GATE 2026 Civil Engineering

'The shopkeeper sells lemons.' In this sentence, the word 'lemons' is the _________.

The figure below is supposed to show three non-overlapping shapes - one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated...

At how many points will the curves y = x² and y = -x² – 2x - 1 intersect in the real (x, y) plane?

'If Anish had scored hundred runs in today's match, he would have been made the captain of his team. He would have then become the youngest captain in his team's history. Unfortuna...

Which one of the following figures P, Q, R, or S, correctly shows the 45° clockwise-rotated version of figure (I)?

Match the words in Column I with their synonyms in Column II. Column I (i) Lonely (ii) Literal (iii) Lousy (iv) Lethal Column II (p) Verbatim (q) Solitary (r) Deadly (s) Terrible

In the given figure, $\overline{PQ}$ is the diameter of a circle with center $O$. Two points $R$ and $S$ are chosen on the circle such that $\angle ROS = 80^{\circ}$. When $\overli...

Based on the relationship between each polygon and the number inside it, the value of 'X' is

Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states...

P and Q are two positive integers such that P² = Q² + 13. The product of the numbers P and Q is _________

Matrix P is given as $P = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}$ The TRUE option is

Given: $\begin{bmatrix} 1 & 1 \\ 1 & 0 \\ 0 & 2 \end{bmatrix} \begin{Bmatrix} x_1 \\ x_2 \\ x_3 \end{Bmatrix} = \begin{Bmatrix} 0 \\ 0 \end{Bmatrix}$ The above system of equations...

A thin-walled spherical gas balloon of radius R and wall thickness t (t << R) is subjected to an internal (gauge) pressure p. The maximum tensile and shear stresses in the balloon...

Black dot shown in the figure qualitatively represents the shear centre of the angle section. The option which represents the position of the shear centre is:

Which one of the following is utilized to determine the long-term deformation of concrete under sustained loading?

Two reservoirs having different water levels are connected by two long parallel pipelines of same length and same material but having diameters of 600 mm and 400 mm. Using Darcy-We...

An irrigation canal is to be designed to deliver 10 cumec to meet the peak demand of 7500 hectare of cropped area. The estimated canal losses are 50 % of the head discharge. The du...

The name of a person in Column 1 is to be matched with the test mentioned in Column 2. Column 1 (I) Menard (II) Marchetti (III) Casagrande (IV) Proctor Column 2 (P) Dilatometer tes...

Corrections are applied to the basic length of the runway strip considering: (i) The elevation H (in m) of the airport above Mean Sea Level (MSL) (ii) Corrected air temperature T (...

The Whole Circle Bearing (WCB) of line AB is 150°. The length of AB is 100 m. The latitude and departure values, respectively, for this line are:

A rapid sand filter bed of depth 0.8 m has 40% porosity during service cycle. It is recommended that during backwash operation, the expanded filter bed should have 70% porosity. Th...

The settling velocity of inorganic particles in the sedimentation tank of a water treatment plant is governed by

Gradually Varied Flow (GVF) profiles in open channels given in Column 1 are to be matched with the water surface slopes in Column 2 in the table below. Column 1 GVF Profile (P) M1...

Cant C on a Broad Gauge railway track is calculated for an equilibrium speed V (in km/h), dynamic gauge G (in mm) and radius of curve R (in m) using formula/formulae:

Which of the following components is/are NOT removed in the secondary treatment of sewage?

Bag I contains 4 white and 6 black balls. Bag II contains 4 white and 3 black balls. One ball is drawn at random from any one of the two bags and it is found to be a black ball. Th...

A matrix is given as: $$\begin{bmatrix} 9 & 15 \\ 15 & 50 \end{bmatrix}$$ By performing Cholesky decomposition, $|L_{22}|$ of the lower triangular matrix is ________ (in integer).

It is given that x and y are integers in the following equation: $(x + y - 7)^2 + (y + 3x - 13)^2 = 0$ The value of $(x^3 + y^3)$ is ________ (in integer).

