GATE XE (Engineering Sciences) 2023 Question Paper & Solutions

Question 1

The village was nestled in a green spot, _______ the ocean and the hills.

Accepted Answer

between

Answer

through

Answer

in

Answer

at

Question 2

Disagree : Protest : : Agree : _______ (By word meaning)

Accepted Answer

Recommend

Answer

Refuse

Answer

Pretext

Answer

Refute

Question 3

A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?

Accepted Answer

80

Answer

125

Answer

720

Answer

60

Question 4

Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?

Accepted Answer

At most half the candidates have a score that is larger than the median.

Answer

The median is at least as large as the mean.

Answer

The mean is at least as large as the median.

Answer

At most half the candidates have a score that is larger than the mean.

Question 5

In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of the hill?

Accepted Answer

Q

Answer

P

Answer

R

Answer

S

Question 6

Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of these academicians are authors of some best-selling books. Based only on the information provided above, which one of the following statements can be logically inferred with certainty?

Answer

Some residents of the complex who are well established in their fields are also authors of some best-selling books.

Answer

All academicians residing in the complex are well established in their fields.

Answer

Some authors of best-selling books are residents of the complex who are well established in their fields.

Answer

Some academicians residing in the complex are well established in their fields.

Question 7

Ankita has to climb 5 stairs starting at the ground, while respecting the following rules: 1. At any stage, Ankita can move either one or two stairs up. 2. At any stage, Ankita cannot move to a lower step. Let 𝐹(𝑁) denote the number of possible ways in which Ankita can reach the 𝑁𝑡ℎ stair. For example, 𝐹(1) = 1, 𝐹(2) = 2, 𝐹(3) = 3. The value of 𝐹(5) is _______.

Accepted Answer

8

Answer

7

Answer

6

Answer

5

Question 8

The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides: Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). The information contained in DNA can then be thought of as a sequence of these four nucleotides: A, T, C, and G. DNA has coding and non-coding regions. Coding regions—where the sequence of these nucleotides are read in groups of three to produce individual amino acids—constitute only about 2% of human DNA. For example, the triplet of nucleotides CCG codes for the amino acid glycine, while the triplet GGA codes for the amino acid proline. Multiple amino acids are then assembled to form a protein. Based only on the information provided above, which of the following statements can be logically inferred with certainty? (i) The majority of human DNA has no role in the synthesis of proteins. (ii) The function of about 98% of human DNA is not understood.

Accepted Answer

neither (i) nor (ii)

Answer

only (i)

Answer

only (ii)

Answer

both (i) and (ii)

Question 9

Which one of the given figures P, Q, R and S represents the graph of the following function? 𝑓(𝑥) = | |𝑥+ 2| −|𝑥−1| |

Accepted Answer

P

Answer

Q

Answer

R

Answer

S

Question 10

An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?

Accepted Answer

S

Answer

P

Answer

Q

Answer

R

Question 11

Let 𝐴 be a 3 × 3 real matrix having eigenvalues 1, 2, and 3. If 𝐵= 𝐴2 + 2𝐴+ 𝐼, where 𝐼 is the 3 × 3 identity matrix, then the eigenvalues of 𝐵 are

Accepted Answer

4, 9, 16

Answer

1, 2, 3

Answer

1, 4, 9

Answer

4, 16, 25

Question 12

Let 𝑓: ℝ2 →ℝ be a function defined by 𝑓(𝑥, 𝑦) = { 𝑥𝑦 |𝑥| + 𝑦 , 𝑦≠−|𝑥| 0 , otherwise. Then which one of the following statement is TRUE?

Accepted Answer

𝑓 is NOT continuous at (0,0).

Answer

𝜕𝑓 𝜕𝑥(0,0) = 0, and 𝜕𝑓 𝜕𝑦(0,0) = 1.

Answer

𝜕𝑓 𝜕𝑥(0,0) = 1, and 𝜕𝑓 𝜕𝑦(0,0) = 0.

Answer

𝜕𝑓 𝜕𝑥(0,0) = 1, and 𝜕𝑓 𝜕𝑦(0,0) = 1.

