Mechanical Engineering Gate Yearwise
Mechanical Engineering Gate 2023 Questions with Answer
Ques 14 GATE 2023
The figure shows the plot of a function over the interval [-4,4]. Which one of the options given CORRECTLY identifies the function?
Ques 15 GATE 2023
A vector field
B(x,y,z)=xî+yĵ-2zk
is defined over a conical region having height h=2, base radius r=3 and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin. If n denotes the unit outward normal to the curved surface S of the cone, the value of the integral
(Answer in integer)
Ques 16 GATE 2023
A linear transformation maps a point (x', y') in the plane to the point (x,y) according to the rule x'=3y y'=2x. Then, the disc x2+y2≤1.
gets transformed to a region with an area equal to _______.
(Rounded off to two decimals)
Use π=3.14
Ques 17 GATE 2023
The value of k that makes the complex-valued function f(z)=e-kx(cos 2y-i sin 2y) analytic, where z=x+iy, is _______.
(Answer in integer)
Ques 18 GATE 2023
Which one of the options given is the inverse Laplace transform of 1/(s3-s)?
u(t) denotes the unit-step function.
Ques 19 GATE 2023
A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?
Take the acceleration due to gravity to be g=9.8 m/s2. Options have been rounded off to one decimal place.
Ques 20 GATE 2023
The velocity field of a certain two-dimensional flow is given by V(x, y) = k(xî − yĵ), where k = 2 s-1.
The coordinates x and y are in meters. Assume gravitational effects to be negligible.
If the density of the fluid is 1000 kg/m3 and the pressure at the origin is 100 kPa, the pressure at the location (2 m, 2 m) is _____________ kPa.
(Answer in integer)
Ques 21 GATE 2023
An explosion at time t = 0 releases energy E at the origin in a space filled with a gas of density ρ. Subsequently, a hemispherical blast wave propagates radially outwards as shown in the figure.
Let R denote the radius of the front of the hemispherical blast wave. The radius R follows the relationship R = k ta Eb ρc, where k is a dimensionless constant.
The value of exponent a is ___________.
(Rounded off to one decimal place)
Ques 22 Gate 2023
The figure shows two fluids held by a hinged gate. The atmospheric pressure is
Pa = 100 kPa. The moment per unit width about the base of the hinge is
____________ kNm/m. (Rounded off to one decimal place)
Take the acceleration due to gravity to be g = 9.8 m/s2.
Ques 23 Gate 2023
Consider a unidirectional fluid flow with the velocity field given by
where 𝑢(0,𝑡)=1. If the spatially homogeneous density field varies with time
the value of 𝑢(2,1) is ______________. (Rounded off to two decimal places)
Assume all quantities to be dimensionless.
Ques 24 GATE 2023
Consider an isentropic flow of air (ratio of specific heats = 1.4) through a duct as shown in the figure.
The variations in the flow across the cross-section are negligible. The flow conditions at Location 1 are given as follows:
P1=100 kPa, ρ1=1.2 kg/m3, u1=400 m/s
The duct cross-sectional area at Location 2 is given by A2=2A1, where A1 denotes the duct cross-sectional area at Location 1. Which one of the given statements about the velocity u2 and pressure P2 at Location 2 is TRUE?
Ques 25 GATE 2023
A certain country has 504 universities and 25951 colleges. These are categorised into Grades I, II, and III as shown in the given pie charts.
What is the percentage, correct to one decimal place, of higher education institutions (colleges and universities) that fall into Grade III?
Ques 26 GATE 2023
The symbols ◯ 🞳,△ and ◻ are to be filled, one in each box, as shown below. The rules for filling in the four symbols are as follows.
1) Every row and every column must contain each of the four symbols.
2) Every 2×2 square delineated by bold lines must contain each of the four symbols. Which symbol will occupy the box marked with '?' in the partially filled figure?
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