GATE XE (Engineering Sciences) 2024 Question Paper & Solutions

Question 1

If ‘→’ denotes increasing order of intensity, then the meaning of the words [walk → jog → sprint] is analogous to [bothered → ________ → daunted]. Which one of the given options is appropriate to fill the blank?

Accepted Answer

fazed

Answer

phased

Answer

phrased

Answer

fused

Question 2

Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all possible orders. They also decide to work independently. After trying all possible combination of elements, they conclude that the spell does not work. How many attempts does each wizard make before coming to this conclusion, independently?

Accepted Answer

24

Answer

48

Answer

16

Answer

12

Question 3

In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th of the number of students who like other branches. The number of students who like both their core and other branches is 500. The number of students who like their core branches is

Accepted Answer

1,800

Answer

3,500

Answer

1,600

Answer

1,500

Question 4

For positive non-zero real variables 𝑥 and 𝑦, if ln (𝑥+ 𝑦 2 ) = 1 2 [ln⁡(𝑥) + ln⁡(𝑦)] then, the value of 𝑥 𝑦+ 𝑦 𝑥 is

Accepted Answer

2

Answer

1

Answer

1/2

Answer

4

Question 5

In the sequence 6, 9, 14, x, 30, 41, a possible value of 𝑥 is

Accepted Answer

21

Answer

25

Answer

18

Answer

20

Question 6

Sequence the following sentences in a coherent passage. P: This fortuitous geological event generated a colossal amount of energy and heat that resulted in the rocks rising to an average height of 4 km across the contact zone. Q: Thus, the geophysicists tend to think of the Himalayas as an active geological event rather than as a static geological feature. R: The natural process of the cooling of this massive edifice absorbed large quantities of atmospheric carbon dioxide, altering the earth’s atmosphere and making it better suited for life. S: Many millennia ago, a breakaway chunk of bedrock from the Antarctic Plate collided with the massive Eurasian Plate.

Accepted Answer

SPRQ

Answer

QPSR

Answer

QSPR

Answer

SRPQ

Question 7

A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In selling these two items, the person made a total of

Accepted Answer

1% loss

Answer

1% profit

Answer

2% profit

Answer

2% loss

Question 8

The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years 2007 and 2023. The renewable sources of electricity generation consist of Hydro, Solar and Wind. Assuming that the total electricity generated remains the same from 2007 to 2023, what is the percentage increase in the share of the renewable sources of electricity generation over this period?

Accepted Answer

62.5% Coal 35% Gas 25% Wind 5% Hydro 30% Solar 5% Year 2007 Coal 20% Gas 15% Wind 10% Hydro 35% Solar 20% Year 2023

Answer

25%

Answer

50%

Answer

77.5%

Question 9

A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube. The minimum number of such cuts required is

Accepted Answer

3

Answer

4

Answer

7

Answer

8

Question 10

In the 4 × 4 array shown below, each cell of the first three rows has either a cross (X) or a number. The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is

Accepted Answer

11

Answer

10

Answer

12

Answer

9

Question 11

Let 𝑓(𝑥) = {𝜋+ 𝑥,⁡⁡⁡⁡⁡⁡⁡ −𝜋≤𝑥< 0, ⁡⁡⁡0,⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡0 ≤𝑥< 𝜋, with 𝑓(𝑥+ 2𝜋) = 𝑓(𝑥). If 𝐹(𝑥) represents the Fourier series of 𝑓(𝑥), then the value of 𝐹(− 𝜋 2) + 𝐹(0) is

Accepted Answer

𝜋

Answer

0

Answer

𝜋 2

Answer

3𝜋 2

Question 12

Let 𝑦 be a non-zero quadratic polynomial satisfying the differential equation (2 + 𝑥2) 𝑑2𝑦 𝑑𝑥2 + 𝑥𝑑𝑦 𝑑𝑥−𝑘𝑦= 0, where 𝑘 is a real constant. If 𝑦(1) = 1, then the value of the integral ∫2𝑦⁡𝑑𝑥 1 0 ⁡ is