The required centre-to-centre spacing of 10 mm diameter bars is 150 mm to resist the design moment in a concrete slab. Instead of 10 mm diameter bars, if 12 mm diameter bars of the...

Two steel plates are to be connected together by a 5 mm fillet weld of length 150 mm to transfer a design load. If the size of the fillet weld used to connect the same two plates i...

For a liquid, the permeability of a sandy soil having a void ratio of 0.60 was determined as 0.14 cm/s. Considering the same liquid and by using Taylor's equation, the permeability...

To obtain undisturbed clay soil sample, an Area Ratio of 10 % needs to be achieved for a thin walled sampling tube. If the outer diameter of the tube is 50.8 mm, the inner diameter...

The travel times of three vehicles on a 2 km stretch of road are 4, 5, and 8 minutes. Assuming the speed of each vehicle to be constant in this stretch, the Space Mean Speed (in km...

A 30 m long tape is standardized at 25 °C. It was used to measure the length of a line which came out to be 200 m. The temperature during the measurement was 35°C. The coefficient...

The height of the plane of collimation of a levelling instrument is 100.000 m from a datum. The levelling instrument measures a Back Sight of 1.500 m on a vertically held staff at...

Let $f(x)$ be a continuous function defined in $[0,2] \rightarrow \mathbb{R}$ and satisfying the equation $\int_{0}^{2} f(x)[x - f(x)]dx = \frac{2}{3}$. The value of $f(1)$ is

An ordinary differential equation is given below. $x^2 \frac{d^2y}{dx^2} = 6y$ Considering $a$ and $b$ as arbitrary constants, the general solution of the equation is

A plane truss consists of two linearly elastic, homogeneous, identical members, namely PQ and QR. Both members have length (L), cross-sectional area (A), and modulus of elasticity...

The plane frame has a hinge and a roller support, and is loaded as shown in the figure. Both the columns have same height. (Figure not to scale) What is the absolute value of the m...

For a hydraulic jump formed in a rectangular horizontal channel, the sequent depth ratio is 2. The Froude number of supercritical stream is

In a laminar flow of a Newtonian fluid through a circular pipe of radius 5 cm, the maximum velocity is found to be 2 m/s. The velocity (in m/s) at a radial distance of 2.50 cm from...

A road is divided into four sections having varying widths as shown in the figure. Section-2 (S2) represents a a capacity constrained condition with respect to the traffic flow pas...

Locations P and Q are separated by a wide valley. The difference in levels of locations P and Q measured by a levelling instrument stationed near P is 3.0 m. The same instrument st...

The average sewage from a city is 90 million litres per day and the average 5-day Biochemical Oxygen Demand (BOD5) is 300 mg/l. Average standard BOD5 of the domestic sewage is 0.08...

Select ALL CORRECT option(s) which can be considered to check whether the flexural stresses in a prestressed concrete beam are within the allowable stresses at the transfer and the...

As per the Rankine's earth pressure theory, which of the following statements is/are FALSE?

Which of the following statements is/are TRUE in the context of the geometric design of highways?

Starting with the first approximation as x = 0.5, the second approximation for the root of the following function by the Newton-Raphson method is ________ (rounded off to two decim...

Values of y for different values of x are tabulated below. If a second-degree interpolating polynomial P_2(x) is used to represent y, the value of P_2(0) is ________ (rounded off t...

Two identical blocks A and B are connected by a rigid rod. The blocks rest against vertical and horizontal planes, as shown in the figure. The coefficient of static friction at the...

A homogenous, linearly elastic rod AB is connected to a linearly elastic spring BC in between the fixed supports at A and C, as shown in the figure. The cross-sectional area, modul...

The cross-section of a steel T-beam is shown in the figure where all dimensions are in mm. The plastic section modulus of the given cross-section is ________ × 10⁴ mm³ (in integer)...

A fully-penetrating well of 20 cm diameter is provided in an unconfined aquifer. The height of the ground water table is 30 m from the bottom of the aquifer. After a long period of...

