \mathbf{b_2} \), 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? 

The figure below shows a plane PQR in a unit cell. The Miller indices of the plane PQR is: 

An oil of density \(870 \, {kg/m}^3\) and viscosity \(0.036 \, {Pa.s}\) flows through a straight pipe of 10 cm diameter and 1.5 km length at the flow rate of 250 liters per minute under the steady and incompressible flow conditions.
To control the flow rate of oil, a valve is fixed at the middle of the pipe causing no change in the total length of the pipe. The total head loss measured across the two ends of the pipe is \(11.60 \, {m}\). Using gravitational acceleration as \(10 \, {m/s}^2\), the minor head loss contributed by the presence of the valve in m {(rounded off to 2 decimal places) is ..........}

A fixed control volume has four one-dimensional boundary sections (1, 2, 3, and 4). For a steady flow inside the control volume, the flow properties at each section are tabulated below: 

The rate of change of energy of the system which occupies the control volume at this instant is \( E \times 10^6 \, {J/s} \). The value of \( E \) (rounded off to 2 decimal places) is ........

A liquid flows under steady and incompressible flow conditions from station 1 to station 4 through pipe sections P, Q, R, and S as shown in the figure. Consider, \( d \), \( V \), and \( h \) represent the diameter, velocity, and head loss, respectively, in each pipe section with subscripts ‘P’, ‘Q’, ‘R’, and ‘S’. \( \Delta h \) represents the head difference between the inlet (station 1) and outlet (station 4). All the pipe sections are placed on the same horizontal plane for which the figure shows the top view. 
(Insert diagram here, if possible)

Figure shows the steady and incompressible flow of a fluid in the direction of the arrow from section A to section D. Three pipe connectors are to be placed between sections at A and D having Total Energy Line (TEL) and Hydraulic Grade Line (HGL) as depicted in the figure. Consider, \( g \), \( P \), \( Q \), \( V \), \( \gamma \), and \( Z \) denote gravitational acceleration, pressure, volume flow rate, velocity, specific weight, and elevation of the centerline of the pipe connectors from the datum, respectively. Which one of the following options, in sequence, indicates the correct nature of connectors between sections A and B, B and C, and C and D in the direction of flow?

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?

Suppose that 2 is an eigenvalue of the matrix 

Then the value of \( \alpha \) is equal to (Answer in integer):

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:
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.]
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 \(287 \times 10^5 \, {J K}^{-1} \, {kg}^{-1}\).]
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 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).
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.]
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\(^{-1}\).]