GATE Civil Engineering

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...

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

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

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...

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...

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:

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

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

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

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...

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

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...

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...

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:

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...

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...

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

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

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...

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 one of the following statements is TRUE?

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

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 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...

The grown algae are useful in the operation of

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...

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).

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...

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...

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 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 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...

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...

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 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...

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 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...

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...

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

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...

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...

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...

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...

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...

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...

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

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...

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

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

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).

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

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...

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...

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 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...

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...

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)...

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...

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...

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 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 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...

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 ________ (...