GATE XE (Engineering Sciences) 2025 Question Paper & Solutions

Question 1

Even though I had planned to go skiing with my friends, I had to __________ at the last moment because of an injury. Select the most appropriate option to complete the above sentence.

Accepted Answer

back out

Answer

back up

Answer

back of

Answer

back on

Question 2

The President, along with the Council of Ministers, ___________ to visit India next week. Select the most appropriate option to complete the above sentence.

Accepted Answer

wishes

Answer

wish

Answer

will wish

Answer

is wishing

Question 3

An electricity utility company charges ₹ 7 per kWh (kilo watt-hour). If a 40-watt desk light is left on for 10 hours each night for 180 days, what would be the cost of energy consumption? If the desk light is on for 2 more hours each night for the 180 days, what would be the percentage-increase in the cost of energy consumption?

Accepted Answer

₹ 504; 20%

Answer

₹ 604.8; 10%

Answer

₹ 604.8; 12%

Answer

₹ 720; 15%

Question 4

In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively? N U F (i) 21 14 9 6 H L (ii) O 12 (iv) 15 (iii)

Accepted Answer

I, J, 10, and 8

Answer

Q, M, 12, and 8

Answer

K, L, 10 and 14

Answer

L, K, 12 and 8

Question 5

A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained: (i) The sum of Yellow balls and twice the number of Violet balls is 50. (ii) The sum of Violet and Green balls is 50. (iii) The sum of Yellow and Red balls is 50. (iv) The sum of Violet and twice the number of Red balls is 50. Which one of the following Pie charts correctly represents the balls in the bag?

Accepted Answer

Answer

V 10% R 20% Y 30% G 40% V 40% R 10% Y 20% G 30%

Answer

V 30% R 40% Y 10% G 20% V 20% R 30% Y 40% G 10%

Question 6

“His life was divided between the books, his friends, and long walks. A solitary man, he worked at all hours without much method, and probably courted his fatal illness in this way. To his own name there is not much to show; but such was his liberality that he was continually helping others, and fruits of his erudition are widely scattered, and have gone to increase many a comparative stranger’s reputation.” (From E.V. Lucas’s “A Funeral”) Based only on the information provided in the above passage, which one of the following statements is true?

Accepted Answer

The solitary man described in the passage is dead.

Answer

Strangers helped create a grand reputation for the solitary man described in the passage.

Answer

The solitary man described in the passage found joy in scattering fruits.

Answer

The solitary man worked in a court where he fell ill.

Question 7

For the clock shown in the figure, if O* = O Q S Z P R T, and X* = X Z P W Y O Q , then which one among the given options is most appropriate for P* ?

Accepted Answer

P R T O Q S U

Answer

P U W R T V X

Answer

P T V Q S U W

Answer

P S U P R T V

Question 8

Consider a five-digit number 𝑃𝑄𝑅𝑆𝑇 that has distinct digits 𝑃, 𝑄, 𝑅, 𝑆, and 𝑇, and satisfies the following conditions: 𝑃< 𝑄 𝑆> 𝑃> 𝑇 𝑅< 𝑇 If integers 1 through 5 are used to construct such a number, the value of 𝑃 is:

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 9

A business person buys potatoes of two different varieties P and Q, mixes them in a certain ratio and sells them at ₹ 192 per kg. The cost of the variety P is ₹ 800 for 5 kg. The cost of the variety Q is ₹ 800 for 4 kg. If the person gets 8% profit, what is the P:Q ratio (by weight)?

Accepted Answer

5:4

Answer

3:4

Answer

3:2

Answer

1:1

Question 10

Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km, as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road? Note: The figure shown is representative.

Accepted Answer

12.0

Answer

10.5

Answer

11.0

Answer

12.5 P Q R 14 km 13 km 15 km

Question 11

Let 𝑋 and 𝑌 be two random variables with mean 0, variance 1, and correlation coefficient 1 3 . Then the value of Var(𝑋+ 3𝑌) is equal to

Accepted Answer

12

Answer

9

Answer

10

Answer

11

Question 12

Consider the second order Partial Differential Equation (PDE) 4𝑥2 𝜕2𝑢 𝜕𝑥2 + 4(𝑥+ 𝑦) 𝜕2𝑢 𝜕𝑥𝜕𝑦+ (𝑥2 + 𝑦2) 𝜕2𝑢 𝜕𝑦2 − 𝑢= 0. Then which one of the following statements is correct ?