A wide unlined channel carries sediment-free water. The depth of water is 1 m. The specific weight of water is 10 kN/m³. To prevent scouring, the maximum permissible tractive stres...

A bridge with an expected life of 50 years is designed for a flood of 10000 m³/s corresponding to the return period of 100 years. The risk associated with this design is ________ (...

An infinite slope with slope angle β = 22° consists of soil with the following properties: Unit weight γ = 15.72 kN/m³ Cohesion c' = 12 kPa Angle of internal friction φ' = 15° The...

A circular pile of 600 mm diameter and 6 m length is embedded in a saturated clayey soil. Undrained cohesion of the soil is 80 kPa. Unit weight of the soil is 19.20 kN/m³. The adhe...

A group of 25 circular piles is arranged in 5 × 5 uniform pattern in a soft clay soil with equal spacing in both the directions. These are friction piles with negligible end bearin...

A shallow strip footing of width 2 m is embedded at a depth of 1.5 m below the ground surface in a homogeneous pure clay with an angle of internal friction zero. Consider unit weig...

Traffic is moving on a 6-lane dual carriageway road. Traffic volume per direction during peak hour (08:00 am to 09:00 am) is 6000 veh/h. It is assumed that the traffic is distribut...

In a bituminous mix, the percentage by weight of coarse aggregate, fine aggregate, filler, and bituminous binder is 58, 25, 12, and 5, respectively. The corresponding specific grav...

The following consecutive readings (in m) were taken with a dumpy level and a levelling staff at a common interval of 20 m: 0.385; 1.030; 1.925; 2.825; 3.730; 4.850; 1.045; 2.005;...

An Activated Sludge Process (ASP) has an inlet wastewater flowrate of 20000 m³/day with a Biochemical Oxygen Demand (BOD) concentration of 250 mg/l. It produces treated wastewater...

The intensity-duration relationship for a a rainfall on a rectangular plot ABCD of area 7 ha (1 ha = 10^4 m²) can be modelled by the following equation: I = 25 / (t + 10) where I i...

The maximum demand at a water purification plant has been estimated as 12 million litres per day. For the raw supplies, a rectangular sedimentation tank is to be designed with mech...

'The team ________ more than 300 runs in 20 overs ________ rains. However, some players needed to improve their batting skills.' Choose the option with the correct sequence of word...

If a positive real x satisfies the following equation log₂ x + log√₂ x = 48, then the value of x is

The next figure (indicated by '?') in the sequence is

'All the mangoes in the basket are good.' If the above statement is false, then which one of the following statements is necessarily true?

Consider the following statements about four numbers: (S1) The average of the four numbers is 25 (S2) Each number is at most 40 (S3) Each number is at least 20 Choose the option th...

'People are crowding around ____ pit into which ____ elephant has fallen. I have never seen an elephant looking more bewildered ____ miserable. Here it is in a most undignified pos...

The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The following observat...

Consider a string P of length l that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Fig...

The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels. They are seated in rows and columns as shown in the figure with exactly one...

Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?

Matrix A has the eigenvalues 1, 2, and 3. The Trace of A² is

A fifth-degree polynomial in $x$ is defined for $x > 0$. All coefficients of the polynomial are positive. The first derivative of the polynomial is obtained numerically at a point...

Periodic function $f(x)$ is given below. $f(x) = \begin{cases} -1, & \text{when} & -\pi < x < 0 \\ 1, & \text{when} & 0 < x < \pi \end{cases} ; f(x + 2\pi) = f(x)$ The CORRECT opti...

A rectangular singly reinforced concrete beam has a width of 300 mm and an effective depth of 550 mm. The grades of steel and concrete are Fe500 and M25, respectively. The area of...

As per IS:800-2007, design of a cantilever steel beam section for its moment capacity requires fulfilment of an upper bound, expressed as: $M_d \leq 1.5Z_e \frac{f_y}{\gamma_{m0}}$...

