List of top Questions asked in GATE XE- 2023

Match the lattice planes and directions (in Column I) with the corresponding Miller indices (in Column II):

Match the hardness test (in Column I) with its indenter type (in Column II):

Axial velocity profile $u(r)$ for an axisymmetric flow through a circular tube of radius $R$ is given as, \[ \frac{u(r)}{U} = \left(1 - \frac{r}{R}\right)^{1/n} \] where $U$ is the centerline velocity. If $V$ refers to the area-averaged velocity (volume flow rate per unit area), then the ratio $V/U$ for $n = 1$ (rounded off to two decimal places) is $________________$.

A stationary circular pipe of radius $R = 0.5$ m is half filled with water (density = 1000 kg/m$^3$), whereas the upper half is filled with air at atmospheric pressure, as shown in the figure. Acceleration due to gravity is $g = 9.81$ m/s$^2$. The magnitude of the force per unit length (in kN/m, rounded off to one decimal place) applied by water on the pipe section AB is $________________$.

In age-hardening of an aluminium alloy, the purpose of solution treatment followed by quenching is to

The magnetization (M) – magnetic field (H) curves for four different materials are given below. Which one of these materials is most suitable for use as a permanent magnet?

The band gap of a semiconducting material is $\sim 2$ eV. Which one of the following absorption (A) vs. energy (in eV) curves is correct?

Figures (i) and (ii) show a binary phase diagram and the corresponding Gibbs free energy (G) vs. composition ($X_B$) diagram, respectively. Figure (ii) corresponds to which one of the temperatures shown in Figure (i)?

Aliovalent doping of $MgCl_2$ in $NaCl$ leads to the formation of defects. Which one of the following is the correct defect reaction?

A water jet (density = 1000 kg/m$^3$) is approaching a vertical plate, having an orifice at the center, as shown in the figure. While a part of the jet passes through the orifice, remainder flows along the plate. Neglect friction and assume both the inlet and exit jets to have circular cross-sections. If $V = 5$ m/s, $D = 100$ mm and $d = 25$ mm, magnitude of the horizontal force (in N, rounded off to one decimal place) required to hold the plate in its position is $________________$.

Water (density = 1000 kg/m$^3$) and alcohol (specific gravity = 0.7) enter a Y-shaped channel at flow rates of 0.2 m$^3$/s and 0.3 m$^3$/s, respectively. Their mixture leaves through the other end of the channel, as shown in the figure. The average density (in kg/m$^3$) of the mixture is $________________$.

The velocity and acceleration of a fluid particle are given as $\vec{V} = (-\hat{i} + 2\hat{j})$ m/s and $\vec{a} = (-2\hat{i} - 4\hat{j})$ m/s$^2$, respectively. The magnitude of the component of acceleration (in m/s$^2$, rounded off to two decimal places) of the fluid particle along the streamline is $________________$.

A hydraulic turbine with rotor diameter of 100 mm produces 200 W of power while rotating at 300 rpm. Another dynamically-similar turbine rotates at a speed of 1500 rpm. Consider both turbines to operate with the same fluid (identical density and viscosity), and neglect any gravitational effect. Then the power (in W, rounded off to nearest integer) produced by the second turbine is $________________$.

Water (density = 1000 kg/m$^3$) flows steadily with a flow rate of 0.05 m$^3$/s through a venturimeter having throat diameter of 100 mm. If the pipe diameter is 200 mm and losses are negligible, the pressure drop (in kPa, rounded off to one decimal place) between an upstream location in the pipe and the throat (both at the same elevation) is $________________$.

Water flows around a thin flat plate (0.25 m long, 2 m wide) with a free stream velocity ($U_\infty$) of 1 m/s, as shown in the figure. Consider linear velocity profile $\left(\frac{u}{U_\infty} = \frac{y}{\delta}\right)$ for which the laminar boundary layer thickness is expressed as $\delta = \frac{3.5x}{\sqrt{Re_x}}$. For water, density = 1000 kg/m$^3$ and dynamic viscosity = 0.001 kg/m·s. Net drag force (in N, rounded off to two decimal places) acting on the plate, neglecting the end effects, is $________________$.

For a potential flow, the fluid velocity is given by $\vec V(x,y)=u\,\hat{\imath}+v\,\hat{\jmath}$. The slope of the {potential line} at $(x,y)$ is

Consider steady incompressible flow of a Newtonian fluid over a horizontal flat plate, as shown in the figure. The boundary layer thickness is proportional to

In a steady two-dimensional {compressible} flow, $u$ and $v$ are the $x$- and $y$-components of velocity, and $\rho$ is the fluid density. Among the following pairs of relations, which one(s) perfectly satisfies/satisfy the definition of stream function, $\psi$, for this flow?

Which of the following statements are true? (i) Conservation of mass for an unsteady incompressible flow can be represented as $\nabla\! . \vec V = 0$, where $\vec V$ denotes velocity vector.
(ii) Circulation is defined as the line integral of {vorticity} about a closed curve.
(iii) For some fluids, shear stress can be a nonlinear function of the shear strain rate.
(iv) Integration of the Bernoulli’s equation along a streamline under steady-state leads to the Euler’s equation.

For a two-dimensional flow field given as $\vec V = -x\,\hat{\imath} + y\,\hat{\jmath}$, a streamline passes through points $(2,1)$ and $(5,p)$. The value of $p$ is

A stationary object is fully submerged in a static fluid, as shown in the figure. Here, CG and CB stand for the center of gravity and the center of buoyancy, respectively. Which one(s) among the following statements is/are true?

Consider steady fully-developed incompressible flow of a Newtonian fluid between two infinite parallel flat plates. The plates move in the opposite directions, as shown in the figure. In the absence of body force and pressure gradient, the ratio of shear stress at the top surface ($y=H$) to that at the bottom surface ($y=0$) is

A two-dimensional incompressible flow field is defined as \[ \vec V(x,y)=(Axy)\,\hat{\imath}+(By^2)\,\hat{\jmath}, \] where $A$ and $B$ are constants. The dynamic viscosity is $\mu$. In the absence of body force, which expression represents the {pressure gradient} at the location $(5,0)$ in the concerned flow field?

Let $u(x,t)$ be the solution of the initial–boundary value problem \[ \frac{\partial u}{\partial t}-\frac{\partial^2 u}{\partial x^2}=0, x\in(0,2),\ t>0, \] \[ u(x,0)=\sin(\pi x), x\in(0,2),\qquad u(0,t)=u(2,t)=0. \] Then the value of $e^{\pi^2}\!\left(u\!\left(\tfrac{1}{2},1\right)-u\!\left(\tfrac{3}{2},1\right)\right)$ is ________________ (in integer).

Match the following measuring instruments with the appropriate figures: I – Pitot probe II – Pitot-static probe III – Piezometer

Figures: (P), (Q), (R)