Accepted Answer

4 3

Answer

1 3

Answer

2 3

Answer

1

Question 13

There are four cities, namely, 𝐶1, 𝐶2, 𝐶3 and 𝐶4. The cities are directly connected by four roads as shown in the picture given below, that is, 𝐶1 is connected with 𝐶2, 𝐶2 is connected with 𝐶3, 𝐶3 is connected with 𝐶4, and 𝐶4 is connected with 𝐶1. The probability of any road getting independently blocked is 1 3 . Let 𝐸1 be the event of travelling from 𝐶1 to 𝐶3 via 𝐶2 and 𝐸2 be the event of travelling from 𝐶1 to 𝐶3 via 𝐶4. Then, which of the following statements is correct ?

Accepted Answer

𝑃(𝐸1 ∪𝐸2) = 56 81⁡

Answer

𝑃(𝐸1 ∪𝐸2) = 8 9

Answer

𝑃(𝐸1|𝐸2) ≠𝑃(𝐸1) = 4 9

Answer

𝑃(𝐸1 ∩𝐸2) = 0

Question 14

Assume that 𝑓: [0, 1] →ℝ is continuous on [0, 1] and differentiable on (0, 1) such that 𝑓(𝑥+ ℎ) = 𝑓(𝑥) + ℎ𝑓′(𝑥+ 𝜃ℎ) for some 0 < 𝜃< 1. If 𝑓(𝑥) = 𝑥2(1 + 𝑥), and 𝜃 is expressed in terms of 𝑥 and ℎ, then the value of lim ℎ→0 𝜃(𝑥, ℎ) is

Accepted Answer

1 2

Answer

1 3

Answer

1 4

Answer

4 5

Question 15

Let 𝐴 be a 3 × 3 matrix whose eigenvalues are 2, 3, 4 and let 𝐼 be the identity matrix of order 3. If 𝐴−1 = 1 2𝑘(𝐴2 −9𝐴) + 13 𝑘𝐼 for some integer 𝑘≠0, then the value of 𝑘 is ______

Accepted Answer

12

Question 16

For some integer 𝑘, the differential equation 𝑥2 𝑑2𝑦 𝑑𝑥2 −3𝑥𝑑𝑦 𝑑𝑥+ (𝑘+ 2)𝑦= 0 is transformed into (𝐷−2)2𝑦= 0, where 𝐷= 𝑑 𝑑𝑡 and 𝑡= log𝑒𝑥. Then, the value of 𝑘 is _____

Accepted Answer

2

Question 17

The approximate value (rounded off to two decimal places) of the integral ∫𝑒−𝑥2⁡𝑑𝑥 1/2⁡ 0 , using the Trapezoidal rule with step-size ℎ= 1 8 , is ______

Accepted Answer

0.42 to 0.55

Question 18

Consider 𝑓(𝑧) = 𝑒𝑧, where 𝑧= 𝑥+ 𝑖𝑦⁡and 𝑖= √−1. Which of the following statements is correct ?

Accepted Answer

𝑓 is periodic

Answer

𝑓 is not periodic

Answer

|𝑓| = 1

Answer

arg(𝑓) = 𝑦± 𝑛𝜋⁡⁡for⁡all⁡𝑛= 0, 1, 2, …

Question 19

Let 𝑃 and 𝑄 be two square matrices of the same order. Then, which of the following matrices is/are necessarily equal to (𝑃+ 2𝑄)2 ?

