GATE XE (Engineering Sciences) 2022 Question Paper & Solutions

Question 1

The movie was funny and I _________.

Accepted Answer

couldn’t help laughing

Answer

could help laughing

Answer

couldn’t help laughed

Answer

could helped laughed

Question 2

𝑥∶𝑦∶𝑧ൌ ଵ ଶ: ଵ ଷ: ଵ ସ. What is the value of ௫ା௭ି௬ ௬ ?

Accepted Answer

1.25

Answer

0.75

Answer

2.25

Answer

3.25

Question 3

Both the numerator and the denominator of ଷ ସ are increased by a positive integer, 𝑥, and those of ଵହ ଵ଻ are decreased by the same integer. This operation results in the same value for both the fractions. What is the value of 𝑥?

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 4

A survey of 450 students about their subjects of interest resulted in the following outcome. • 150 students are interested in Mathematics. • 200 students are interested in Physics. • 175 students are interested in Chemistry. • 50 students are interested in Mathematics and Physics. • 60 students are interested in Physics and Chemistry. • 40 students are interested in Mathematics and Chemistry. • 30 students are interested in Mathematics, Physics and Chemistry. • Remaining students are interested in Humanities. Based on the above information, the number of students interested in Humanities is

Accepted Answer

45

Answer

10

Answer

30

Answer

40

Question 5

For the picture shown above, which one of the following is the correct picture representing reflection with respect to the mirror shown as the dotted line?

Accepted Answer

Question 6

In the last few years, several new shopping malls were opened in the city. The total number of visitors in the malls is impressive. However, the total revenue generated through sales in the shops in these malls is generally low. Which one of the following is the CORRECT logical inference based on the information in the above passage?

Accepted Answer

More people are visiting the malls but not spending enough

Answer

Fewer people are visiting the malls but spending more

Answer

More people are visiting the malls and spending more

Answer

Fewer people are visiting the malls and not spending enough

Question 7

In a partnership business the monthly investment by three friends for the first six months is in the ratio 3: 4: 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months. What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?

Accepted Answer

63 : 86 : 110

Answer

22 : 23 : 24

Answer

22 : 33 : 50

Answer

33 : 46 : 60

Question 8

Consider the following equations of straight lines: Line L1: 2𝑥െ3𝑦 ൌ5 Line L2: 3𝑥൅2𝑦 ൌ8 Line L3: 4𝑥െ6𝑦ൌ5 Line L4: 6𝑥െ9𝑦ൌ6 Which one among the following is the correct statement?

Accepted Answer

L4 is perpendicular to L2 and L4 is parallel to L3

Answer

L1 is parallel to L2 and L1 is perpendicular to L3

Answer

L2 is parallel to L4 and L2 is perpendicular to L1

Answer

L3 is perpendicular to L4 and L3 is parallel to L2

Question 9

Given below are two statements and four conclusions drawn based on the statements. Statement 1: Some soaps are clean. Statement 2: All clean objects are wet. Conclusion I: Some clean objects are soaps. Conclusion II: No clean object is a soap. Conclusion III: Some wet objects are soaps. Conclusion IV: All wet objects are soaps. Which one of the following options can be logically inferred?

Accepted Answer

Only conclusion I and conclusion III are correct

Answer

Only conclusion I is correct

Answer

Either conclusion I or conclusion II is correct

Answer

Either conclusion III or conclusion IV is correct

Question 10

An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east. The ant first turns 72o anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting. 1. moves forward for 10 cm. 2. turns 144o clockwise. The pattern made by the trace left behind by the ant is

Accepted Answer

Question 11

The value of lim ௫→଴ 1 𝑥 න ቀ𝑡൅ ඥ𝑡ଶ൅5 ቁ 𝑑𝑡 ଶା௫ ଶ is

Accepted Answer

5

Answer

0

Answer

4

Answer

6

Question 12

Let Χ ൌ ൛𝑧ൌ𝑥൅𝑖𝑦∶𝑥and 𝑦are real numbers, 𝑖ൌ√െ1 ൟ be the set of complex numbers. Let the function 𝑓ሺ𝑧ሻൌ𝑢ሺ𝑥, 𝑦ሻ൅𝑖 𝑣ሺ𝑥, 𝑦ሻ for 𝑧ൌ𝑥൅𝑖𝑦 Î Χ be analytic in Χ, where 𝑢ሺ𝑥, 𝑦ሻൌ𝑥 𝑦ଷെ𝑦 𝑥ଷ and 𝑣ሺ𝑥, 𝑦ሻൌ 𝑥ସ 4 ൅ 𝑦ସ 4 െ 3 2 𝑥ଶ𝑦ଶ. If 𝑓ᇱሺ𝑧ሻ denotes the derivative of 𝑓ሺ𝑧ሻ, then