Question 13

If the quadrature formula ∫𝑓(𝑥)𝑑𝑥 1 −1 ≈1 9 (𝑐1𝑓(−1) + 𝑐2𝑓(1 2) + 𝑐3𝑓(1)) is exact for all polynomials of degree less than or equal to 2, then

Accepted Answer

𝑐1 + 𝑐2 4 + 𝑐3 = 6

Answer

𝑐1 + 𝑐2 3 + 𝑐3 = 4

Answer

𝑐1 + 𝑐2 2 + 𝑐3 = 2

Answer

𝑐1 + 𝑐2 + 𝑐3 = 5

Question 14

The second smallest eigenvalue of the eigenvalue problem 𝑑2𝑦 𝑑𝑥2 + (𝜆−3)𝑦= 0, 𝑦(0) = 𝑦(𝜋) = 0, is

Accepted Answer

7

Answer

4

Answer

3

Answer

9

Question 15

Which one of the following functions is differentiable at 𝑧= 0 but NOT differentiable at any other point in the complex plane ℂ?

Accepted Answer

𝑓(𝑧) = 𝑧|𝑧|, 𝑧∈ℂ

Answer

𝑓(𝑧) = sin(𝑧), 𝑧∈ℂ

Answer

𝑓(𝑧) = {𝑒 1 𝑧, 𝑧≠0 0, 𝑧= 0 for 𝑧∈ℂ

Answer

𝑓(𝑧) = 𝑒−𝑧2, 𝑧∈ℂ

Question 16

If the polynomial 𝑃(𝑥) = 𝑎0 + 𝑎1𝑥+ 𝑎2𝑥(𝑥−1) + 𝑎3𝑥(𝑥−1)(𝑥−2) interpolates the points (0, 2), (1, 3), (2, 2), and (3, 5), then the value of 𝑃( 5 2) is _________ (round off to 2 decimal places).

Accepted Answer

2.60 to 2.65

Question 17

The value of 𝑚 for which the vector field 𝐹⃗(𝑥, 𝑦) = (4𝑥𝑚𝑦2 −2 𝑥 𝑦𝑚)𝑖̂ + (2𝑥4𝑦−3𝑥2𝑦2)𝑗̂ is a conservative vector field, is _________________ (in integer).

Accepted Answer

3

Question 18

Let 𝑃= [ 4 −2 2 6 −3 4 3 −2 3 ], and 𝑄= [ 3 −2 2 4 −4 6 2 −3 5 ] . The eigenvalues of both 𝑃 and 𝑄 are 1, 1, and 2. Which one of the following statements is TRUE?

Accepted Answer

𝑃 is diagonalizable but 𝑄 is NOT diagonalizable

Answer

Both 𝑃 and 𝑄 are diagonalizable

Answer

𝑃 is NOT diagonalizable but 𝑄 is diagonalizable

Answer

Both 𝑃 and 𝑄 are NOT diagonalizable

Question 19

The surface area of the portion of the paraboloid 𝑧= 𝑥2 + 𝑦2 that lies between the planes 𝑧= 0 and 𝑧= 1 4 is

Accepted Answer

𝜋 6 (2√2 −1)

Answer

𝜋 2 (2√2 −1)

Answer

𝜋(2√2 −1)

Answer

𝜋 3 (2√2 −1)

Question 20

The probability of a person telling the truth is 4 6 . An unbiased die is thrown by the same person twice and the person reports that the numbers appeared in both the throws are same. Then the probability that actually the numbers appeared in both the throws are same is __________ (round off to 2 decimal places).

Accepted Answer

0.26 to 0.30

Question 21

Let 𝑢(𝑥, 𝑡) be the solution of the initial boundary value problem 𝜕𝑢 𝜕𝑡− 𝜕2𝑢 𝜕𝑥2 = 0, 𝑥∈(0, 2), 𝑡> 0 𝑢(𝑥, 0) = sin(𝜋𝑥), 𝑥∈(0, 2) 𝑢(0, 𝑡) = 𝑢(2, 𝑡) = 0. Then the value of 𝑒𝜋2 (𝑢( 1 2 , 1) −𝑢( 3 2 , 1)) is __________ (in integer).

Accepted Answer

2

Question 22

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

Accepted Answer

I – R; II – Q; III – P

Answer

I – P; II – Q; III – R

Answer

I – R; II – P; III – Q

Answer

I – Q; II – P; III – R

Question 23

Among the following non-dimensional numbers, which one characterizes periodicity present in a transient flow?

Accepted Answer

Strouhal number

Answer

Froude number

Answer

Peclet number

Answer

Lewis number

Question 24

For an incompressible boundary layer flow over a flat plate shown in the figure, the momentum thickness is expressed as

Accepted Answer

∫ 𝑢 𝑈∞ (1 −𝑢 𝑈∞ ) 𝑑𝑦 ∞ 0

Answer

∫ 𝑢 𝑈∞ 𝑑𝑦 ∞ 0

Answer

∫ (1 −𝑢 𝑈∞ ) 𝑑𝑦 ∞ 0

Answer

∫ (1 −𝑢2 𝑈∞2 ) 𝑑𝑦 ∞ 0

Question 25

Among the shear stress versus shear strain rate curves shown in the figure, which one corresponds to a shear thinning fluid?