Accepted Answer

The PDE is hyperbolic in the region {(𝑥, 𝑦) ∈ℝ2: −1 < 𝑥< 0, 𝑦< 0}

Answer

The PDE is hyperbolic in the region {(𝑥, 𝑦) ∈ℝ2: 1 < 𝑥< ∞, 𝑦< 0}

Answer

The PDE is elliptic in the region {(𝑥, 𝑦) ∈ℝ2: 0 < 𝑥< 1, 𝑦> 0}

Answer

The PDE is parabolic in the region {(𝑥, 𝑦) ∈ℝ2: 1 < 𝑥< ∞, 𝑦< 0}

Question 13

Consider the infinite series (𝑃): ∑ 1 (𝑛log 𝑛)1/𝑛 ∞ 𝑛=2 (𝑄): ∑𝑛𝑛 (2𝑛)! ∞ 𝑛=1 Then which one of the following statements is correct ?

Accepted Answer

Series (𝑃) diverges and series (𝑄) converges

Answer

Series (𝑃) and (𝑄) both converge

Answer

Series (𝑃) converges and series (𝑄) diverges

Answer

Series (𝑃) and (𝑄) both diverge

Question 14

Suppose the polynomial 𝑎+ 𝑏𝑥+ 𝑐𝑥2 + 𝑑𝑥3 interpolates the data, (−1, 1), (0, 3), (1, 2) and (2, 4). Then which one of the following statements is correct ?

Accepted Answer

𝑎= −2𝑐, 𝑑= −2𝑏

Answer

𝑎= 2𝑐, 𝑑= 2𝑏

Answer

𝑏= 3𝑐, 𝑎= 2𝑑

Answer

𝑏= 2𝑐, 𝑎= 3𝑑

Question 15

Let 𝐶 be the positively oriented boundary of the domain bounded by the curves 𝑦= 2𝑥2 and 𝑦2 = 4𝑥. Then the value of the line integral ∮(2𝑦2 + 2𝑥𝑦+ 4𝑦)𝑑𝑥+ (𝑥2 + 4𝑥𝑦+ 8𝑥)𝑑𝑦 𝐶 is equal to

Accepted Answer

8 3

Answer

2 3

Answer

4 3

Answer

1 3

Question 16

Let 𝑦(𝑥) be the solution of the initial value problem, 𝑥2𝑦′′ + 𝑥𝑦′ −𝑦= 0, 𝑥> 0, 𝑦(1) = 0, 𝑦′(1) = 2. Then the value of 𝑦′ ( 1 2) is equal to (Answer in integer) _______

Accepted Answer

5

Question 17

Suppose that 2 is an eigenvalue of the matrix [ 0 3 −𝛼 0 1 0 1 −1 3 ] Then the value of 𝛼 is equal to (Answer in integer) __________

Accepted Answer

2

Question 18

Let 𝑓(𝑧) be an analytic function such that 𝑅𝑒(𝑓′(𝑧)) = 3𝑥2 −4𝑦−3𝑦2, 𝑓(𝑖) = 0, 𝑓′(0) = 0, where 𝑖= √−1. Then the value of 𝑓(1) is equal to

Accepted Answer

1 + 5𝑖

Answer

4 + 2𝑖

Answer

1 −𝑖

Answer

4 −2𝑖

Question 19

Consider the function 𝑓(𝑥, 𝑦) = 𝑥2𝑦+ 2𝑥𝑦2 −2𝑥2𝑦2. Then which one of the following statements is correct ?

Accepted Answer

( 3 2 , 3 4) is a saddle point of 𝑓.

Answer

( 3 2 , 0) is a point of local maxima of 𝑓.

Answer

(0, 3 4) is a point of local minima of 𝑓.

Answer

( 3 2 , 3 4) is a point of local maxima of 𝑓.