Accepted Answer

|𝑓ᇱሺെ1 ൅𝑖ሻ|ଶൌ8

Answer

|𝑓ᇱሺെ1 ൅𝑖ሻ|ଶൌ1

Answer

|𝑓ᇱሺെ1 ൅𝑖ሻ|ଶൌ7

Answer

|𝑓ᇱሺെ1 ൅𝑖ሻ|ଶൌ10

Question 13

If the partial differential equation ሺ𝑥൅2ሻ𝜕ଶ𝑢 𝜕𝑥ଶ൅2ሺ𝑥൅𝑦ሻ𝜕ଶ𝑢 𝜕𝑥 𝜕𝑦൅2ሺ𝑦െ1ሻ𝜕ଶ𝑢 𝜕𝑦ଶെ3𝑦ଶ 𝜕𝑢 𝜕𝑦ൌ0 is parabolic on the circle ሺ𝑥െ𝑎ሻଶ൅ሺ𝑦െ𝑏ሻଶൌ𝑟ଶ, then the values of 𝑎, 𝑏 and 𝑟 are given by

Accepted Answer

𝑎ൌെ1, 𝑏ൌ2, 𝑟ൌ1

Answer

𝑎ൌ1, 𝑏ൌ2, 𝑟ൌ1

Answer

𝑎ൌ1, 𝑏ൌെ2, 𝑟ൌ1

Answer

𝑎ൌെ1, 𝑏ൌെ2, 𝑟ൌ1

Question 14

Let G be the positively oriented circle 𝑥ଶ൅𝑦ଶൌ9 in the 𝑥𝑦-plane. If ර൫3𝑦൅𝑒௫ୱ୧୬௫൯ 𝑑𝑥൅ ൫7𝑥൅ √𝑒௬൅2 ൯ 𝑑𝑦 ൌ𝛼 𝜋 G , where 𝛼 is a real constant, then 𝛼 is equal to ________.

Accepted Answer

36

Question 15

Let 𝑦ଵሺ𝑥ሻ and 𝑦ଶሺ𝑥ሻ be two linearly independent solutions of 𝑥ଶ 𝑑ଶ𝑦 𝑑𝑥ଶെ 2𝑥 𝑑𝑦 𝑑𝑥൅2𝑦ൌ0, 𝑥 ൐0. Let 𝑊ሺ𝑦ଵ, 𝑦ଶሻሺ𝑥ሻ denote the Wronskian of 𝑦ଵሺ𝑥ሻ and 𝑦ଶሺ𝑥ሻ at 𝑥. If 𝑊ሺ𝑦ଵ, 𝑦ଶሻሺ1ሻൌ1 then 𝑊ሺ𝑦ଵ, 𝑦ଶሻሺ2ሻ is equal to _______.

Accepted Answer

4

Question 16

Let 𝐴ൌ ቎ 2 0 1 2 1 1 5 െ5 0 0 0 0 3 0 1 3 ቏. Then the sum of the geometric multiplicities of the distinct eigenvalues of 𝐴 is equal to ________.

Accepted Answer

2

Question 17

In a cosmopolitan city, the population comprises of 30% female and 70% male. Suppose that 5% of female and 30% of male in the population are foreigners. A person is selected at random from this population. Given that the selected person is a foreigner, the probability that the person is a female is ________ (round off to three decimal places).

