List of top Questions asked in GATE CE- 2025

Let y be the solution of the initial value problem \( y'' + 0.8y' + 0.16y = 0 \) where \( y(0) = 3 \) and \( y'(0) = 4.5 \). Then, \( y(1) \) is equal to ......... (rounded off to 1 decimal place).
The maximum value of the function \( h(x) = -x^3 + 2x^2 \) in the interval \([-1, 1.5]\) is equal to ......... (rounded off to 1 decimal place).
Consider the differential equation given below. Using the Euler method with the step size \( h \) of 0.5, the value of \( y \) at \( x = 1.0 \) is equal to ........ rounded off to 1 decimal place).

For the beam and loading shown in the figure, the second derivative of the deflection curve of the beam at the mid-point of AC is given by \( \frac{\alpha M_0}{8EI} \). The value of \( \alpha \) is ........ (rounded off to the nearest integer). 

Consider the rigid bar ABC supported by the pin-jointed links BD and CE and subjected to a load \(P\) at the end \(A\), as shown in the figure. The axial rigidities of BD and CE are 22500 kN and 15000 kN, respectively. If CE elongates by 5 mm due to the load \(P\), the magnitude of the downward deflection (in mm) of the end \(A\) would be ........ (rounded off to the nearest integer). 

Consider a reinforced concrete beam section of 300 mm width and 700 mm depth. The beam is reinforced with the tension steel of 2000 mm² area at an effective cover of 50 mm. Concrete in the tension zone is assumed to be cracked. Assume the modular ratio of 12 and Young's modulus of 200 GPa for steel. When the extreme fibre in the compression zone undergoes the strain of 0.0004 due to the applied bending moment, the stress in the steel (in MPa) is ..... (rounded off to the nearest integer).

Consider the beam section shown in the figure, with \( y \) indicating the depth of neutral axis (NA). The section is only subjected to an increasing bending moment. It is given that \( y = 18.75 \, {mm} \), when the section has not yielded at the top and bottom fibres. Further, \( y \) decreases to 5 mm, when the entire section has yielded. The shape factor of the section is ........ (rounded off to 2 decimal places). 

Consider the built-up column made of two I-sections as shown in the figure, with each batten plate bolted to a component I-section of the column through 6 black bolts. Each connection of the batten plate with the component section is to be designed for a longitudinal shear of 70 kN and moment of 10 kN.m. The minimum bolt value required (in kN) is ....... (rounded off to the nearest integer).
A cut slope is made in a silty clay soil for a new road project, as shown in the figure. The locations of the ground water table (GWT) and potential failure surface are shown in the figure. After the cut is made, the excess pore water pressure is fully dissipated, and the shear stress at the point A is 60 kN/m². The factor of safety at the point A for long-term stability is .......... (rounded off to 2 decimal places).

A 6 m \(\times\) 6 m square footing constructed in clay is subjected to a vertical load of 2500 kN at its centre. The base of the footing is 2 m below the ground surface, as shown in the figure. The footing is made of 2 m thick concrete. The ground water table is at a great depth. Considering Terzaghi's bearing capacity theory, the factor of safety of footing against the bearing capacity failure is ....... (rounded off to 2 decimal places). 

A clayey soil has a moisture content of 18%, a specific gravity of soil solids of 2.74, and a degree of saturation of 65%. The soil soaks up water during a rain event, and the degree of saturation increases to 85.2%. The change of the volume during the soakage is negligible. The new moisture content (in %) of the soil will be ......... (rounded off to 2 decimal places).
A single pile with 450 mm diameter has been driven into a homogeneous clay layer, which has an undrained cohesion (\(c_u\)) of 20 kPa and unit weight of 18 kN/m³. The ground water table is found to be at the surface of the clay layer. The adhesion factor (\(\alpha\)) of the soil is 0.95 and bearing capacity factor (\(N_c\)) is 9. The pile is supporting a column load of 144 kN with a factor of safety of 3.0 against ultimate axial pile capacity in compression. The required embedment depth of the pile (in m) is ......... (rounded off to the nearest integer).
A hydraulic jump is formed in a 5 m wide rectangular channel, which has a horizontal bed and is carrying a discharge of 15 m³/s. The depth of water upstream of the jump is 0.5 m. The power dissipated by the jump (in kW) is ........ (rounded off to the nearest integer).
A symmetrical trapezoidal canal is 100 km long. The bottom width is 10 m and the side slope is 1 Horizontal : 1 Vertical. The average flow depth in the canal is 2.5 m throughout the month of April. The measurement from a Class-A evaporimeter in the vicinity of the canal indicated an average evaporation rate of 0.5 cm/day in April. The volume of water evaporated from the canal (in m³) in the month of April is close to ........ \(\times 10^3\) (rounded off to 1 decimal place).
A 5.0 m wide rectangular channel carries a discharge of 10 m³/s at a depth of 1.5 m under uniform flow. To produce critical flow conditions without affecting the upstream conditions, the channel bottom elevation should be raised (in m) by ........ (rounded off to 2 decimal places).