Question 20

For 𝑎, 𝑏∈ℝ, consider the system of linear equations 𝑥+ 𝑦+ 𝑎𝑧= 2 2𝑦+ 2𝑧= 1 𝑎𝑥+ 2𝑧= 𝑏 If the system has infinitely many solutions, then which of the following statements is/are correct ?

Accepted Answer

𝑎= 2, 𝑏= 3

Accepted Answer

𝑎= −1, 𝑏= − 3 2

Answer

𝑎= 2, 𝑏= 5

Answer

𝑎= 3, 𝑏= 5

Question 21

Let 𝑢(𝑥, 𝑡) be the solution of the initial boundary value problem 𝜕𝑢 𝜕𝑡−𝜕2𝑢 𝜕𝑥2 −𝑢= 0, 0 < 𝑥< 𝜋, 𝑡> 0, 𝑢(𝑥, 0) = 2 sin (3𝑥 2 ) cos (𝑥 2) , 0 < 𝑥< 𝜋, 𝑢(0, 𝑡) = 𝑢(𝜋, 𝑡) = 0, 𝑡> 0. Then the value of lim 𝑡→∞𝑢( 3𝜋 4 , 𝑡) is equal to (rounded off to two decimal places)___________

Accepted Answer

0.68 to 0.73

Question 22

Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end. Which one of the following options correctly represents the velocity field in the converging section in cylindrical (𝑟, 𝜃, 𝑧) coordinates?

Accepted Answer

Two-dimensional function of 𝑟 and 𝑧

Answer

One-dimensional function of 𝑟

Answer

Two-dimensional function of 𝑟 and 𝜃

Answer

One-dimensional function of 𝑧

Question 23

A sharp flat plate of length L and infinite width is immersed parallel to a fluid stream having velocity 𝑢∞. At a point on the plate, far away from the leading edge and not near the trailing edge, the boundary layer thickness, the displacement thickness, and the momentum thickness are denoted as 𝛿, 𝛿∗, and 𝜃, respectively. Which one of the following options correctly represents the relation between these thicknesses?

Accepted Answer

𝛿> 𝛿∗> 𝜃

Answer

𝛿> 𝜃> 𝛿∗

Answer

𝛿∗> 𝛿> 𝜃

Answer

𝜃> 𝛿∗> 𝛿

Question 24

Consider the following Statements [1] and [2]. Statement [1]: The Eulerian study focusses attention on individual particle and its motion is observed as a function of time. Statement [2]: The Lagrangian study focusses attention on the motion of the particles passing through an identified point. Which one of the following options identifies the correctness of the given statements?

Accepted Answer

Both [1] and [2] are NOT correct.

Answer

Both [1] and [2] are correct.

Answer

[1] is correct, but [2] is NOT correct.

Answer

[1] is NOT correct, but [2] is correct.

Question 25

Statement of Reynolds Transport Theorem is given below with three blanks. The rate of change of ________ extensive property can be calculated by summing the rate of change of the amount of same property in the ________ and the rate at which the property is ________ the surface of the control volume. Which one of the following options correctly fills the blanks by using its comma-separated phrases in sequence?

Accepted Answer

system, control volume, exiting

Answer

control volume, system, exiting

Answer

system, control volume, entering

Answer

control volume, control volume, entering

Question 26

For a steady and incompressible flow, the velocity field (𝑉⃗ ) in Cartesian (𝑥, 𝑦, 𝑧) coordinate system is given as: 𝑉⃗ = 5𝑥𝑖−𝑃𝑦𝑗+ 3𝑘 Here, 𝑖, 𝑗, and 𝑘 are unit vectors along x, y, and z directions, respectively and 𝑃 is a constant. Which one of the following options is the correct value of 𝑃 that satisfies the conservation of mass for the given velocity field?

Accepted Answer

5

Answer

−5

Answer

8

Answer

2

Question 27

Conservation of mass for a steady axisymmetric flow field in the cylindrical (r, z) coordinates is: 1 𝑟 𝜕(𝑟𝑉𝑟) 𝜕𝑟 + 𝜕𝑉𝑧 𝜕𝑧= 0 Here, 𝑉𝑟 and 𝑉𝑧 are radial and axial components of velocity, respectively. Which one of the following options is correct if 𝜓 is the stream function?