Accepted Answer

0.066 to 0.068

Question 18

Let 𝑓: ሺ0, ∞ሻ→ℝ be the continuous function such that 𝑓ሺ𝑥ሻൌ2 ൅ ௚ሺ௫ሻ ௫ for all 𝑥൐0, where 𝑔ሺ𝑥ሻൌ ׬ 𝑓ሺ𝑡ሻ ௫ ଵ 𝑑𝑡 for all 𝑥൐0. Then 𝑓ሺ2ሻ is equal to

Accepted Answer

2 ൅ log௘4

Answer

2 ൅ log௘2

Answer

2 െ log௘2

Answer

2 െ log௘4

Question 19

Let 𝐴 and 𝐵 be 𝑛ൈ𝑛 matrices with real entries. Consider the following statements: P: If 𝐴 is symmetric then 𝑟𝑎𝑛𝑘ሺ𝐴ሻൌ Number of nonzero eigenvalues (counting multiplicity) of 𝐴. Q: If 𝐴𝐵ൌ𝟎 then 𝑟𝑎𝑛𝑘ሺ𝐴ሻ൅𝑟𝑎𝑛𝑘ሺ𝐵ሻ൑𝑛. Then

Accepted Answer

both P and Q are TRUE

Answer

P is TRUE and Q is FALSE

Answer

P is FALSE and Q is TRUE

Answer

both P and Q are FALSE

Question 20

Let 𝑓: ℝଶ→ℝ be given by 𝑓ሺ𝑥, 𝑦ሻൌ4𝑥𝑦െ2𝑥ଶെ𝑦ସ൅1. The number of critical points where 𝑓 has local maximum is equal to ________.

Accepted Answer

2

Question 21

If the quadrature rule න𝑓ሺ𝑥ሻ𝑑𝑥 ଵି ଵ ൎ𝑓ሺ𝛼ሻ൅ 𝛾 𝑓ሺ𝛽ሻ, where 𝛼, 𝛽 and 𝛾 are real constants, is exact for all polynomials of degree ൑3, then 𝛾൅3 ሺ𝛼ଶ൅ 𝛽ଶሻ൅ሺ𝛼ଷ൅𝛽ଷሻ is equal to _______.

Accepted Answer

3

Question 22

A heavy horizontal cylinder of diameter D supports a mass of liquid having density 𝜌 as shown in the figure. Find out the vertical component of force exerted by the liquid per unit length of the cylinder if g is the acceleration due to gravity.

Accepted Answer

𝜋𝐷ଶ 8 𝜌𝑔

Answer

𝜋𝐷ଶ 4 𝜌𝑔

Answer

𝜋𝐷ଶ 2 𝜌𝑔

Answer

𝜋𝐷ଶ 3 𝜌𝑔

Question 23

The figure shows the developing zone and the fully developed region in a pipe flow where the steady flow takes place from left to right. The wall shear stress in the sections A, B, C, and D are given by 𝜏஺, 𝜏஻, 𝜏஼, and 𝜏஽, respectively. Select the correct statement.

Accepted Answer

𝜏஺൐ 𝜏஻

Answer

𝜏஻൐ 𝜏஺

Answer

𝜏஼൐ 𝜏஻

Answer

𝜏஼൐ 𝜏஽

Question 24

The left hand column lists some non-dimensional numbers and the right hand column lists some physical phenomena. Indicate the correct combination 1. Reynolds number i. Wave drag 2. Froude number ii. Compressible flow 3. Mach number iii. Viscous drag 4. Weber number iv. Spray formation

Accepted Answer

1-iii, 2-i, 3-ii, 4-iv

Answer

1-i, 2-ii, 3-iv, 4-iii

Answer

1-iv, 2-iii, 3-iv, 4-iii

Answer

2-iv, 1-iii, 3-ii, 4-i

Question 25

As temperature increases

Accepted Answer

the dynamic viscosity of a gas increases.

Accepted Answer

the dynamic viscosity of a liquid decreases.

Answer

the dynamic viscosity of a liquid does not change.

Answer

the dynamic viscosity of a gas decreases.

Question 26

Which of the following statement(s) regarding a venturimeter is/are correct?

Accepted Answer

In the direction of flow, it consists of a converging section, a throat, and a diverging section.

Accepted Answer

Pressure tappings are provided just upstream of the venturimeter and at the throat.

Answer

In the direction of flow, it consists of a diverging section, a throat, and a converging section.

Answer

It is used for flow measurement at a very low Reynolds number.

Question 27

Which of the following statement(s) is/are true for streamlines in a steady incompressible flow?

Accepted Answer

Two streamlines cannot intersect each other.

Accepted Answer

Stream function has a constant value along a streamline.

Answer

Flow rate increases between two diverging streamlines.

Answer

Flow rate decreases between two diverging streamlines.

