All 65 questions of GATE 2025 CE (Set 2)

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.

The President, along with the Council of Ministers, ___________ to visit India next week.

Select the most appropriate option to complete the above sentence.

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?

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?

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?

“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?

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 $P^*$?

Consider a five-digit number $PQRST$ that has distinct digits $P,Q,R,S,$ and $T$, and satisfies the following conditions:

If integers 1 through 5 are used to construct such a number, the value of $P$ is:

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 variety P is ₹ 800 for 5 kg.
The cost of variety Q is ₹ 800 for 4 kg.

If the person gets 8% profit, what is the P:Q ratio (by weight)?

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.

For the matrix $[A]$ given below, the transpose is ______.

$[A] = \begin{bmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{bmatrix}$

Integration of $\ln(x)$ with $x$ i.e., $\int \ln(x)\,dx =$ ______.

Consider the following statements:

(P): Fly ash and ground granulated blast furnace slag can be used as mineral admixtures in concrete.

(Q): As per IS 456:2000, the minimum moist curing period becomes higher when a mineral admixture is added to concrete.

Identify the CORRECT option.

Consider the pin-jointed truss shown in the figure. Influence line is drawn for the axial force in the member G-I, when a unit load travels on the bottom chord of the truss. Identify the CORRECT influence line from the following options:

Note: Positive value corresponds to tension and negative value corresponds to compression in the member.

The most suitable test for measuring the permeability of clayey soils in the laboratory is ______.

A hydraulic jump occurs in an open channel when the slope of the channel changes from ______.

The bacteria mainly responsible for crown corrosion in a sewer is ______.

The recommended minimum traffic growth rate and design period considered for structural design of flexible pavements for national highways in India as per IRC 37:2018 is ______ percentage and ______ years, respectively.

After applying the correction for elevation and temperature, the runway length is 700 m. The corrected runway length (in m) for an effective gradient of 1% is ______ (round off to the nearest integer).

The point where the road alignment changes from a tangent to a curve is known as ______.

Consider a velocity vector, $\vec{V}$ in (x, y, z) coordinates given below. Pick one or more CORRECT statements(s) from the choices given below.

$\vec{V} = u\hat{x} + v\hat{y}$

Given that $A$ and $B$ are not null sets, which of the following statements regarding probability is/are CORRECT?

In the context of construction materials, which of the following statements is/are CORRECT?

Which of the following statements is/are INCORRECT?

Pick one or more CORRECT statement(s) in the context of upstream and downstream cut-offs provided below the concrete apron of weirs/barrages constructed across alluvial rivers.

In the context of the effect of drainage density on run-off generation and the hydrograph at the catchment outlet, all other factors remaining the same, pick one or more CORRECT statement(s).

Identify the treatment technology/technologies NOT recommended for highly biodegradable organic solid wastes.

Which of the following statements is/are INCORRECT?

The “order” of the following ordinary differential equation is ______:

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, following information are 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 in the downstream side is 1 m.

If the soil below the dam is having a saturated unit weight of 21 kN/m³ and unit weight of water is 9.81 kN/m³, 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 surfaces due to sand strata. The time to complete 50% consolidation is 2 years. The coefficient of volume change $m_v$ is $1.51\times10^{-3}$ m²/kN and unit weight of water is 9.81 kN/m³.

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).

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 µmoles/l) in water is ________________ (round off to one decimal place).

$\text{HOCl} \rightleftharpoons \text{H}^+ + \text{OCl}^-, \qquad pK = 7.50$

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).

Pick the CORRECT solution for the differential equation

A circular tube of thickness 10 mm and diameter 250 mm is welded to a flat plate using a 5 mm fillet weld along the circumference. Assume Fe410 steel and shop welding.

As per IS 800:2007, the torque that can be resisted by the weld (in kN·m) is ______ (round off to one decimal place).

The figure shows a propped cantilever with uniform flexural rigidity $EI$ (in N.m²) and subjected to a moment $M$ (in N.m). Consider forces and displacements in the upward direction as positive. Find the upward reaction at the propped support B (in N) when this support settles by $(-\Delta)$, given in metres.

Let the state of stress at a point in a body be the difference of two plane states of stress shown in the figure. Consider all the possible planes perpendicular to the x-y plane and passing through that point. The magnitude of the maximum compressive stress on any such plane is $k\sigma_0$, where k is equal to _____ (round off to one decimal place).