Accepted Answer

𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 1 𝑟 𝜕𝜓 𝜕𝑟

Answer

𝑉𝑟= 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 1 𝑟 𝜕𝜓 𝜕𝑟

Answer

𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= 1 𝑟 𝜕𝜓 𝜕𝑟

Answer

𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 𝜕𝜓 𝜕𝑟

Question 28

Group-I indicates different properties of fluid and Group-II defines their basic dimensions in terms of Force (𝐹), Length (𝐿), and Time (𝑇). Group-I Group-II P Dynamic viscosity 1 𝐹𝐿−4𝑇2 Q Surface tension 2 𝐹𝐿−2𝑇 R Density 3 𝐹𝐿−1 Which one of the following options identifies the correct match between Group-I and Group-II?

Accepted Answer

P−2, Q−3, R−1

Answer

P−1, Q−3, R−2

Answer

P−2, Q−1, R−3

Answer

P−3, Q−2, R−1

Question 29

Consider the steady, incompressible, and fully developed laminar flow of a fluid through a circular pipe. Here, ∆𝑃 is the pressure drop in the direction of the flow and 𝑉 is the average axial velocity of the fluid at any cross-section. The relation between ∆𝑃 and 𝑉 is: ∆𝑃= 𝐾 𝑉𝑛 Here, 𝐾 and 𝑛 are constants. Which one of the following options is the correct value of 𝑛?

Accepted Answer

1

Answer

2

Answer

1.75

Answer

0.5

Question 30

A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together. Which one of the following options correctly represents the nature of the product of the strength and the distance between them during approach?

Accepted Answer

Remains always constant

Answer

Continuously decreases

Answer

Continuously increases

Answer

First increases and then continuously decreases after reaching a maximum

Question 31

Figure shows two parallel plates (upper plate at 𝑥= 𝑏 and lower one at 𝑥= −𝑏) of length L (aligned in 𝑧 direction) and infinite width (in 𝑦 direction, normal to the plane of the figure). Two immiscible, incompressible liquids are flowing steadily in the 𝑧 direction through the thin passage between the plates under the influence of horizontal pressure gradient (𝑃0 −𝑃𝐿) L ⁄ . During the flow, the passage is always half-filled with denser fluid I (viscosity 𝜇𝐼) at the bottom and rest is occupied by lighter fluid II (viscosity 𝜇𝐼𝐼; 𝜇𝐼𝐼< 𝜇𝐼). Considering exactly planar interface between the fluids and no instabilities in the flow, the shear stress, 𝜏𝑥𝑧 is expressed as: 𝜏𝑥𝑧= (𝑃0 −𝑃𝐿)𝑏 L [(𝑥 𝑏) −1 2 (𝜇𝐼−𝜇𝐼𝐼 𝜇𝐼+ 𝜇𝐼𝐼)] Which one of the following options correctly identifies the location of the point having maximum velocity of the flow?

Accepted Answer

Above the interface

Answer

Below the interface

Answer

At the interface

Answer

At the top plate

Question 32

Group-I shows different two-dimensional bodies and Group-II mentions their total drag coefficient (𝐶𝐷) based on frontal area while facing parallel flow of fluid having Reynolds number 𝑅𝑒≥104 along the direction of arrow. The bodies are placed symmetrically with respect to the flow direction. Group-I Group-II P 1 1.2 Q 2 1.6 R 3 2.1 S 4 2.3 Which one of the following options identifies the correct match between Group-I and Group-II, as per the concept of degree of streamlining?

Accepted Answer

P−3, Q−2, R−1, S−4

Answer

P−3, Q−2, R−4, S−1

Answer

P−2, Q−3, R−1, S−4

Answer

P−3, Q−1, R−2, S−4

Question 33

A solid body of uniform specific gravity floats in a deep liquid pool. Take 𝐵, 𝐺, and 𝑀 as the centre of buoyancy, centre of gravity, and metacentre of the body, respectively. Which one of the following options is correct for the stable floatation of the body in the pool when the body is given a small tilt angle?