A plane strain problem (in X-Y plane) must satisfy the condition:

Which one of the following stress conditions represents the state of pure shear stress?

The horizontal beam shown in the figure has fixed supports at F and L. Internal hinges are provided at locations G and J. The beam supports vertically downward concentrated loads a...

The Culturable Command Area (CCA) for a canal is 10000 hectares. The base period for a crop in the CCA is 140 days. Watering depth for the crop is 40 cm. The outlet discharge (in m...

Following statements are made with respect to the mass curve of rainfall: (I) Slope at a point on the curve can be positive. (II) Slope at a point on the curve can be zero. Which o...

Based on the Casagrande's plasticity chart, plasticity index (in %) of inorganic clays having a liquid limit of 40 %, ranges between

Information related to foundation design is provided in table below. Column 1 (I) Converse-Labarre formula (II) Hiley formula (III) Newmark's influence chart (IV) Skempton's equati...

An incident occurred on one side of a median on a four-lane dual carriageway road section. This incident disrupted the traffic movement in one direction. Traffic police diverted th...

Which one of the following statements is TRUE?

The primary purpose of the Windrose diagram is for the design of

Which one of the following statements is TRUE with respect to levelling survey?

Column I presents common air pollutants, and column II presents treatment technologies commonly employed to control air pollutants. Air pollutant 1 Dust (size 5-25 µm) 2 Carbon mon...

One-third of the solid matter in a sludge containing 90% water is composed of fixed mineral solids with specific gravity 2.5, and two-third is composed of volatile solids with spec...

The grown algae are useful in the operation of

A partial differential equation is given below. $\frac{\partial^2 u}{\partial x^2} - \frac{\partial^2 u}{\partial y^2} = 0$ Possible solution(s) is/are:

The eigenvalues of $[A] = \begin{bmatrix} 2 & -3.5 & 6 \\ 3.5 & 5 & 2 \\ 8 & 1 & 8.5 \end{bmatrix}$ are $\lambda_1 = -1.547$, $\lambda_2 = 12.330$, and $\lambda_3 = 4.711$. The abs...

The probability (in %) that a storm having return period of 15 years may occur in the next 10 years is ________ (rounded off to two decimal places).

A fully saturated sandy soil deposit has water content 20 % and specific gravity 2.65. The critical hydraulic gradient for seepage through the soil to create the quicksand conditio...

A downgrade of 1 in 100 meets an upgrade of 1 in 125 on a road. If the rate of change of grade is 0.10% per 30 m, the length (in m) of the vertical curve between the two grades is...

A tourist visiting a city holds a map prepared at a scale of 1:25000. The tourist measures the distance between place A and place B in the city as 12.0 cm on the map. Assuming both...

Let $f(x) = \begin{vmatrix} x^3 & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^2 & p^3 \end{vmatrix}$ where $p$ is a constant. The value of $\frac{d^3}{dx^3} f(x)$ at $x = 0$ is

Vector field $\vec{V}$ is defined as $\vec{V} = 3x^2yz \hat{i} - 5xy \hat{j} + 6yz^2 \hat{k}$ The curl of $\vec{V}$ at point (2,-1,1) is

A simply supported, linearly elastic, homogeneous, prismatic beam of length L and flexural rigidity EI is shown in the figure. The expression for the Influence Line Diagram (ILD) o...

The plane truss shown in the figure is hinge-supported at E and F. The truss is subjected to vertical downward force at R and horizontal force at G. (Figure not to scale) The force...

Consider the following statements with respect to rigid pavements: Statement-1: Bottom-up cracking (BUC) in rigid pavements is caused at the edge of the slab due to combined effect...

For the traverse given below, the benchmark is at ground point L. The Reduced Level (RL) of L is 150.000 m. The direction of the traverse is from L to N. The readings on levelling...

The 2.4 ml of raw sewage is diluted to 240 ml. The Dissolved Oxygen (DO) of the diluted sample at the beginning of Biochemical Oxygen Demand (BOD) test was 8 mg/l and it was 6 mg/l...