A one-way, single lane road has traffic that consists of 30% trucks and 70% cars. The speed of trucks (in km/h) is a uniform random variable on the interval (30, 60), and the speed of cars (in km/h) is a uniform random variable on the interval (40, 80). The speed limit on the road is 50 km/h. The percentage of vehicles that exceed the speed limit is ........ (rounded off to 1 decimal place). 

In levelling between two points A and B on the opposite banks of a river, the readings are taken by setting the instrument both at A and B, as shown in the table. If the RL of A is 150.000 m, the RL of B (in m) is ....... (rounded off to 3 decimal places). 

During determination of the bulk specific gravity of compacted bituminous specimen, the mass in air of the specimen is 1260 g and volume is 525 cm³. The density of water is 1.0 g/cm³. The theoretical maximum specific gravity of mix is 2.510. The percentage air voids in the compacted specimen is ......... (rounded off to 2 decimal places).
The “order” of the following ordinary differential equation is __________.
\[ \frac{d^3 y}{dx^3} + \left( \frac{d^2 y}{dx^2} \right)^6 + \left( \frac{dy}{dx} \right)^4 + y = 0 \]
The design shear strength of a reinforced concrete rectangular beam with a width of 250 mm and an effective depth of 500 mm, is 0.3 MPa. The torsional moment capacity of the section (in kN.m) under pure torsion, as per IS 456:2000, is __________ (round off to one decimal place).
From a flow-net diagram drawn under a concrete dam, the following information is obtained:
(i) The head difference between upstream and downstream side of the dam is 9 m.
(ii) The total number of equipotential drops between upstream and downstream side of the dam is 10.
(iii) The length of the field nearest to the toe of the dam on the downstream side is 1 m.
If the soil below the dam is having a saturated unit weight of 21 kN/m\(^3\) and the unit weight of water is 9.81 kN/m\(^3\), then the factor of safety against the quick condition will be __________ (round off to two decimal places).
A 6 m thick clay stratum has drainage at both its top and bottom surface due to the presence of sand strata. The time to complete 50% consolidation is 2 years.
The coefficient of volume change (\(m_v\)) is \(1.51 \times 10^{-3}\ {m}^2/{kN}\) and the unit weight of water is \(9.81\ {kN/m}^3\).
The coefficient of permeability (in m/year) is __________ (round off to three decimal places).
Consider steady flow of water in the series pipe system shown below, with specified discharge. The diameters of Pipes A and B are 2 m and 1 m, respectively. The lengths of pipes A and B are 100 m and 200 m, respectively. Assume the Darcy-Weisbach friction coefficient, \( f \), as 0.01 for both the pipes.
The ratio of head loss in Pipe-B to the head loss in Pipe-A is __________ (round off to the nearest integer).
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Free residual chlorine concentration in water was measured to be 2 mg/l (as Cl\(_2\)). The pH of water is 8.5. By using the chemical equation given below, the HOCl concentration (in \(\mu\)moles/l) in water is __________ (round off to one decimal place).
\[ {HOCl} \rightleftharpoons {H}^+ + {OCl}^-, \quad pK = 7.50 \] Atomic weight: Cl = 35.5
A surveyor measured the distance between two points on the plan drawn to a scale of 1 cm = 40 m and the result was 468 m. Later, it was discovered that the scale used was 1 cm = 20 m.
The true distance between the points (in m) is __________ (round off to the nearest integer).