Accepted Answer

𝑀𝐺̅̅̅̅̅ is the metacentric height and 𝐺 should lie below 𝑀

Answer

𝑀𝐺̅̅̅̅̅ is the metacentric height and 𝐵 should lie above 𝑀

Answer

𝑀𝐵̅̅̅̅̅ is the metacentric height and 𝐵 should lie below 𝑀

Answer

𝑀𝐵̅̅̅̅̅ is the metacentric height and 𝐺 should lie above 𝑀

Question 34

Figure shows the steady and incompressible flow of a fluid in the direction of arrow from section A to section D. Three pipe connectors are to be placed between sections at A and D having Total Energy Line (TEL) and Hydraulic Grade Line (HGL) as depicted in the figure. Consider, g, P, Q, V, γ, and Z denote gravitational acceleration, pressure, volume flow rate, velocity, specific weight, and elevation of centerline of the pipe connectors from the datum, respectively. Which one of the following options, in sequence, indicates the correct nature of connectors between sections A and B, B and C, and C and D in the direction of flow?

Accepted Answer

Converging, Constant area, Diverging

Answer

Diverging, Constant area, Converging

Answer

Constant area, Constant area, Constant area

Answer

Constant area, Converging, Diverging

Question 35

A liquid flows under steady and incompressible flow conditions from station 1 to station 4 through pipe sections P, Q, R, and S as shown in figure. Consider, 𝑑, 𝑉, and ℎ represent the diameter, velocity, and head loss, respectively, in each pipe section with subscripts ‘P’, ‘Q’, ‘R’, and ‘S’. ∆ℎ represents the head difference between the inlet (station 1) and outlet (station 4). All the pipe sections are placed on the same horizontal plane for which the figure shows the top view. Which one of the following options is correct for the given flow loop?

Accepted Answer

∆ℎ= ℎ𝑃+ ℎ𝑄+ ℎ𝑅 and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 + 𝑉𝑆𝑑𝑆 2

Answer

∆ℎ= ℎ𝑃+ ℎ𝑄+ ℎ𝑅+ ℎ𝑆 and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 = 𝑉𝑆𝑑𝑆 2

Answer

∆ℎ= ℎ𝑃+ ℎ𝑄+ ℎ𝑅 and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 = 𝑉𝑆𝑑𝑆 2

Answer

∆ℎ= ℎ𝑃+ ℎ𝑄+ ℎ𝑅+ ℎ𝑆 and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 + 𝑉𝑆𝑑𝑆 2

Question 36

Consider, 𝑖 and 𝑗 are unit vectors along x and y directions of a Cartesian (𝑥, 𝑦) coordinate system, respectively and 𝑡 is time. Temperature (𝑇) and fluid velocity (𝑉⃗ ) are given for a flow field as: 𝑇= 𝑥2 + 𝑦𝑡+ 35 𝑉⃗ = (4𝑥𝑦)𝑖+ (𝑥𝑡−2𝑦2)𝑗 The total rate of change of temperature in the flow field (in integer) for time 𝑡= 2 at a point (2, 3) is ________

Accepted Answer

71

Question 37

Driven by a pressure gradient of 100 kPa/m, a fluid of dynamic viscosity 0.1 Pa.s flows between two fixed infinitely large parallel plates under steady, incompressible, and fully developed laminar conditions. The average velocity of the flow is 2 m/s. The gap between the parallel plates in mm (rounded off to 2 decimal places) is ________

Accepted Answer

4.80 to 5.00

Question 38

An incompressible fluid is flowing between two infinitely large parallel plates separated by 5 mm distance. The bottom plate is stationary and the top plate is moving at a constant velocity of 5 mm/s in the direction parallel to the bottom plate. The flow of the fluid between the plates is steady, two-dimensional, laminar, and the variation of fluid velocity is linear between the plates. A square fluid element of 1 mm side is considered at equal distance from both the plates in the flow field such that one of its sides is parallel to the plates. The magnitude of circulation in mm2/s (in integer) along the edges of the square fluid element is ________