Accepted Answer

R

Answer

P

Answer

Q

Answer

S

Question 26

Consider steady incompressible flow over a flat plate, where the dashed line represents the edge of the boundary layer, as shown in the figure. Which one among the following statements is true?

Accepted Answer

Bernoulli’s equation cannot be applied in Region I.

Answer

Bernoulli’s equation can be applied in Region I between any two arbitrary points.

Answer

Bernoulli’s equation can be applied in Region I only along a streamline.

Answer

Bernoulli’s equation cannot be applied in Region II.

Question 27

An inviscid steady incompressible flow is formed by combining a uniform flow with velocity 𝑈∞ and a clockwise vortex of strength 𝐾 at the origin, as shown in the figure. Velocity potential (𝜙) for the combined flow in polar coordinate (𝑟, 𝜃) is

Accepted Answer

𝜙= 𝐾𝜃 2 𝜋−𝑈∞𝑟 cos 𝜃

Answer

𝜙= 𝐾𝜃 2 𝜋−𝑈∞𝑟 sin 𝜃

Answer

𝜙= 𝐾ln 𝑟+ 𝑈∞𝑟 cos 𝜃

Answer

𝜙= −𝐾ln 𝑟+ 𝑈∞𝑟 sin 𝜃

Question 28

Which of the following statements are true? (i) Conservation of mass for an unsteady incompressible flow can be represented as ∇⋅𝑉⃗⃗= 0, where 𝑉⃗⃗ 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.

Accepted Answer

(i) and (iii) only

Answer

(i), (ii) and (iv) only

Answer

(i), (ii) and (iii) only

Answer

(ii) and (iv) only

Question 29

For a two-dimensional flow field given as 𝑉⃗⃗= −𝑥𝑖̂ + 𝑦𝑗̂, a streamline passes through points (2, 1) and (5, p). The value of p is

Accepted Answer

2/5

Answer

5

Answer

5/2

Answer

2

Question 30

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

Accepted Answer

The object is in stable equilibrium if 𝑦𝐶𝐺> 𝑦𝐶𝐵.

Accepted Answer

The object is in neutral equilibrium if 𝑦𝐶𝐺= 𝑦𝐶𝐵.

Answer

The object is in stable equilibrium if 𝑦𝐶𝐺< 𝑦𝐶𝐵.

Answer

The object is in unstable equilibrium if 𝑦𝐶𝐺= 𝑦𝐶𝐵.

Question 31

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

Accepted Answer

1

Answer

𝑈1 𝑈2

Answer

𝑈1 −𝑈2 𝑈2

Answer

𝑈1 + 𝑈2 𝑈2

Question 32

A two-dimensional incompressible flow field is defined as, 𝑉⃗⃗(𝑥, 𝑦) = (𝐴𝑥𝑦) 𝑖̂ + (𝐵𝑦2) 𝑗̂ where, 𝐴 and 𝐵 are constants. The dynamic viscosity of the Newtonian fluid is 𝜇. In the absence of body force, which among the following expressions represents the pressure gradient at the location (5, 0) in the concerned flow field?

Accepted Answer

𝜇𝐴(−𝑗̂)

Answer

𝜇𝐴(5 𝑖̂ + 𝑗̂)

Answer

𝜇(−5𝐵 𝑖̂ + 𝐴 𝑗̂)

Answer

𝜇𝐴(5 𝑖̂)

Question 33

For a potential flow, the fluid velocity is given by 𝑉⃗⃗(𝑥, 𝑦) = 𝑢𝑖̂ + 𝑣𝑗̂ . The slope of the potential line at (𝑥, 𝑦) is

Accepted Answer

−𝑢 𝑣

Answer

𝑢 𝑣

Answer

𝑣 𝑢

Answer

−𝑣 𝑢

Question 34

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

Accepted Answer

𝑥1/2

Answer

𝑥1/4

Answer

𝑥−1/2

Answer

𝑥2

Question 35

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

Accepted Answer

𝜌𝑢= 𝜕𝜓 𝜕𝑦 and 𝜌𝑣= − 𝜕𝜓 𝜕𝑥

Accepted Answer

𝜌𝑢= − 𝜕𝜓 𝜕𝑦 and 𝜌𝑣= 𝜕𝜓 𝜕𝑥

Answer

𝑢= 𝜕𝜓 𝜕𝑦 and 𝑣= − 𝜕𝜓 𝜕𝑥

Answer

𝑢= − 𝜕𝜓 𝜕𝑥 and 𝑣= − 𝜕𝜓 𝜕𝑦

Question 36

A water jet (density = 1000 kg/m3) 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 ___________.