Consider a reinforced concrete beam section of width 350 mm and overall depth 600 mm. The tension steel area is 800 mm² at an effective cover of 40 mm. Concrete is M20 and steel is Fe415.

The IS 456:2000 concrete stress block is replaced by an equivalent rectangular stress block with no change in: (a) area of the stress block, (b) design strength of concrete at strain 0.0035, and (c) neutral-axis location at flexural collapse.

The ultimate moment of resistance (in kN·m), rounded to the nearest integer, is:

For a partially saturated soil deposit at a construction site, water content (w) is 15%, degree of saturation (S) is 67%, void ratio (e) is 0.6 and specific gravity of solids in the soil (G$_s$) is 2.67. Consider unit weight of water as 9.81 kN/m³. To fully saturate 5 m³ of this soil, the required weight of water (in kN) will be ______ (round off to the nearest integer).

Consider flow in a long and very wide rectangular open channel. Width of the channel can be considered as infinity compared to the depth of flow. Uniform flow depth is 1.0 m. The bed slope of the channel is 0.0001. The Manning roughness coefficient value is 0.02. Acceleration due to gravity, g can be taken as 9.81 m/s². The critical depth (in m) corresponding to the flow rate resulting from the above conditions is ______ (round off to one decimal place).

Match Column I with Column II.

Consider the function given below and pick one or more CORRECT statement(s) from the following choices.

$f(x) = x^3 - \frac{15}{2}x^2 + 18x + 20$

Pick the CORRECT eigen value(s) of the matrix $[A]$ from the following choices.

$[A] = \begin{bmatrix} 6 & 8 \\ 4 & 2 \end{bmatrix}$

In the pin-jointed truss shown in the figure, the members that carry zero force are identified. Which of the following options is/are zero-force members?

In the context of shear strength of soil, which of the following statements is/are CORRECT?

The drag force, $F_D$ on a sphere due to a fluid flowing past the sphere is a function of viscosity, µ, the mass density, ρ, the velocity of flow, V, and the diameter of the sphere, D. Pick the relevant (one or more) non-dimensional parameter(s) pertaining to the above process from the following list.

A compound has a general formula C$_a$H$_b$O$_c$N$_d$ and molecular weight 187. A 935 mg/l solution of the compound is prepared in distilled deionized water. The Total Organic Carbon (TOC) is measured as 360 mg/l (as C). The Chemical Oxygen Demand (COD) and the Total Kjeldahl Nitrogen (TKN) are determined as 600 mg/l (as O$_2$) and 140 mg/l (as N), respectively (as per the chemical equation given below). Which of the following options is/are CORRECT?

$\text{C}_a\text{H}_b\text{O}_c\text{N}_d + \frac{4a + b - 2c - 3d}{4}\,\text{O}_2 \rightarrow a\,\text{CO}_2 + \frac{b - 3d}{2}\,\text{H}_2\text{O} + d\,\text{NH}_3$

Atomic weight: C(12), H(1), O(16), N(14)

The free flow speed of a highway is 100 km/h and its capacity is 4000 vehicle/h. Assume speed density relation is linear. For a traffic volume of 2000 vehicle/h, choose all the possible speeds (in km/h) from the options given below (round off to two decimal places).

Consider a discrete random variable X whose probabilities are given below. The standard deviation of the random variable is ______ (round off to one decimal place).

A steel beam supported by three parallel pin-jointed steel rods is shown in the figure. The beam has moment of inertia $8\times10^7$ mm⁴ and steel modulus $E=210$ GPa. It carries a uniformly distributed load of 6.25 kN/m including self-weight.

The axial force (in kN) in the centre rod CD is ______ (round off to one decimal place).

The network diagram for a construction project is shown below. Activities A, B, C, D, E and F are represented by arrows and their durations are shown in days.

The total float available for activity E, in days, is ______ (round off to the nearest integer).

A reinforced concrete beam has a support section with width of 300 mm and effective depth of 500 mm. The support section is reinforced with 3 bars of 20 mm diameter at the tension side. Two-legged vertical stirrups of 10 mm diameter and Fe415 steel at a spacing of 100 mm are provided as shear reinforcement. Assume that there is no possibility of diagonal compression failure at the section. As per IS 456:2000, the maximum shear resisted by the vertical stirrups (in kN), as per limit state design, is ___________ (round off to one decimal place).