Accepted Answer

1

Question 39

Consider, a kite weighing 100 grams as essentially a rigid flat plate making an angle 8° with the horizontal and having a planform area of 0.045 m2 when exposed to horizontal parallel wind of 60 km/h. The thread string of the kite makes an angle 45° with the horizontal. A tension of 450 grams in the thread is necessary to float the kite steadily. Take air density as 1.2 kg/m3 and gravitational acceleration as 9.81 m/s2. The lift coefficient (𝐶𝐿) associated with the air flow around steadily floating kite (rounded off to 2 decimal places) is ________

Accepted Answer

0.50 to 0.60

Question 40

A fixed control volume has four one-dimensional boundary sections (1, 2, 3, and 4). For a steady flow inside the control volume, the flow properties at each section are tabulated below: Boundary Section Type Density (kg/m3) Surface Normal Velocity (m/s) Cross-sectional Area (m2) Specific Energy (J/kg) 1 Inlet 1000 10 0.5 200 2 Inlet 1000 2 3.0 50 3 Outlet 1000 5 1.0 100 4 Outlet 1000 4 1.5 80 The rate of change of energy of the system which occupies the control volume at this instant is 𝐸× 106 J/s. The value of 𝐸 (rounded off to 2 decimal places) is ________

Accepted Answer

-0.32

Question 41

A ship is to be operated in a fluid medium with kinematic viscosity 0.032 × 10−3 m2/s. A one-tenth scale model of the ship is built for testing. Consider, inertia, viscous and gravity forces are dominant for the ship and its model during the operation. The required kinematic viscosity of the liquid for testing the model is 𝑃× 10−6 m2/s. The value of 𝑃 (rounded off to 2 decimal places) is ________

Accepted Answer

0.95 to 1.05

Question 42

Water flows through a pipe of diameter 20 cm at a flow rate of 0.025 m3/s. A pitot- static tube is placed at the centre of the pipe and indicates the pressure difference of 5 cm of water column. Theoretical velocity measured through pitot-static tube when multiplied with velocity coefficient 𝐶𝑉 gives the actual velocity of the flow. If the mean velocity in the pipe is 90% of the actual velocity at the centre of the pipe and the gravitational acceleration is 10 m/s2, the value of 𝐶𝑉 (rounded off to 2 decimal places) is ________

Accepted Answer

0.85 to 0.90

Question 43

An oil of density 870 kg/m3 and viscosity 0.036 Pa.s flows through a straight pipe of 10 cm diameter and 1.5 km length at the flow rate of 250 liters per minute under the steady and incompressible flow conditions. To control the flow rate of oil, a valve is fixed at the middle of the pipe causing no change in the total length of the pipe. The total head loss measured across the two ends of the pipe is 11.60 m. Using gravitational acceleration as 10 m/s2, the minor head loss contributed by the presence of the valve in m (rounded off to 2 decimal places) is ________

Accepted Answer

0.85 to 1.28

Question 44

Consider a spring-mass system with mass m and spring stiffness k as shown in the illustration. At time t=0, the mass is displaced by P units and the velocity of the mass is zero. The displacement of the mass, x(t), is measured from the equilibrium position. Which one of the following functions represent x(t)?

Accepted Answer

𝑃𝑐𝑜𝑠(√𝑘 𝑚𝑡)

Answer

𝑃 𝑐𝑜𝑠(√𝑘 𝑚𝑡)+ 𝑃 𝑠𝑖𝑛(√𝑘 𝑚𝑡)

Answer

𝑃 𝑠𝑖𝑛(√𝑘 𝑚𝑡)

Answer

𝑃 2 𝑐𝑜𝑠(√𝑘 𝑚𝑡)+ 𝑃 2 𝑠𝑖𝑛(√𝑘 𝑚𝑡)

Question 45

A ball of mass 5m approaches a stationary ball of mass m with a horizontal velocity of 2 m/s from left to right. After a perfectly elastic central collision, the horizontal velocity of the heavier ball is 1 m/s from left to right. Which one of the following statements, regarding the velocity (in m/s) of the lighter ball after impact, is TRUE?