Accepted Answer

𝑃(𝑃+ 2𝑄) + 𝑄(2𝑃+ 4𝑄)

Accepted Answer

(𝑃+ 2𝑄)(2𝑄+ 𝑃)

Accepted Answer

𝑃2 + 2𝑃𝑄+ 2𝑄𝑃+ 4𝑄2

Answer

𝑃2 + 4𝑃𝑄+ 4𝑄2

Question 20

If ∫ ∫𝑒𝑦3 1 √𝑥/𝛼⁡ 𝛼 0 𝑑𝑦𝑑𝑥= 𝑒−1, 𝛼> 0, then the value (in integer) of 𝛼 is _____

Accepted Answer

3

Question 21

Consider the vector field 𝐹⁡⃗⃗⃗ = (2𝑥+ 𝑦2)⁡𝑖̂ + (2𝑥𝑦+ 3𝑦)⁡𝑗̂ and 𝛼𝑚= ∫ 𝐹⁡⃗⃗⃗ 𝐶𝑚 ⋅𝑑𝑟 , 𝑚= 1, 2, where 𝐶1 is an arc of the unit circle connecting the points (1, 0) and (0, 1) and 𝐶2 is the straight line connecting the points (1, 0) and (0, 1). Then, the value (in integer) of 2(𝛼1 2 + 3𝛼2 2) is ______

Accepted Answer

2

Question 22

Which one of the following figures shows the CORRECT dependence of apparent viscosity (η) on rate of shear strain (𝑑𝑢/𝑑𝑦) for pseudoplastic fluids?

Accepted Answer

Question 23

The locus of temporary locations of all particles that have passed through a fixed point in the flow field at a particular instant is known as

Accepted Answer

streakline.

Answer

streamline.

Answer

pathline.

Answer

timeline.

Question 24

Consider the velocities 𝑢, 𝑣, and 𝑤 in x-, y-, and z-directions, respectively. The vorticity expression in the y-z plane is

Accepted Answer

𝜕𝑤 𝜕𝑦−𝜕𝑣 𝜕𝑧

Answer

𝜕𝑣 𝜕𝑥−𝜕𝑢 𝜕𝑦

Answer

𝜕𝑣 𝜕𝑦−𝜕𝑤 𝜕𝑧

Answer

𝜕𝑢 𝜕𝑧−𝜕𝑤 𝜕𝑥

Question 25

For the laminar, incompressible flow over a flat plate with uniform free stream velocity, the axial pressure gradient within the boundary layer is

Accepted Answer

equal to zero.

Answer

greater than zero.

Answer

less than zero.

Answer

equal to the axial velocity gradient.

Question 26

Let 𝑟 , 𝑉⃗ , and 𝑚 be position vector, velocity vector, and mass, respectively in a control mass system. Which one of the following properties is considered as conserved extensive property in Reynolds Transport Theorem to obtain the angular momentum equation?

Accepted Answer

𝑟 × 𝑚𝑉⃗

Answer

𝑟 × 𝑉⃗

Answer

𝑚𝑉⃗

Answer

𝑚

Question 27

The hydraulic diameter for a circular pipe of radius 𝑅 is

Accepted Answer

2R

Answer

0.5R

Answer

R

Answer

4R

Question 28

For incompressible, laminar, fully-developed flow through a circular pipe, Darcy friction factor and Fanning friction factor are represented as 𝑓 and 𝐶𝑓, respectively. Which one of the following options is correct?

Accepted Answer

𝑓= 4𝐶𝑓

Answer

𝑓= 0.25𝐶𝑓

Answer

𝑓= 0.5𝐶𝑓

Answer

𝑓= 2𝐶𝑓

Question 29

For an immersed neutrally buoyant body to be in stable equilibrium, the center of gravity of the body is directly

Accepted Answer

below the center of buoyancy.

Answer

above the metacenter.

Answer

below the metacenter.

Answer

above the center of buoyancy.

Question 30

The absolute pressure in a chamber is measured as 400 mm Hg at a location where the atmospheric pressure is 700 mm Hg. A vacuum gauge connected to the chamber reads ________ mm Hg (answer in integer).