Accepted Answer

183.0 to 185.0

Question 37

Water (density = 1000 kg/m3) and alcohol (specific gravity = 0.7) enter a Y-shaped channel at flow rates of 0.2 m3/s and 0.3 m3/s, respectively. Their mixture leaves through the other end of the channel, as shown in the figure. The average density (in kg/m3) of the mixture is _______.

Accepted Answer

820

Question 38

The velocity and acceleration of a fluid particle are given as 𝑉⃗⃗= (−𝑖̂ + 2𝑗̂) m/s and 𝑎⃗= (−2𝑖̂ −4𝑗̂) m/s2, respectively. The magnitude of the component of acceleration (in m/s2, rounded off to two decimal places) of the fluid particle along the streamline is _______.

Accepted Answer

2.60 to 2.75

Question 39

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 _______________.

Accepted Answer

430 to 460

Question 40

Water (density = 1000 kg/m3) flows steadily with a flow rate of 0.05 m3/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 _______.

Accepted Answer

18.5 to 19.5

Question 41

Water flows around a thin flat plate (0.25 m long, 2 m wide) with a free stream velocity (𝑈∞) of 1 m/s, as shown in the figure. Consider linear velocity profile ( 𝑢 𝑈∞= 𝑦 𝛿) for which the laminar boundary layer thickness is expressed as 𝛿= 3.5𝑥 √𝑅𝑒𝑥 . For water, density = 1000 kg/m3 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 ________.

Accepted Answer

1.10 to 1.20

Question 42

Axial velocity profile 𝑢(𝑟) for an axisymmetric flow through a circular tube of radius 𝑅 is given as, 𝑢(𝑟) 𝑈 = (1 −𝑟 𝑅) 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 ______________.

Accepted Answer

0.32 to 0.34

Question 43

A stationary circular pipe of radius 𝑅= 0.5 m is half filled with water (density = 1000 kg/m3), 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/s2. 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 _______. Material Science (XE-C)

Accepted Answer

2.2 to 2.4

Question 44

A plane truss is simply supported at P and R as shown. A downward force F is applied at hinge Q. The axial force developed in member PS is

Accepted Answer

√5 2 𝐹 Compressive

Answer

√5 2 𝐹 Tensile

Answer

√5 𝐹 Tensile

Answer

√5 𝐹 Compressive

Question 45

A massless rigid rod OP of length L is hinged frictionlessly at O. A concentrated mass m is attached to end P of the rod. Initially, the rod OP is horizontal. Then, it is released from rest. There is gravity as shown. The rod acquires an angular velocity as it swings. The clockwise angular velocity of the rod, when it first reaches the vertical position as shown, is

Accepted Answer

√ 2 𝑔 𝐿

Answer

2√𝑔 𝐿

Answer

√𝑔 𝐿

Answer

1 2 √𝑔 𝐿

Question 46

Two equivalent descriptions of the state of stress at a point are shown in the figure. The normal stresses 𝜎1 and 𝜎2 as shown on the right must be, respectively,

Accepted Answer

𝜏o and −𝜏o

Answer

−𝜏o and 𝜏o

Answer

𝜏o √2 and − 𝜏o √2

Answer

− 𝜏o √2 and 𝜏o √2

Question 47

The state of strain at a point in a machine component is given as 𝜀𝑥𝑥= 2.5 × 10−4, 𝜀𝑦𝑦= 2.0 × 10−4, 𝜀𝑧𝑧= −1.5 × 10−4, 𝜀𝑥𝑦= 2.5 × 10−4, 𝜀𝑦𝑧= −0.5 × 10−4, 𝜀𝑧𝑥= −1.0 × 10−4. The volumetric strain at this point is

Accepted Answer

3 × 10−4

Answer

4 × 10−4

Answer

−5 × 10−4

Answer

−3 × 10−4

Question 48

A thin walled, closed cylindrical vessel of inside diameter 𝑑 and wall thickness 𝑡 contains a fluid under pressure 𝑝. The figure below shows a part of the cylindrical vessel; end caps are not shown. Consider the small element shown with sides parallel and perpendicular to the axis of the cylinder. The stresses 𝜎1 and 𝜎2 are