Accepted Answer

Moves from left to right at 5 m/s

Answer

Comes to rest

Answer

Moves from right to left at 5 m/s

Answer

Moves from left to right at 1m/s

Question 46

The Mohr’s circle corresponding to an infinitesimal element is shown in the figure. The plane PQ in the infinitesimal element, at an angle of 𝜃 from the x-axis, is in a state of pure shear. Which one of the following values of 𝜃 (in degrees) is CORRECT?

Accepted Answer

45

Answer

90

Answer

60

Answer

120

Question 47

The two-dimensional state of stress, in an infinitesimal element, is given by 𝜎𝑥𝑥= 800 MPa, 𝜎𝑥𝑦= 300 MPa and 𝜎𝑦𝑦= 0 MPa. Which one of the following options is the maximum shear stress (in MPa) in the element?

Accepted Answer

500

Answer

400

Answer

800

Answer

300

Question 48

Two cars P and Q are travelling on a straight path and are 60 m apart as shown in the figure; Car P is moving with a constant velocity of 36 kmph, while car Q is moving at a constant velocity of 18 kmph. At this instant, the driver in car P applies the brake and collision occurs with car Q after 30 seconds. Assuming uniform deceleration due to braking, which one of the following is the CORRECT velocity (in m/s) of the car P just before the collision?

Accepted Answer

4

Answer

1

Answer

16

Answer

5

Question 49

The natural frequency of a spring-mass system is 10 rad/s. Which of the following statements is/are CORRECT?

Accepted Answer

The mass is 1.25 kg and the stiffness is 125 N/m.

Accepted Answer

The stiffness is 620 N/m and the mass is 6.2 kg.

Answer

The mass is 100 kg and the stiffness is 1 N/m.

Answer

The stiffness is 62 N/m and the mass is 620 kg.

Question 50

Consider a beam with a square box cross-section as shown in the figure. The outer square has a length of 10 mm. The thickness of the section is 1 mm. The area moment of inertia about the x-axis is _____ mm4 (in integer).

Accepted Answer

490 to 494

Question 51

For a certain linear elastic isotropic material, the Young’s modulus is 140 GPa and the shear modulus is 50 GPa. The Poisson’s ratio for the material is _____ (rounded off up to two decimal places).

Accepted Answer

0.40

Question 52

A force of P = 100 N is applied at the ends of the pliers as shown in the figure. Neglecting friction, the force exerted by the upper jaw on the workpiece is _____ N (in integer).

Accepted Answer

400

Question 53

Consider two blocks, P of mass 100 kg and Q of mass 150 kg, resting as shown in the figure. The angle 𝜃= 30°. The coefficient of friction between the two blocks is 0.2. Assume no friction exists at all other interfaces. The minimum force required to move the block P upward is W. Which one of the following options is closest to the CORRECT magnitude of W (in N)?

Accepted Answer

862.2

Answer

1116.6

Answer

2900.0

Answer

406.2

Question 54

Which one of the following vertical columns, of circular cross-section, sustains the highest load without buckling?

Accepted Answer

Cantilever column with a length L and cross-section diameter 2d

Answer

Cantilever column with a length L and cross-section diameter d

Answer

Column with hinge at one end and roller at the other end with a length 2L and cross-section diameter d

Answer

Column with hinge at one end and roller at the other end with a length L and cross-section diameter d

Question 55

The figure shows a rod PQ, hinged at P, rotating counter-clockwise with a uniform angular speed of 15 rad/s. A block R translates along a slot cut out in rod PQ. At the instant shown the distance PR = 0.5 m and θ = 60o. The relative velocity of R with respect to the rod PQ is 5 m/s at the instant shown. The relative acceleration of R with respect to the rod PQ is zero at the instant shown. Which one of the following is the CORRECT magnitude of the absolute acceleration (in m/s2) of block R?

Accepted Answer

187.5

Answer

135.2

Answer

112.5

Answer

150.0

Question 56

The frame shown in the figure is loaded at S with a force of 2000 N. The reactions at T are denoted by Tx and Ty, while the reaction at W is Wy. Neglect the weight of the members. Which one of the following options for the magnitudes of the forces (in N), Tx, Ty and Wy, is CORRECT?