Accepted Answer

300

Question 31

A thin film of an incompressible, Newtonian liquid (density 𝜌,⁡viscosity 𝜇) with an uniform thickness (h) is flowing down on a vertical plate. The flow is driven by gravity (𝑔) alone. Assume zero shear stress condition at the free surface. The maximum velocity is given by

Accepted Answer

1 2𝜇𝜌𝑔ℎ2

Answer

1 4𝜇𝜌𝑔ℎ2

Answer

1 𝜇𝜌𝑔ℎ2

Answer

1 8𝜇𝜌𝑔ℎ2

Question 32

A one-eighth scale model of a car is to be tested in a wind tunnel. If the air velocity over the car is 16 m/s, what should be the air velocity (in m/s) in the wind tunnel in order to achieve similarity between the model and the prototype?

Accepted Answer

128

Answer

2

Answer

16

Answer

64

Question 33

A set of basic dimensions, mass, length, and time are represented by M, L, and T, respectively. What will be the dimensions of pressure in M-L-T system?

Accepted Answer

ML−1T −2

Answer

MLT −2

Answer

MLT −1

Answer

ML−1T −1

Question 34

Consider a fluid flow around an airfoil as shown in figure. The directions of drag force and lift force, respectively are along

Accepted Answer

OB and OD.

Answer

OA and OC.

Answer

OA and OD.

Answer

OB and OC.

Question 35

A vessel which contains a volatile liquid and its vapour is connected with a mercury manometer as shown in figure. Both the liquid and vapour phases are at equilibrium. The vapour pressure and density of the volatile liquid are 107.6 kPa and 700 kg/m3, respectively. The density of the mercury is 13600 kg/m3. Acceleration due to gravity (g) is 10 m/s2 and atmospheric pressure is 101 kPa. Hydrostatic pressure created by the weight of the vapour is neglected. The height, h (in m, rounded off to two decimal places) of the mercury column in figure is _________.

Accepted Answer

0.09 to 0.11

Question 36

The velocity in a one-dimensional flow is given by 𝑢(𝑥) = 𝑎 (𝑏−𝑥)2 m/s, where 𝑎= 8 m3/s and 𝑏= 4 m. The acceleration (in m/s2, answer in integer) at 𝑥= 2 m is _____.

Accepted Answer

4

Question 37

Consider two parallel plates separated by a distance of 1 cm filled with a Newtonian fluid of viscosity 10-3 Pa.s. The top plate is moving with a velocity of 1 m/s whereas the bottom plate is stationary. The shear stress (in Pa, rounded off to one decimal place) on the top plate is _____ .

Accepted Answer

0.1

Question 38

A circular water jet of diameter 50 mm impinges with a velocity of 18 m/s normal to a plate. The density of water is 1000 kg/m3 and gravity force is neglected. The magnitude of net force (in N, rounded off to two decimal places) imparted by the jet on the stationary plate is _______________.

Accepted Answer

635.00 to 637.00

Question 39

Consider the steady, incompressible flow of water in a horizontal pipe of constant diameter 1 m with an inlet velocity of 12 m/s. As shown in figure, water is lost through a circular hole of diameter 0.6 m at the rate of 4.53 m3/s. The outlet velocity (in m/s, rounded off to two decimal places) of water in the pipe is ______.

Accepted Answer

6.00 to 6.50

Question 40

The axial velocity profile of a laminar, incompressible and fully-developed flow in a circular pipe of radius (R) is given as 𝑢𝑧= − 1 4𝜇 𝜕𝑝 𝜕𝑧𝑅2 (1 − 𝑟2 𝑅2), where r, 𝑧, 𝜇, and 𝑝 are radial direction, axial direction, fluid viscosity, and pressure, respectively. If the average velocity of the flow is given by 𝑢𝑧,𝑎𝑣𝑔= 1 𝐾(− 𝑅2 𝜇 𝜕𝑝 𝜕𝑧), then the value of K (answer in integer) is ______.