Types of flood routing and methods are given in the table below. Column 1 Type of Flood Routing (P) Hydrologic routing (Q) Hydraulic routing (R) Reservoir routing (S) Channel routi...

A shallow footing is subjected to a vertical load. Within the elastic limit of the underlying soil, the TRUE statement(s) is/are:

Which of the following statements is/are TRUE with respect to the type of stresses to be considered for the design of rigid pavements?

Consider differential equation $\frac{dy}{dx} + xy = x$ with the condition as y = 0 at x = 0. The value of y at x = 1.0 is ________ (rounded off to two decimal places).

The age (in years) of a population is normally distributed with a mean of 36 and standard deviation of 12. The height (in cm) of the same population is also normally distributed wi...

A 250 mm wide × 600 mm deep rectangular concrete beam is prestressed by means of 4 high-tensile tendons, each of 14 mm diameter. The centre of the tendons is 200 mm from the soffit...

A rigid-jointed portal frame, shown in the figure, consists of beam and columns of equal length L. The frame has a fixed support at one end and a roller support at the other end. T...

Linearly elastic, homogeneous, uniform bars BCD and FG shown in the figure have fixed supports at B and G, respectively. For both the bars, axial rigidity is 20000 kN. A gap of 2 m...

A simply-supported rectangular reinforced concrete beam has a width 250 mm and an overall depth 600 mm. The effective span of the beam is 6.23 m. The beam carries a live load of 5...

Width (in m) of a rectangular channel required to carry a discharge of 96 m³/s at a critical depth of 9.8 m is __________ (rounded off to two decimal places). Use acceleration due...

The cross section of a 0.5 m wide vertical gate holding water and oil is shown in the figure. The unit weights of water and oil are 10 kN/m³ and 7.5 kN/m³, respectively. The horizo...

A centrifugal pump is delivering water from an underground tank to an overhead reservoir against a static head of 35 m through a 2 km long, 250 mm diameter pipe. The head-discharge...

The flow depth for a discharge of 10 m³/s in a wide rectangular channel is 2.0 m. Assume that the flow is uniform. If the discharge is doubled, the flow depth (in m) in this channe...

For a clayey soil stratum, the time required for degree of consolidation from 25 % to 50 % is 30 days. The total time (in days) required for 90 % degree of consolidation of the sam...

The ultimate bearing capacity of a 1 m wide strip footing is 532.80 kPa, when it is embedded at 1 m depth in dry cohesionless soil. The soil has a unit weight of 18 kN/m$^3$. The u...

A building is proposed in an area having thick deposit of silty clay. The water table is at the ground surface. The saturated unit weight of soil is 18 kN/m$^3$ and unit weight of...

A soil sample has following properties: Natural water content = 30 % Plasticity index = 40 % Liquidity index = 50 % The estimated plastic limit (in %) of the soil is ________ (roun...

For a given traffic stream, the speed-density relationship is given as: $v = v_o \ln \left(\frac{k_j}{k}\right)$ where $v$ is the mean speed (in km/h), and $k$ is the density (in v...

A vertical curve is formed by a descending gradient of 1 in 40 meeting an ascending gradient of 1 in 50. Consider the following: Stopping Sight Distance (SSD) = 90 m Height of head...

Interior angles measured at the locations of a closed traverse ABCDA are given in table below. Location | Interior angle ---|--- A | 71° 1' 40" B | 104° 54′ 23" C | 107° 54′ 10″ D...

The analysis of major cations and anions in a water sample collected from a city's water supply is given below. Ions present in minor concentrations are not given. Anions Cl- SO4^2...

Anaerobic bacteria are being utilized for the destruction of biodegradable organic content of wastewater measured in terms of Chemical Oxygen Demand (COD). The yield coefficient (Y...

In an industry, a cyclone collector with 80% efficiency is installed for air purification, followed by an electrostatic precipitator with 50% efficiency. The concentration of parti...