Accepted Answer

𝜎1 = 𝑝𝑑 2𝑡; 𝜎2 = 𝑝𝑑 4𝑡

Answer

𝜎1 = 𝑝𝑑 𝑡; 𝜎2 = 𝑝𝑑 2𝑡

Answer

𝜎1 = 𝑝𝑑 4𝑡; 𝜎2 = 𝑝𝑑 2𝑡

Answer

𝜎1 = 𝑝𝑑 2𝑡; 𝜎2 = 0

Question 49

A spring mass system is shown in the figure below. Take the acceleration due to gravity as 𝑔 = 9.81 m/s2. The static deflection due to weight and the time period of oscillations, respectively, are

Accepted Answer

0.392 m and 1.26 s

Answer

0.392 m and 3.52 s

Answer

0.626 m and 1.26 s

Answer

0.626 m and 3.52 s

Question 50

A rod is subjected to three forces as shown in the figure on the left. An equivalent force system with forces F1, F2 and moment M is shown in the figure on the right. The value of M (in N-m) is______(rounded off to one decimal place).

Accepted Answer

117.0 to 118.0

Question 51

A simply supported beam of length 3 m is loaded as shown in the figure. The magnitude of the shear force (in kN) at the mid-point of the beam is______(rounded off to one decimal place).

Accepted Answer

4.9 to 5.1

Question 52

For a plane stress problem, the principal stresses are 100 MPa and 50 MPa. The magnitude of maximum shear stress (in MPa) in the material is______(rounded off to one decimal place).

Accepted Answer

49.5 to 50.5

Question 53

A solid uniform rigid disk of mass 𝑚 and radius 𝑅 rolls without slipping along a horizontal surface PQ. The speed of the center of the disk is 𝑣. The disk then strikes a hurdle of height 3𝑅 20 at point S. During the impact, there is no rebound or slip at S and no impulse from the surface PQ. The magnitude of the velocity of the center of the disk immediately after the impact is

Accepted Answer

0.9𝑣

Answer

0.1𝑣

Answer

0.3𝑣

Answer

0.7𝑣

Question 54

A cylinder made of rubber (length = L and diameter = d) is inserted in a rigid container as shown in the figure. The rubber cylinder fits snugly in the rigid container. There is no wall friction. The modulus of elasticity of the rubber is E and its Poisson’s ratio is ν. The cylinder is subjected to a small uniform pressure 𝑝 as shown in the figure. The resulting axial strain (𝜀𝑧𝑧) is

Accepted Answer

− 𝑝 𝐸[(1 + ν)(1 −2ν) (1 −ν) ]

Answer

− 𝑝 𝐸

Answer

− 𝑝 𝐸(1 −2ν)

Answer

− 𝑝 𝐸[(1 −ν)(1 −2ν) (1 + ν) ]

Question 55

The state of stress at the critical location in a structure is 𝜎𝑥𝑥 = 420 MPa, 𝜎𝑦𝑦 = 100 MPa, 𝜎𝑧𝑧= 𝜎𝑥𝑦 = 𝜎𝑦𝑧= 𝜎𝑧𝑥= 0. The yield stress of the material in uniaxial tension is 400 MPa. Select the correct statement among the following.

Accepted Answer

The structure is unsafe by Tresca (maximum shear stress) theory and safe by von-Mises (distortion energy) theory.

Answer

The structure is safe by both Tresca (maximum shear stress) theory and von-Mises (distortion energy) theory.

Answer

The structure is safe by Tresca (maximum shear stress) theory and unsafe by von-Mises (distortion energy) theory.

Answer

The structure is unsafe by both Tresca (maximum shear stress) theory and von-Mises (distortion energy) theory.

Question 56

The figure shows a column of rectangular cross section 100 mm × 80 mm. It carries a load of 60 kN at a point 30 mm from the edge 𝑃𝑄. The values of stress component 𝜎𝑧𝑧 on surfaces 𝑃𝑄𝑄′𝑃′ and 𝑆𝑅𝑅′𝑆′, at points far away from both ends of the column, are respectively

