Gate Mock Test Civil Engineering (CE)- 6 - Civil Engineering (CE)

Directions: In the following question, choose the word which best fills the blank from the four options given.

The uncalled-for remarks by the leader ______ the situation and many of his followers turned violent

Let u_n+1 = 2u_n + 1, (n = 0, 1, 2, .......) and u₀ = 0, then, u₁₀ would be nearest to

In Indore, Annapurna area has 2000 telephone subscribers and government collects fixed charges of Rs. 280 per month from each subscriber. The government proposes to increase the tariff and if it is forecasted for each rupee increase, there will be an equivalent amount of subscribers discontinuing. So, what increase will bring maximum revenue to the government?

In an event, A rows his boat upstream in a river flowing with a steady speed of 6 km/hr and then returns to the same point without rowing (i.e. only with the speed of river). If the total distance covered by A is 42 km and the time taken in rowing the boat upstream is 4 hours more than his return journey, find the speed of A in still water.

Directions: In the following question, a set of three figures X, Y and Z shows a sequence in which a piece of paper is folded and finally cut from one or more sections. Below these figures, a set of answer figures marked (a), (b), (c) and (d) shows the design which the paper actually acquires when it is unfolded. You have to select the answer figure which most closely resembles the unfolded piece of paper.

A piece of paper is folded and punched as shown below:

From the following alternative figures, indicate how this piece of paper will appear when unfolded.

Directions: Rearrange the jumbled letters in the following four options and find the odd word among them.

The rank of matrix is

The recursion relative to solve x = e^-x using Newton-Raphson method is

The shape of the cumulative distribution function of Gaussian distribution is:

The solution of differential equation xdy/dx + y(x²–1) = 2x³ is

Gypsum is typically added in cement to

A column of height h with a rectangular cross section of size a x 2a has a buckling load of P. If the cross section is changed to 0.5a x 3a and its height changed to 1.5h, the buckling load of the redesigned column will be

In an Oedometer apparatus, a specimen of fully saturated clay has been consolidated under a vertical pressure of 50 kN/m² and is presently at equilibrium. The effective stress and pore water pressure immediately on increasing the vertical stress to 150 kN/m² respectively are

For the velocity profile for laminar boundary flow , the wall shear stress on the plate is given by _______. (Here, b is the width of the plate.)

If water is flowing at the same depth in most hydraulically efficient triangular and rectangular channel sections, then the ratio of hydraulic radius of triangular section to that of rectangular section is

A plane truss with applied loads is shown in the figure.

The members which do not carry any force are

Which one of the following statements is correct?

Find delta (in cm) when duty is 2000 hectare cumec and base period is 30 days.

The liquid forms of particulate air pollutants are

Match each differential equation in Group I to its family of solution curves in Group II:

A highway designed for 80 km/h speed has a horizontal curve section with radius 250 m. If the design lateral friction is assumed to develop fully, the required super elevation is

The equation of streamline passing through the point (4, 5) for a flow field is

Which of the following is/are correct statement(s)?

At a road curve of radius 450 m, for a vehicle speed of 120 km/h, the total super elevation required is ___________ m. Take the width of the road as 20 m and the coefficient of friction as 0.20. (Answer up to two decimal places)

The volume determined from ∫∫∫v 8xyz dv for V = [2, 3] × [1, 2] × [0, 1] (in integers) is __________.

Find the total hardness (in mg/l) of CaCO₃ if the values of hardness of calcium and magnesium ions respectively are 50 mg/l and 72 mg/l, and the combined weights of CaCO₃, calcium and magnesium ions are 50 mg, 20 mg and 12 mg, respectively. (Answer up to the nearest integer)

The equation of deformation is derived to be y = x² - xL for a beam shown in the figure.

The curvature of the beam at the mid-span (in units, in integer) will be _________.

A 2% gradient meets a 1.5% gradient at a chainage of 2000 m and reduced level of 100 m. When the sight distance is 500 m and eye level of the driver above the road surface is 1.5 m, the length of vertical curve is ________ m. (Answer up to one decimal place)

The cohesion (c), angle of internal friction (Φ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m³, respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is ________________.