Accepted Answer

8

Question 41

The velocity potential function in a two-dimensional flow field is given by 𝜙(𝑥, 𝑦) = −(𝑎𝑥𝑦+ 𝑏𝑥2 −𝑏𝑦2) m2/s where a = 2 per second and b = 0.5 per second. The magnitude of the velocity (in m/s, answer in integer) at 𝑥= 2 m, 𝑦= 1 m is _____.

Accepted Answer

5

Question 42

Consider the incompressible, steady and irrotational flow through a concentric reducer in a horizontal pipeline. The pipe diameter reduces from d1 = 12 cm to d2 = 4 cm as shown in figure. The pressure at position 1 and position 2 of the reducer is p1 = 55 kPa and p2 = 27 kPa, respectively. The specific weight of fluid is 7 kN/m3. Acceleration due to gravity is 10 m/s2. Neglecting frictional effects, the mass flow rate (in kg/s, rounded off to two decimal places) of the fluid through the reducer is _____.

Accepted Answer

7.85 to 8.11

Question 43

Consider the incompressible fluid flow over a flat plate with a free stream velocity, 𝑈∞= 1 m/s. The fluid kinematic viscosity is 10−6 m2/s and density is 1 kg/m3. The velocity profile within the boundary layer at any location 𝑥 is given by 𝑢(𝑦) = 𝑈∞( 3 2 𝑦 𝛿− 1 2 𝑦2 𝛿2), where boundary layer thickness, 𝛿= 4.64𝑥 √𝑅𝑒𝑥. The local wall shear stress at 𝑥= 1 m from the leading edge is _____ × 10 -3 N/m2 (rounded off to two decimal places).

Accepted Answer

0.30 to 0.35

Question 44

The engineering stress (𝜎) vs. engineering strain (𝜀) curve obtained by conducting uniaxial tension test on a steel specimen is shown in the figure (the sketched curve is not to the scale). The specimen exhibits cup-and-cone failure within its gage length. Which point on the curve corresponds to the beginning of necking in the test specimen?

Accepted Answer

S

Answer

P

Answer

Q

Answer

R

Question 45

An L-shaped rigid member is fixed at the midpoint of a simply-supported beam, as shown in figure (i). The member is subjected to a vertically downward force P at its free end. In an equivalent system, the member along with the applied load is replaced with a force Q = P and a moment M (see figure (ii)). Which of the following statements is correct? (Neglect the mass of the beam and of the rigid member)

Accepted Answer

M = P a

Answer

M = P b

Answer

M = P (a + b)

Answer

M = 0

Question 46

A block of weight W, placed on a surface, is subjected to a horizontal force P as shown in the figure. The line of action of force P passes through the center-of- gravity of the block. The magnitude of P is such that the block remains at rest. If N is the resultant normal reaction exerted by the surface, and F is the frictional force acting on the bottom surface of the block, then which of the following represents the correct free body diagram of the block?

Accepted Answer

Question 47

A mass M is hung from a frictionless, massless pulley. The pulley is suspended by using an inextensible, massless rope of which one end is directly fixed to a support, and the other end is connected to the support through a linear spring of stiffness constant k (see figure). The natural frequency of this system is

Accepted Answer

√4𝑘 𝑀

Answer

√2𝑘 𝑀

Answer

√𝑘 𝑀

Answer

√𝑘 2𝑀

Question 48

A simply-supported beam of rectangular cross-section (width w and height h) is subjected to the loads as shown in the figure (i). The enlarged view of the beam cross-section is shown in figure (ii). The coordinate system is indicated in the figures. Assuming Euler-Bernoulli beam approximation, the shear stress 𝜏𝑥𝑧 and normal stress 𝜎𝑥𝑥 at the origin, O are respectively given by

Accepted Answer

0 , 0

Answer

3𝑃 2𝑤ℎ⁡⁡, ⁡ 3𝑃𝐿 2𝑤ℎ2

Answer

0 , ⁡ 3𝑃𝐿 2𝑤ℎ2

Answer

3𝑃 2𝑤ℎ , 0

Question 49

An ice-skater starts spinning during her performance. As she retracts her arms and legs closer to her body, her angular velocity _________________.