Question 28

A flow has a velocity potential given by 𝜙ൌ𝐴𝑥ଷ where ‘A’ is a non-zero constant. Which of the following statement(s) is/are true about the flow?

Accepted Answer

The flow is irrotational.

Accepted Answer

The flow has convective acceleration.

Answer

The flow is incompressible.

Answer

The flow has local acceleration.

Question 29

A boundary layer develops due to a two-dimensional steady flow over a horizontal flat plate. Consider a vertical line away from the leading edge which extends from the wall to the edge of the boundary layer. Which of the following quantity/quantities is/are not constant along the vertical line? 𝑢 and 𝑣 represent the components of velocity in the direction along the plate and normal to it, respectively and x is taken along the length of the plate while p is the pressure. Neglect body forces.

Accepted Answer

𝑢

Accepted Answer

𝜕𝑢 𝜕𝑥

Accepted Answer

𝑣

Answer

𝑝

Question 30

A 10 kg mass placed on an infinitely long horizontal massless flat platform is to be supported by a steady vertical water jet as shown in the figure. The diameter of the jet is 5 cm. What minimum average velocity is required to hold the mass in place? Assume 𝜌௪௔௧௘௥ൌ1000 kg/mଷ, 𝑔ൌ10 ୫ ୱమ and 𝜋ൌ3.14 . Neglect friction. (Round off to two decimal places)

Accepted Answer

6.95 to 7.20

Question 31

Consider an inviscid flow through a smooth pipe which has a pitot-static tube arrangement as shown. Find the centre-line velocity in the pipe. Consider that the density of the fluid is 1000 kg/m3, acceleration due to gravity is 10 m/s2, and the specific gravity of the manometric fluid is 11.

Accepted Answer

2 m/s

Answer

3 m/s

Answer

5 m/s

Answer

7 m/s

Question 32

The speed of propagation, c, of a capillary wave depends on the density of the fluid, ρ, the wavelength of the wave, λ, and the surface tension, σ. If the density and wavelength remain constant, halving the surface tension would lead to a new velocity, c', given by

Accepted Answer

𝑐ᇱൌ ௖ √ଶ

Answer

c' = 2c

Answer

c' = √2c

Answer

c' = c

Question 33

A two-dimensional flow field is described by a combination of a source of strength m at the origin and a uniform flow, U, in the positive x-direction such that the velocity potential is given by 2 2 ln 2 y x m Ux + + = π φ The stagnation streamline is shown in the figure. Find the distance a a ′.

Accepted Answer

U m 2

Answer

U m

Answer

U m 8

Question 34

A typical boundary layer over a flat plate has a linear velocity profile with zero velocity at the wall and freestream velocity, U∞, at the outer edge of the boundary layer. What is the ratio of the momentum thickness to the thickness of the boundary layer?

Accepted Answer

6 1

Answer

2 1

Answer

4 1

Answer

3 1

Question 35

Identify the configuration(s) in which steady two-dimensional internal flow may show boundary layer separation if the flow direction is left to right.

Accepted Answer

Accepted Answer

Question 36

Consider steady fully developed flow of a liquid through two large horizontal flat parallel plates separated by a distance of 2 mm. One of the plate is fixed and the other plate moves at a speed of 0.5 m/s. What is the magnitude of the pressure gradient (in Pa/m) in the direction of the flow required to ensure that the net flow through the plates is zero? Dynamic viscosity of the liquid is 5x10-4 Ns/m2 (Round off to the nearest integer)

Accepted Answer

374 to 376

Question 37

Consider two-dimensional turbulent flow of air over a horizontal flat plate of length 1 m. Skin friction coefficient at a length x from the leading edge of the plate is obtained as: ( ) 2.0 Re 06 .0 x fc = where, Rex is the local Reynolds number. Find out the drag force per unit width (in N/m2) on the plate if the free stream air velocity is 10 m/s. Density and dynamic viscosity of air are given as 1.2 kg/m3 and 1.83x10-5 N-s/m2, respectively. (Round off to three decimal places)

Question 38

For an inviscid fluid with density 1 kg/m3, the Cartesian velocity field is given as: 𝐮ൌሺെ2𝑥൅𝑦ሻ𝑡𝐢൅ሺ2𝑥൅𝑦ሻ𝑡𝐣 m/s Neglecting the body forces, find the magnitude of pressure gradient in (Pa/m) at (x, y) = (1 m, 1 m) at t = 1 s. (Round off to two decimal places)