The canal-bank profile and trial slip circle are shown in the figure. The soil is homogeneous saturated clay with bulk unit weight 20 kN/m³, undrained cohesion 30 kPa, and $\phi_u=0$. The area of sliding mass ABCDEA is 150 m² and its centroid is at P. A 2.5 m deep tension crack DE is completely filled with water. Take $\gamma_w=9.81$ kN/m³ and 1 m run of bank.

The factor of safety against slope failure is ______ (round off to two decimal places).

A designer used plate load test to obtain the value of the bearing capacity factor $N_\gamma$. A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is 16.66 kN/m³. The plate is loaded to failure at a pressure of 1500 kPa. Considering Terzaghi’s bearing capacity theory, the bearing capacity factor $N_\gamma$ is ______ (round off to the nearest integer).

A 4 × 4 group pile, with each pile 20 m long and 500 mm in diameter, is installed in a square pattern in a clayey soil, as shown in the figure. The average unconfined compressive strength of the soil is 100 kN/m², and the adhesion factor is 0.8. Neglect the bearing at the tip of the piles. For a group efficiency factor of 1.0, the centre to centre spacing (s) of the piles (in m) would be ________ (round off to two decimal places).

A 60 cm diameter well completely penetrates a confined aquifer of permeability $5 \times 10^{-4}$ m/s. The length of the strainer (spanning the entire thickness of the aquifer) is 10 m. The drawdown at the well under steady state pumping is 1.0 m. Assume that the radius of influence for this pumping is 300 m. The discharge from the well (in litres per minute) is ______ (round off to the nearest integer).

The peak of flood hydrograph due to a 3-hour duration storm in a catchment is 180 m³/s. The total rainfall depth is 6.6 cm. It can be assumed that the average infiltration loss is 0.2 cm/h. There are no other losses. The base flow is constant at a value of 30 m³/s. The peak value of the 3-hour unit hydrograph for this catchment (in m³/s) is ______ (round off to the nearest integer).

The shaft of a 6 m wide gate in the figure will fail at a moment of 3924 kN.m about the hinge P. The maximum value of water depth h (in m) that the gate can hold is ________________ (round off to the nearest integer).

Note: Density of water = 1000 kg/m³; Acceleration due to gravity = 9.81 m/s²

A water sample has the following concentrations, all expressed as mg/L as CaCO$_3$:

Other anions were not analysed.

The non-carbonate hardness (in mg/L as CaCO$_3$) is ______ (integer).

A community generates 1 million litres/day (MLD) of wastewater. This wastewater is treated using activated sludge process (ASP). The working volume of the aeration tank of the ASP is 250 m³, and the biomass concentration in the tank is 3000 mg/L. Analyses results showed that a biomass concentration of 10 mg/L is present in the treated effluent from the secondary sedimentation tank of the ASP. Sludge wastage from the system is at a rate of 5000 L/day with a biomass concentration of 10000 mg/L. The system is in steady state condition. The biological sludge residence time (BSRT) of the system (in days) is______ (round off to one decimal place).

A settling chamber is used for the removal of discrete particulate matter from air with following conditions. Horizontal velocity of air = 0.2 m/s; Temperature of air stream = 77°C; Specific gravity of particle to be removed = 2.65; Chamber length = 12 m; Chamber height = 2 m; Viscosity of air at 77°C = 2.1 × 10⁻⁵ kg/m.s; Acceleration due to gravity (g) = 9.81 m/s²; Density of air at 77°C = 1.0 kg/m³; Assume the density of water as 1000 kg/m³ and Laminar condition exists in the chamber. The minimum size of particle that will be removed with 100% efficiency in the settling chamber (in µm) is ______ (round off to one decimal place).

On a two-lane highway, a horizontal curve has radius 300 m and design speed 80 km/h. The longest wheelbase expected is 7 m.

The extra widening required (in m) is ______ (round off to two decimal places).

If the fore bearings of lines AB and BC are $60^\circ$ and $122^\circ$, respectively, the interior angle $\angle ABC$ (in degrees) is ______ (round off to the nearest integer).