Accepted Answer

increases

Answer

decreases

Answer

remains the same

Answer

goes to zero

Question 50

A solid circular shaft of diameter 100 mm is subjected to a torque 3𝜋 kNm. Which of the following statements about the state of stress in the shaft is/are correct?

Accepted Answer

The maximum shear stress is 48 MPa

Accepted Answer

The maximum tensile stress is 48 MPa

Accepted Answer

The magnitude of maximum compressive stress is 48 MPa

Answer

The magnitude of shear stress is 48 MPa at all points in the shaft

Question 51

A spring is connected to an elastic bar as shown in the figure. The spring has a stiffness constant of 107 N/m. The bar is 70 mm long, and has an area of cross- section 10 mm2. The Young’s modulus of the bar material is 70,000 MPa. A force F = 5000 N is applied at point O along the axis of the bar and the spring. The resulting deflection of Point O in mm (rounded to one decimal place) is ______

Accepted Answer

0.9 to 1.1

Question 52

A particle of mass 1 kg is attached to one end of a spring having stiffness of 125 N/m. The free length of the spring is 100 mm. The system is rotated about the other end of the spring at a uniform angular velocity of 5 rad/s. Ignore gravity and consider that the elongation of the spring may be comparable to the free length of the spring. The elongation of the spring (in mm, rounded off to the nearest integer) is ______ .

Accepted Answer

24 to 26

Question 53

A 0-45-90 strain gauge rosette is mounted on an aircraft wing. The co-ordinate system is placed such that the strain gauges p, q and r are oriented at angles 0o, 45o and 90o, respectively, from the x axis (see figure). The strain readings associated to p, q and r are denoted by 𝜀𝑝, 𝜀𝑞, and 𝜀𝑟 , respectively. While conducting a test the strain gauges show the following readings. 𝜀𝑝= 150 × 10−6, 𝜀𝑞= 180 × 10−6, 𝜀𝑟= −90 × 10−6 The developed engineering shear strain 𝛾𝑥𝑦 associated to the strain gauge data is

Accepted Answer

300 × 10−6

Answer

120 × 10−6

Answer

180 × 10−6

Answer

240 × 10−6

Question 54

A rigid bar PQR is hinged at its end P. As shown in the figure, the bar is pin- connected through two identical links QS and RT at points Q and R, respectively. The other ends of the links, S and T, are fixed. Both links are made of the same material. If the temperature of the links is uniformly increased by ΔT, then which one of the following statements is correct? (Neglect the weight of the rigid bar)

Accepted Answer

QS will be under compression and RT will be under tension.

Answer

Both QS and RT will be stress free.

Answer

Both QS and RT will be under tension.

Answer

Both QS and RT will be under compression.

Question 55

A pin-jointed truss has a pin support at the point E and a roller support at the point F. A horizontal force P is applied at pin H as shown in the figure. Which one of the members is in compression ?

Accepted Answer

EG

Answer

EF

Answer

FG

Answer

EH

Question 56

Two identical rigid slender bars of length 2L and mass 𝑚 are acted upon by a transverse force F at one of the ends as shown in the figure. In the first case, the bar is pinned at the other end. In the second case, the bar is pinned at its mid-point. What should be the magnitude of the force F such that the resulting angular accelerations of the two bars are equal?