If a single pipe of length 2 m and diameter 30 m is to be replaced by three pipes of the same material, same length and equal diameter to convey the same total discharge under the same head loss, then the value of diameter of the three pipes is _____________ m. (Answer up to one decimal place)

A signalized intersection operates in two phases. The lost time is 3 seconds per phases. The maximum ratios of approach flow to saturation flow for the two phases are 0.37 and 0.40. The optimum cycle length using Webster's method (in seconds, rounded off to one decimal place) is __________.

Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is x (0) = , the system response is x(t) = . If the initial state vector of the system changes to x(0) = , the system response becomes x(t) = .

The eigenvalue and eigenvector pairs (λ_i v_i) for the system are

The value using the trapezoidal rule with four equal subintervals is

The particular integral for the differential equation is given by

A wedge M and a block N are subjected to forces P and Q as shown in the figure.

If force P is sufficiently large, then the block N can be raised. The weights of the wedge and the block are negligible compared to the forces P and Q. The coefficient of friction (μ) along the inclined surface between the wedge and the block is 0.2. All other surfaces are frictionless. The wedge angle is 30°.

The limiting force P, in terms of Q, required for impending motion of block N to just move it in the upward direction is given as P = αQ. The value of the coefficient 'α' (rounded off to one decimal place) is

The relationship between the length l and radius r of an ideal transition curve is

Based on drained triaxial shear tests on sands and clays, the representative variations of volumetric strain(ΔV/V) with the shear strain (y) is shown in the figure.

Choose the CORRECT option regarding the representative behavior exhibited by Curve P and Curve Q.

1. Under reamed piles are precast piles with one or more under reams in each pile.

2. Under reamed piles are designed as bearing piles.

3. The length of traditional under reamed pile ranges from 3 m to 4 m.

Which of the above statements is/are correct?

A water sample is analyzed for coliform organisms by the multiple tube fermentation method. The results of confirmed test are as follows:

The most probable number (MPN) of coliform organisms for the above results is to be obtained using the following MPN index.

The MPN of coliform organisms per 100 mL is

The laboratory test on a soil sample yields the following results: natural moisture content = 18%, liquid limit = 60%, plastic limit = 25%, percentage of clay sized fraction = 25%. The liquidity index and activity (as per the expression proposed by Kempton) of the soil, respectively, are

On a road, the speed-density relationship of a traffic stream is given by u = 70 - 0.7k (where speed, u, is in km/h and density, k, is in veh/km). At the capacity condition, the average time headway will be

Maximum strain at the level of compression steel for a rectangular section having effective cover to compression steel is 2.5 m and neutral axis depth from compression face is 15 m. (Answer up to three decimal places)

Vehicular arrival at an isolated intersection follows the Poisson distribution. The mean vehicular arrival rate is 2 vehicles per minute. The probability (round off to 2 decimal places) that at least 2 vehicles will arrive in any given 1-minute interval is _____________.

Find the discharge (in m³/s) through the trapezoidal notch of height 1.5 m and breadth 0.5 m at sill. Take the side parallel to sill side as 1.4 m and the coefficient of discharge through both the parallel sides as 0.86. (Answer up to two decimal places)

A prismatic cantilever prestressed concrete beam of span length L = 1.5 m has one straight tendon place in the cross-section as shown in the figure (not to scale). The total prestressing force of 50 kN in the tendon is applied at d_c = 50 mm for the top in the cross-section of width, b = 200 mm and depth, d = 300 mm.

If the concentrated load, P = 5 kN, the resultant stress (in MPa, in integer) experienced at point 'Q' will be _________.

When the slope of the ground is 15° and the measured distance is 150 m, the correction is _________ m. (Answer up to two decimal places)

Employ the stiffness matrix approach for the simply supported beam as shown in the figure to calculate unknown displacements rotations. Take length L= 8 m, modulus of elasticity, E = 3 × 10⁴ N/mm²; Moment of inertia, I = 225 × 10⁶ mm⁴.

The mid-span deflection of the beam (in mm, rounded off to an integer) under P = 100 kN in downward direction will be _________.