Accepted Answer

5.60 to 5.70

Question 39

Consider a lawn sprinkler with horizontal arms of radius, a = 10 cm which has water introduced vertically through the centre, as shown in the figure. The exit area of the jet is 25 cm2 and the jet velocity is 1 m/s. The water is ejected orthogonal to the sprinkler arm and the jet makes an angle of 60° with the horizontal plane. Find the torque (in N-m) required to hold the sprinkler stationary. Consider water density 1000 kg/m3. Neglect the effects of friction and gravity. (Round off to two decimal places)

Accepted Answer

0.24 to 0.26

Question 40

A wooden cylinder (specific gravity = 0.6) of length L and diameter D floats in water (density 1000 kg/m3). Find out the minimum value of D/L for which the cylinder floats with its axis vertical. (Round off to three decimal places)

Accepted Answer

1.380 to 1.390

Question 41

Consider a cart of mass 10 kg placed on an inclined plane (angle of inclination 60° with horizontal) as shown in the figure. A turning vane of negligible weight is mounted on the cart. A horizontal steady water jet is issued from a stationary nozzle of area 0.1 m2 and strikes the turning vane as shown in the figure. The vane turns the jet downward parallel to the inclined plane. Find out the minimum jet velocity (in m/s) which will not allow the cart to come down. Neglect friction, consider density of water = 1000 kg/m3 and acceleration due to gravity = 10 m/s2. (Round off to two decimal places)

Accepted Answer

0.74 to 0.78

Question 42

A siphon is used to drain out water (density 1000 kg/m3) from a tank as shown in the figure. What can be the maximum height z (in meter) of the point C? Consider acceleration due to gravity = 10 m/s2, pressure at point A = 101 kPa, vapour pressure of water = 29.5 kPa and neglect friction. (Round off to two decimal places)

Accepted Answer

5.1 to 5.2

Question 43

The horizontal belt of negligible weight shown in the figure moves with a steady velocity (V) of 2.5 m/s and skims over the top surface of an oil-film of depth h = 3 cm. The length (L) and width (b) of the belt are, respectively, 2 m and 60 cm. Find the viscosity of the oil (in Pa-s), given that the minimum power required to move the belt is 100 W. Neglect the end effects. (Round off to two decimal places)

Accepted Answer

0.39 to 0.41

Question 44

A force 𝐹 is applied at an angle 𝜃ൌ30௢ on an elastic column as shown in the figure. 𝐸 and 𝐼 are respectively the Young’s modulus and area moment of inertia. The smallest magnitude of 𝐹 needed to cause buckling is

Accepted Answer

ଶ √ଷ గమாூ ௅మ

Answer

√ଷ ଶ గమாூ ௅మ

Answer

గమாூ ଶ௅మ

Answer

ଶగమாூ ௅మ

Question 45

The shear stress due to a transverse shear force in a linear elastic isotropic beam of rectangular cross-section

Accepted Answer

is maximum at the neutral axis

Answer

varies linearly along the depth in the transverse direction of the beam

Answer

is zero at the neutral axis

Answer

remains constant along the depth in the transverse direction of the beam

Question 46

A massless semicircular rod held fixed at end A is in the xy-plane, as shown in the figure. A force P along the negative z direction is acting at point B on the rod. The unit vectors along x, y and z directions are denoted respectively as i, j and k. Due to the applied force P, the cross-section of the rod at point D will be subjected to

Accepted Answer

a twisting moment 𝑃𝑅ሺ1 െcos 𝜃ሻ𝐢, a bending moment 𝑃𝑅sin 𝜃 𝐣, and a shear force െ𝑃 𝐤

Answer

a twisting moment 𝑃𝑅ሺ1 െsin 𝜃ሻ𝐢, a bending moment 𝑃𝑅cos 𝜃 𝐣, and a shear force 𝑃 𝐤

Answer

a twisting moment 𝑃𝑅ሺcos 𝜃െ1ሻ𝐢, a bending moment െ𝑃𝑅sin 𝜃 𝐣, and a shear force െ𝑃 𝐤

Answer

a twisting moment 𝑃𝑅sin 𝜃𝐢, a bending moment 𝑃𝑅ሺ1 െcosሻ𝜃 𝐣, and a shear force 𝑃 𝐤

Question 47

In the truss shown in the figure, all the members are pin jointed to each other. The members AB, BD, DE and DC have the same length. For the given loading, which of the following is the correct statement?