Accepted Answer

13.13 N/mm2 (Compressive) and 1.88 N/mm2 (Compressive)

Answer

18.75 N/mm2 (Compressive) and 3.75 N/mm2 (Tensile)

Answer

18.75 N/mm2 (Compressive) and 3.75 N/mm2 (Compressive)

Answer

13.13 N/mm2 (Compressive) and 1.88 N/mm2 (Tensile)

Question 57

Consider an electric pole with dimensions as shown in the figure. Let the end R be subjected to a vertical force F. The flexural rigidity of both vertical and horizontal bars is EI. Neglect the axial deflection of the vertical bar, and all effects of self-weight. The vertical deflection at end R is

Accepted Answer

7𝐹𝐿3 3𝐸𝐼

Answer

10𝐹𝐿3 3𝐸𝐼

Answer

5𝐹𝐿3 3𝐸𝐼

Answer

8𝐹𝐿3 3𝐸𝐼

Question 58

A uniform cantilever beam has flexural rigidity 𝐸𝐼 and length 𝐿. It is subjected to a concentrated force 𝐹 and moment 𝑀= 2𝐹𝐿 at the free end as shown. The deflection (𝛿) at the free end is

Accepted Answer

4𝐹𝐿3 3𝐸𝐼

Answer

11𝐹𝐿3 12𝐸𝐼

Answer

8𝐹𝐿3 9𝐸𝐼

Answer

7𝐹𝐿3 6𝐸𝐼

Question 59

A steel ball of mass 𝑚 = 10 kg is suspended from the ceiling of a moving carriage by two inextensible strings making 60° with the horizontal as shown. The carriage has an acceleration 𝑎 such that the tension in the string on the right is double the tension in the string on the left. Take the acceleration due to gravity (g) as 10 m/s2. The acceleration 𝑎 (in m/s2) is______(rounded off to one decimal place).

Accepted Answer

1.8 to 2.0

Question 60

A block of mass 𝑚= 10 kg is lying on an inclined plane PQ. The mass is restrained from sliding down the inclined plane by a force 𝐹. The coefficient of friction between the block and the inclined plane is 0.3. Take the acceleration due to gravity as 10 m/s2. The smallest force 𝐹 (in N) required to prevent the block from sliding down is______(rounded off to one decimal place).

Accepted Answer

23.0 to 25.0

Question 61

A spherical rigid ball of mass 10 kg is moving with a speed of 2 m/s in the direction shown. The ball collides with a rigid frictionless wall and rebounds at an angle 𝛼 with a speed of 𝑣, as shown. The coefficient of restitution is 0.9. The angle 𝛼 (in degrees) is______(rounded off to one decimal place).

Accepted Answer

57.0 to 58.0

Question 62

A thin steel plate is loaded in the x-y plane as shown in the figure. Take the Poisson’s ratio of steel to be 0.3 and the modulus of elasticity of steel to be 200 GPa. The strain along the 𝑧-direction is 𝜀𝑧𝑧= −3 × 10−4. The value of 𝜎𝑦𝑦 (in MPa) is______(rounded off to one decimal place).

Accepted Answer

79.5 to 80.5

Question 63

A composite rod made of steel and copper is fixed immovably at its ends as shown in the figure. The length of each portion of the rod is 1 m as shown. The cross-sections of both portions are the same. The moduli of elasticity of steel and copper are 200 GPa and 100 GPa, respectively. The coefficients of thermal expansion of steel and copper are 12 × 10−6 /℃ and 18 × 10−6 /℃, respectively. The composite rod is initially stress free. Then, the temperature of the composite rod is increased by 100 ℃. The magnitude of axial stress (in MPa) developed in the steel rod is______(rounded off to one decimal place).

Accepted Answer

199.0 to 201.0

Question 64

A slender uniform elastic rod of length 1 m and of solid circular cross-section of diameter 50 mm is originally straight. It is then loaded by equal and opposite end moments as indicated in the figure. The resulting lateral displacement of the mid-point of the rod is 10 mm (displacements are exaggerated in the figure). The maximum longitudinal strain in the rod is 𝑝 × 10−3, where 𝑝 is______(rounded off to one decimal place).

Accepted Answer

1.9 to 2.1

GATE XE (Engineering Sciences) 2023 Question Paper & Solutions

General Aptitude

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Engineering Mathematics

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Fluid Mechanics

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41

Question 42

Question 43

Solid Mechanics

Question 66

Question 67

Question 68

Question 69

Question 70

Question 71

Question 72

Question 73

Question 74

Question 75

Question 76

Question 77

Question 78

Question 79

Question 80

Question 81

Question 82

Question 83

Question 84

Question 85

Question 86

Question 87

Thermodynamics

Question 88

Question 89

Question 90

Question 91

Question 92

Question 93

Question 94

Question 95

Question 96