Accepted Answer

Tx = 0, Ty = 500 and Wy = 1500

Answer

Tx = 0, Ty = 1000 and Wy = 1000

Answer

Tx= 0, Ty =1500 and Wy = 500

Answer

Tx = 0, Ty = 800 and Wy = 1200

Question 57

A closed thin cylindrical tank with a mean diameter d = 300 mm and thickness t = 2 mm, is subjected to a uniform internal gas pressure p. The allowable shear stress on the curved wall of the tank is 70 MPa. Based on the Tresca criteria, which one of the following options for the maximum safe value of p (in MPa) is CORRECT?

Accepted Answer

1.87

Answer

3.73

Answer

7.46

Answer

5.60

Question 58

An infinitesimal square element PQRS is shown in the figure. The x and y axes are also marked in the figure. The strains on the element are given by 𝜀𝑥𝑥= 500 × 10−6, 𝜀𝑦𝑦= 100 × 10−6 and 𝜀𝑥𝑦= 0. Which of the following statements is/are CORRECT?

Accepted Answer

Percentage change in length of the diagonal PR is 0.03.

Accepted Answer

Change in angle between PR and QS is 4 × 10−4 rad.

Accepted Answer

Percentage change in length of the diagonal QS is 0.03.

Answer

Change in angle between PR and QS is 2 × 10−4 rad.

Question 59

The figure shows the stress distribution across an internal surface of a rectangular beam of height 30 mm and depth 10 mm. The normal stress distribution is given by the expression 𝜎𝑥𝑥= 200𝑦+ 500 N/mm2; y is the distance in mm from the centroidal axis of the beam. Assume that there is no variation in the stress distribution along the z-direction. Which of the following statements is/are CORRECT?

Accepted Answer

The net force in the x direction is 150 kN.

Accepted Answer

The net moment about the z axis is 4500 Nm.

Answer

The net force in the x direction is 75 kN.

Answer

The net moment about the z axis is 2250 Nm.

Question 60

A vertical column fixed at one end is subjected to a compressive axial load at the free end. The column’s section modulus, EI, is 9.82 × 105 Nm2 and the cross-section area is 7.85 × 10−3 m2. The length of the column is 2 m. The yield stress of the material is 145 MPa. If the column can fail either in buckling or by Tresca’s criterion, the maximum load that the structure can safely sustain is _____ kN (rounded off to one decimal place).

Accepted Answer

603.5 to 607.5

Question 61

A simply-supported beam, with a point load P = 150 kN at a distance of L/3 from the left end, is shown in the figure. The elastic-strain energy (U) of the beam is given by the following expression: U = 2 243 P2L3 EI where the section modulus, EI, is 16.66 × 105 Nm2 and the length of the beam L is 1 m. The deflection at the loading point is ____ mm (rounded off to two decimal places).

Accepted Answer

1.46 to 1.50

Question 62

A simply-supported beam has a circular cross-section with a diameter of 20 mm, area of 314.2 mm2, area moment of inertia of 7854 mm4 and a length L of 4 m. A point load P =100 N acts at the center and an axial load Q = 20 kN acts through the centroidal axis as shown in the figure. The magnitude of the offset between the neutral axis and the centroidal axis, at L/2 from the left, is __________ mm (rounded off to one decimal place).

Accepted Answer

4.9 to 5.1

Question 63

A massless cantilever beam, with a tip mass m of 10 kg, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length L = 1 m, with a circular cross-section of diameter d = 20 mm. The Young’s modulus of the beam material is 200 GPa. The natural frequency of the spring-mass system is _____ Hz (rounded off to two decimal places).

Accepted Answer

3.43 to 3.47

Question 64

An electric motor’s rotor is spinning at 1500 rpm when its load and power are cut- off. The rotor which has a mass of 50 kg and a radius of gyration of 200 mm, then coasts down to rest. Due to kinetic friction, a constant torque of 10 Nm acts on the rotor as it coasts down. The number of revolutions executed by the rotor before it comes to rest is _____ (in integer).

Accepted Answer

392 to 394

GATE XE (Engineering Sciences) 2025 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

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Question 15

Question 16

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Question 18

Question 19

Question 20

Question 21

Fluid Mechanics

Question 22

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Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

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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

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Question 69

Question 70

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Question 73

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Question 76

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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