Accepted Answer

𝑚⁡𝑔 2

Answer

𝑚⁡𝑔

Answer

𝑚⁡𝑔 4

Answer

𝑚⁡𝑔 6

Question 57

A critical point on a component is subjected to the state of stress [𝜎] as given in the following. The yield strength of the material is 400 MPa. By considering maximum shear stress (Tresca) theory, the possible value(s) of 𝜎0 at the onset of yielding is/are, [𝜎] =⁡[ 280 0 0 0 𝜎𝑜 0 0 0 −60 ] MPa

Accepted Answer

340

Accepted Answer

̶ 120

Answer

680

Answer

̶ 460

Question 58

A plane passing through a point Q inside a body is shown. The unit normal of the plane is 𝑛̂ = 0.6⁡𝑖̂ + 0.8⁡𝑗̂ , as shown in the figure. The traction (stress) vector on the plane at point Q is given by 𝑡 = (50⁡𝑖̂ + 20⁡𝑗̂) MPa. Given that at point Q, 𝜎𝑥𝑥= 𝜎𝑦𝑦 , the shear stress component 𝜏𝑥𝑦 (in MPa, rounded off to two decimal places) is ___________ .

Accepted Answer

99.00 to 101.00

Question 59

A rigid massless bar PQR is hinged at its end P and supported through a spring of stiffness k at point Q. A vertically downward force W = 560 N is applied at the free end R of the bar. If the vertical component of the displacement at R is 30 mm, then the stiffness of the spring (in kN/m, rounded off to one decimal place) is ___.

Accepted Answer

41.0 to 43.0

Question 60

A beam of rectangular cross-section, as shown in the figure, is made of two perfectly bonded layers of different materials and equal thickness. The Young’s moduli of the two materials are 𝐸1 and 𝐸2, where 𝐸1 = 2𝐸2. The beam is subjected to pure bending. If t = 1 mm, the distance of the neutral plane from the top surface of the beam is ______ (in mm, rounded off to two decimal places).

Accepted Answer

0.80 to 0.85

Question 61

A stepped beam is made of a material whose Young’s modulus is E. The dimensions of the two stepped sections are such that the sectional moments of inertia, 𝐼1⁡and 𝐼2, are related as 𝐼1 = 8𝐼2. The beam is fixed at one end and a load of F is applied at the free end as shown in the figure. Under this loading condition, if the strain energy of the stepped beam is written as 𝑈= 𝛽 𝐹2𝐿3 𝐸𝐼1 , then the value of 𝛽 is ________ (rounded off to two decimal places).

Accepted Answer

0.29 to 0.33

Question 62

A cylindrical pressure vessel is constructed by bolting two symmetric halves of flanged semi-cylindrical shells. A cross-sectional view of the vessel is shown in the figure. The inner diameter of the vessel is 2 m and the length is 10 m. Each row comprises 100 bolts along the length of the vessel. If the vessel is pressurized to a net pressure of 6 x 105 N/m2, and assuming the end caps of the vessel do not take any load in the radial direction, then the load borne by each bolt is __________ (in kN, rounded off to one decimal place)

Accepted Answer

59.5 to 60.5

Question 63

A turn-table is rotating about its center with an angular velocity of 2 rad/s in the counter-clockwise direction. There is a groove in the turn-table within which a marble moves with a constant speed v m/s relative to the turn-table. At a given instant, the marble is at a radial distance of 1 m from the center and the line joining the center of the turn-table with the marble makes an angle of 30° with the groove. The value of v (in m/s, rounded off to one decimal place) for which there is no radial acceleration for the marble at this instant is _____.

Accepted Answer

1.9 to 2.1

Question 64

The system shown in the figure is in static equilibrium. The spring is massless and has a spring constant of K=1 kN/m. The free length of the spring is 1 m. All bodies in the system except the spring are rigid and have mass of M=1 kg. All surfaces are frictionless and pin joints are ideal. The elongation of the spring (in mm, rounded off to the nearest integer) in this configuration is ______. Take the acceleration due to gravity 𝑔= 10 m/s2.

Accepted Answer

14 to 16

GATE XE (Engineering Sciences) 2024 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