Practice Test: Gate Civil Engineering(CE) 2014 Paper - GATE

If y = 5x² + 3, then the tangent at x = 0, y = 3

A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes?

Q. 6 – Q. 10 carry two marks each.

Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK

Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct?

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft?

The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value)

(i) On average, it rains more in July than in December
(ii) Every year, the amount of rainfall in August is more than that in January
(iii) July rainfall can be estimated with better confidence than February rainfall
(iv) In August, there is at least 500 mm of rainfall

Q. 11 – Q. 35 carry one mark each.

 equals to

Given the matrices  the product K^T JK is ___________

The probability density function of evaporation E on any day during a year in a watershed is given by

The sum of Eigen values of the matrix, [M] is

With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates: (x₁, y₁) = (1, 0); (x₂, y₂) = (2, 2); and (x₃, y₃) = (4, 3). The area of the triangle is equal to

Match the information given in Group – I with those in Group - II.

Group – I                                                                             Group – II
P Factor to decrease ultimate strength to                          1 Upper bound on ultimate load
design strength
                                                                             
Q Factor to increase working load to                                  2 Lower bound on ultimate load   
ultimate load for design

R Statical method of ultimate load                                     3 Material partial safety factor
analysis

S Kinematical mechanism method of                                 4 Load factor   
ultimate load analysis

The possible location of shear centre of the channel section, shown below, is

The ultimate collapse load (P) in terms of plastic moment Mp by kinematic approach for a propped cantilever of length L with P acting at its mid-span as shown in the figure, would be

While designing, for a steel column of Fe250 grade, a base plate resting on a concrete pedestal of M20 grade, the bearing strength of concrete (in N/mm²) in limit state method of design as per IS:456-2000 is ________________

A steel section is subjected to a combination of shear and bending actions. The applied shear force is V and the shear capacity of the section is V_s. For such a section, high shear force (as per IS:800- 2007) is defined as

The degree of static indeterminacy of a rigid jointed frame PQR supported as shown in the figure is

In a beam of length L, four possible influence line diagrams for shear force at a section located at a distance of L/4 from the left end support (marked as P, Q, R and S) are shown below. The correct influence line diagram is

The degree of disturbance of the sample collected by the sampler is expressed by a term called the "area ratio". If the outer diameter and inner diameter of the sampler are D_o and D_i respectively, the area ratio is given by

For a saturated cohesive soil, a triaxial test yields the angle of internal friction (φ) as zero. The conducted test is

The action of negative skin friction on the pile is to

A long slope is formed in a soil with shear strength parameters: c' = 0 and φ' = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γ_sat = 18 kN/m3 and γ_w = 10 kN/m³. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would be

An incompressible homogeneous fluid is flowing steadily in a variable diameter pipe having the large and small diameters as 15 cm and 5 cm, respectively. If the velocity at a section at the 15 cm diameter portion of the pipe is 2.5 m/s, the velocity of the fluid (in m/s) at a section falling in 5 cm portion of the pipe is ___________

A conventional flow duration curve is a plot between

In reservoirs with an uncontrolled spillway, the peak of the plotted outflow hydrograph

The dimension for kinematic viscosity is

Some of the nontoxic metals normally found in natural water are

The amount of CO₂ generated (in kg) while completely oxidizing one kg of CH₄ to the end products is ____________

The minimum value of 15 minute peak hour factor on a section of a road is

The following statements are related to temperature stresses developed in concrete pavement slabs with free edges (without any restraint):

P. The temperature stresses will be zero during both day and night times if the pavement slab is considered weightless
Q. The temperature stresses will be compressive at the bottom of the slab during night time if the self-weight of the pavement slab is considered
R. The temperature stresses will be compressive at the bottom of the slab during day time if the self-weight of the pavement slab is considered

The TRUE statement(s) is(are)

The Reduced Levels (RLs) of the points P and Q are +49.600 m and +51.870 m respectively. Distance PQ is 20 m. The distance (in m from P) at which the +51.000 m contour cuts the line PQ is

Q. 36 – Q. 65 carry two marks each.

If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is

If a is amplitude constant for y, then

A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction (θ) of the force (F) with respect to x-axis should be

A particle moves along a curve whose parametric equations are: x = t³ + 2t, y = −3e^−2t and z = 2 sin (5t), where x, y and z show variations of the distance covered by the particle (in cm) with time t (in s). The magnitude of the acceleration of the particle (in cm/s²) at t = 0 is ________