Accepted Answer

AB is in tension, ED is in compression, and BD is a zero-force member

Answer

BD is a zero-force member, and AB and ED are in compression

Answer

AB and DC are in tension, and BC is in compression

Answer

ED is in tension, and DC and BC are in compression

Question 48

End B of the 2 m long rigid rod AB is constrained to move horizontally in the slot as shown in the figure and has a velocity of 1.0 i m/s. The angular velocity of the rod at the instant shown is 2 rad/s. The unit vectors along x and y directions are denoted respectively as i and j. The velocity of point A in m/s is then given by

Accepted Answer

൫1 െ2√3൯𝐢൅2𝐣

Answer

൫1 ൅2√3൯𝐢െ2𝐣

Answer

െ2√3𝐢൅2𝐣

Answer

2√3𝐢െ2𝐣

Question 49

The assembly of four masses connected by rigid mass-less rods is kept on a smooth horizontal floor as shown in the figure. Under the applied force 2F, the magnitude of angular acceleration of the assembly at the instant shown is

Accepted Answer

𝐹 2𝑚𝑐

Answer

𝐹 𝑚𝑐

Answer

2𝐹 3𝑚𝑐

Answer

𝐹 3𝑚𝑐

Question 50

A particle is constrained to move at a constant speed on an inclined plane (ABCD) along the curved path shown in the figure. Edges AD and BC are parallel to the y axis. The inclined plane makes an angle 𝜃 with the 𝑥𝑦-plane. The velocity vector of the particle makes an angle 𝜙 with the dotted line which is parallel to edge AB. If the speed of the particle is 2 m/s, 𝜙ൌ30°, and 𝜃ൌ40°, then the 𝑧-component of the velocity of the particle in m/s is __________

Accepted Answer

െ1.11

Answer

െ1.32

Answer

െ1.00

Answer

െ1.50

Question 51

A uniform elastic rod of constant cross-section is fixed at its left end as shown in the figure. An axial force 𝑃 is acting as shown. Assume that plane sections remain plane during deformation. The ratio of axial displacements at point A ሺ𝑥ൌ4𝐿ሻ to that at point B ሺ𝑥ൌ𝐿ሻ is ______ (rounded off to one decimal place)

Accepted Answer

1.9 to 2.1

Question 52

A thin-walled spherical pressure vessel has a mean radius of 500 mm and wall thickness of 10 mm. The yield strength of the material is 500 MPa. The internal pressure in MPa at which the spherical pressure vessel will yield according to the Tresca criterion is ____________ (rounded off to one decimal place)

Accepted Answer

19 to 21

Question 53

The beam in the figure is subjected to a moment M0 at mid span as shown. Which of the following is the vertical reaction at B?

Accepted Answer

0 9 8 M L

Answer

0 15 8 M L

Answer

0 3 4 M L

Answer

0 9 4 M L

Question 54

A spring-mass system having a mass m and spring constant k, placed horizontally on a foundation, is connected to a vertically hanging mass m with the help of an inextensible string. Ignore the friction in the pulleys and also the inertia of pulleys, string and spring. Gravity is acting vertically downward as shown. The natural frequency of the system in rad/s is

Accepted Answer

ඨ4𝑘 5𝑚

Answer

ඨ4𝑘 3𝑚

Answer

ඨ𝑘 2𝑚

Answer

ඨ𝑘 3𝑚

Question 55

One end of a uniform rigid rod OA of length L and mass m is attached to a frictionless hinge at O. The other end of the rod is connected to the roof at B with a mass-less inextensible thread AB. Initially the rod is horizontal and at rest. The gravity is acting vertically downward as shown. Immediately after the thread AB is cut, the reaction on the rod at O is

Accepted Answer

௠௚ ସ in the positive y-direction

Answer

௠௚ ଶ in the negative y-direction

Answer

ଷ௠௚ ସ in the negative y-direction

Answer

𝑚𝑔 in the positive y-direction

Question 56

A circular shaft is rigidly connected to a wall at one end. The shaft has a solid portion and a hollow portion as shown in the figure. The length of each portion is 𝐿 and the shear modulus of the material is 𝐺. The polar moment of inertia of the hollow portion is 𝐽 and that of the solid portion is 50𝐽. A torque 𝑇 is applied at the right most end as shown. The rotation of the section PQ is