The sag correction in a tape of length 20 m and weight 15 kg/m suspended at its ends is 50 m. Find the pull in kilograms. (Answer up to two decimal places)

A small project has 12 activities - N, P, Q, R, S, T, U, V, W, X, Y and Z. The relationship among these activities and the duration of these activities are given in the table.

The total float of the activity 'V' (in weeks, in integer) is ___________________.

Consider two axially loaded columns, namely, 1 and 2, made of a linear elastic material with Young's modulus 2 x 10⁵ MPa, square cross-section with side 10 mm, and length 1 m. For Column 1, one end is fixed and the other end is free. For Column 2, one end is fixed and the other end is pinned. Based on the Euler's theory, the ratio of the buckling load of Column 2 to the buckling load of Column 1 is _______.

(Answer up to the nearest integer)

A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the top of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is 20. The depth of clay in front of the retaining wall is 2.0 m. The properties of the clay backfill, and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine's earth pressure theory. Take unit weight of water, ɣ_w = 9.81 kN/m³.

The factor of safety (rounded off to two decimal places) against sliding failure of the retaining wall after ignoring the passive earth pressure will be _________.

A body of mass 10 kg is hanging freely and another body of mass 15 kg is lying on a rough inclined surface. If the coefficient of friction and angle of inclination respectively are 0.3 and 30°, then the acceleration of the system (in m/s²) is __________. (Answer up to two decimal places)

An unsupported slope of height 15 m is shown in the figure (not to scale), in which the slope face makes an angle 50° with the horizontal.

The slope material comprises purely cohesive soil having undrained cohesion 75 kPa. A trial slip circle KLM, with a radius 25 m, passes through the crest and toe of the slope and it subtends an angle 60° at its center O. The weight of the active soil mass (W, bounded by KLMN) is 2500 kN/m, which is acting at a horizontal distance of 10 m from the toe of the slope. Consider the water table to be present at a very large depth from the ground surface.

Considering the trial slip circle KLM, the factor of safety against the failure of slope under undrained condition (rounded off to two decimal places) is _________.

A couple of 25 kN/m is acting at one end of a simply supported beam. The maximum deflection of the beam is _____________ x 10^-6 m. Assume length of the beam as 1 m. (Take E = 250 GPa and I = 1000000 mm⁴) (Answer up to two decimal places)

A cylinder (2.0 m diameter, 3.0 m long and 25 kN weight) is acted upon by water on one side and oil (specific gravity = 0.8) on other side as shown in the figure.

The absolute ratio of the net magnitude of vertical forces to the net magnitude of horizontal forces (rounded off to two decimal places) is ______,

If the period of incubation is 20 days at 20°C in the relative conductivity test on sewage, the percentage of relative stability is ____________. (Answer up to the nearest integer)

A baghouse filter has to treat 12 m³/s of waste gas continuously. The baghouse is to be divided into 5 sections of equal cloth area such that one section can be shut down for cleaning and/or repairing, while the other 4 sections continue to operate. An air-to-cloth ratio of 6.0 m³/min-m' cloth will provide sufficient treatment to the gas. The individual bags are of 32 cm in diameter and 5 m in length. The total number of bags (in integer) required in the baghouse is ____________.

A venturimeter is installed in a pipeline of 200 mm diameter. The throat pipe diameter ratio is 1/5 .

Water flows through the installation. The pressure in the pipeline is 1.405 kg/cm² and the vacuum in the throat is 375 cm of mercury. If 4% of the differential head is lost between the gauges, the flow in the pipeline is ____________ m³/s. (Answer up to two decimal places)

Spot speeds of vehicles observed at a point on a highway are 40, 55, 60, 65 and 85 km/h. The space mean speed (in km/h, rounded off to two decimal places) of the observed vehicle is _________.

The beam shown is loaded with two 1000 N point loads. The separation is maintained at 2 m, but the loads may be moved to any location on the beams.

The maximum value for shear at support A is ____________ N. (Answer up to the nearest integer)

Traversing is carried out for a closed traverse PQRS. The internal angles at vertices P, Q, R and S are measured as 92°, 68°, 123° and 77°, respectively. If for bearing of line PQ is 27°, fore bearing of line RS (in degrees, in integer) is ____________.