Accepted Answer

ଶ଻்௅ ଵ଴଴௃ீ

Answer

௅ ସ଴௃ீ

Answer

ହ்௅ ସ௃ீ

Answer

ଷ்௅ ସ௃ீ

Question 57

A rectangular plate of uniform thickness having initial length a and width b is placed between two rigid immovable walls. The temperature of the plate is increased by ΔT. The plate is free to expand along the y and z directions. The mid-surface of the plate remains in the xy-plane. The Poisson’s ratio is ν and the coefficient of thermal expansion is α. Assuming that the plate is initially free of stresses, the change in length of the plate after the increase in temperature is given by

Accepted Answer

(1 ) a T να + Δ

Answer

(1 ) a T να − Δ

Answer

a T αΔ

Answer

2a T αΔ

Question 58

A mass m = 10 kg is attached to a spring as shown in the figure. The coefficient of friction between the mass and the inclined plane is 0.25. Assume that the acceleration due to gravity is 10 m/s2 and that static and kinematic friction coefficients are the same. Equilibrium of the mass is impossible if the spring force is

Accepted Answer

30 N

Answer

45 N

Answer

60 N

Answer

75 N

Question 59

The frame shown in the figure is subjected to a uniformly distributed load of 1000 N/m over a distance of 0.6 m. Neglecting the weight of the frame, the maximum shear force (in N) in the region between the supports A and B of the frame is ________.

Accepted Answer

295 to 305

Question 60

A slider moving in a frictionless slot is connected with a linear spring OA as shown in the figure. The following is known: stiffness of the spring = 2 kN/m, mass of the slider = 10 kg, and the unstretched length of the spring = 1 m. If the slider is released from rest at A the magnitude of its velocity (in m/s) when it passes through point B is ____________(rounded off to the nearest integer)

Accepted Answer

39 to 41

Question 61

A sphere A of mass 𝑚 is thrown into the air at 50 m/s along a direction tanିଵሺ3/4ሻ up from the horizontal. At the topmost point of its trajectory, it has a central (non- oblique) collision with another sphere B which is at rest on top of a vertical pole. Sphere B has a mass of 3𝑚. Acceleration due to gravity is 10 m/s2. Neglect contact friction and air-resistance. If the coefficient of restitution is 0.3, then the speed (in m/s) of sphere A immediately after the collision is_________ (rounded off to one decimal place)

Accepted Answer

0.9 to 1.1

Question 62

The truck shown in the figure is moving on a horizontal road at a speed of 20 m/s. It is carrying a box of mass 1000 kg, which is simply placed on the truck platform. The coefficient of friction between the truck platform and the box is 0.25. Take acceleration due to gravity as 10 m/s2. Assume uniform deceleration during braking, and the coefficients of static and kinetic friction to be the same. The shortest distance in meters in which the truck can be brought to rest without the box slipping is _______(round off to the nearest integer)

Accepted Answer

79 to 81

Question 63

The stepped rod of length 2 m, shown in the figure, is fixed at both ends (A and C). The area of cross-section of portion AB is 200 mm2 and that of portion BC is 100 mm2. Force F is applied at section B such that the section is displaced by 0.1 mm in the direction of the force. Young’s modulus of the rod is 200 GPa. The applied force F in N is _______ (round off to the nearest integer)

Accepted Answer

5990 to 6010

Question 64

A cantilever beam has a span of 1 m and carries a uniformly distributed load of q = 1250 N/m over a portion as shown. A force F =1000 N acts at a distance L from the fixed end. The distance L is such that the bending moment at the fixed end is zero. The beam has a rectangular cross-section of depth 20 mm and width 24 mm. For this loading, the magnitude of the maximum bending stress in the beam in MPa is________________(round off to the nearest integer)

Accepted Answer

123 to 127

GATE XE (Engineering Sciences) 2022 Question Paper & Solutions

General Aptitude

Question 1

Question 2

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Question 10

Engineering Mathematics

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Question 21

Fluid Mechanics

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Question 43

Solid Mechanics

Question 66

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Question 87

Thermodynamics

Question 88

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Question 90

Question 91

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Question 95

Question 96