A traffic office imposes on an average 5 number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Poisson distribution. The probability that there will be less than 4 penalties in a day is ___________

Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of 80 kN hanging vertically. The coordinates of the vertices are given in parentheses. The force in the member QR, F_QR will be 

For the cantilever beam of span 3 m (shown below), a concentrated load of 20 kN applied at the free end causes a vertical displacement of 2 mm at a section located at a distance of 1 m from the fixed end. If a concentrated vertically downward load of 10 kN is applied at the section located at a distance of 1 m from the fixed end (with no other load on the beam), the maximum vertical displacement in the same beam (in mm) is __________

For the truss shown below, the member PQ is short by 3 mm. The magnitude of vertical displacement of joint R (in mm) is _______________

A rectangular beam of width (b) 230 mm and effective depth (d) 450 mm is reinforced with four bars of 12 mm diameter. The grade of concrete is M20 and grade of steel is Fe500. Given that for M20 grade of concrete the ultimate shear strength, τ_uc = 0.36 N/mm² for steel percentage, p = 0.25, and τ_uc = 0.48 N/mm² for p = 0.50. For a factored shear force of 45 kN, the diameter (in mm) of Fe500 steel two legged stirrups to be used at spacing of 375 mm, should be

The tension and shear force (both in kN) in each bolt of the joint, as shown below, respectively are

For a beam of cross-section, width = 230 mm and effective depth = 500 mm, the number of rebars of 12 mm diameter required to satisfy minimum tension reinforcement requirement specified by IS:456-2000 (assuming grade of steel reinforcement as Fe500) is _____________

In a reinforced concrete section, the stress at the extreme fibre in compression is 5.80 MPa. The depth of neutral axis in the section is 58 mm and the grade of concrete is M25. Assuming linear elastic behavior of the concrete, the effective curvature of the section (in per mm) is

Group I contains representative load-settlement curves for different modes of bearing capacity failures of sandy soil. Group II enlists the various failure characteristics. Match the load-settlement curves with the corresponding failure characteristics.

Group I                                                  Group II
P. Curve J                                              1. No apparent heaving of soil around the footing
Q. Curve K                                             2. Rankine’s passive zone develops imperfectly
R. Curve L                                              3. Well defined slip surface extends to ground surface

A given cohesionless soil has emax = 0.85 and emin = 0.50. In the field, the soil is compacted to a mass density of 1800 kg/m³ at a water content of 8%. Take the mass density of water as 1000 kg/m³ and Gs as 2.7. The relative density (in %) of the soil is

The following data are given for the laboratory sample.

If thickness of the clay specimen is 25 mm, the value of coefficient of volume compressibility is ___________ ×10^-4 m²/kN

The flow net constructed for the dam is shown in the figure below. Taking the coefficient of permeability as 3.8×10⁻⁶ m/s, the quantity of flow (in cm³/s) under the dam per meter of dam is ______________

A horizontal jet of water with its cross-sectional area of 0.0028 m² hits a fixed vertical plate with a velocity of 5 m/s. After impact the jet splits symmetrically in a plane parallel to the plane of the plate. The force of impact (in N) of the jet on the plate is

A venturimeter, having a diameter of 7.5 cm at the throat and 15 cm at the enlarged end, is installed in a horizontal pipeline of 15 cm diameter. The pipe carries an incompressible fluid at a steady rate of 30 litres per second. The difference of pressure head measured in terms of the moving fluid in between the enlarged and the throat of the venturimeter is observed to be 2.45 m. Taking the acceleration due to gravity as 9.81 m/s², the coefficient of discharge of the venturimeter (correct up to two places of decimal) is ______________

A rectangular channel having a bed slope of 0.0001, width 3.0 m and Manning’s coefficient ‘n’ 0.015, carries a discharge of 1.0 m³/s. Given that the normal depth of flow ranges between 0.76 m and 0.8 m. The minimum width of a throat (in m) that is possible at a given section, while ensuring that the prevailing normal depth is not exceeded along the reach upstream of the contraction, is approximately equal to (assume negligible losses)

Three rigid buckets, shown as in the figures (1), (2) and (3), are of identical heights and base areas. Further, assume that each of these buckets have negligible mass and are full of water. The weights of water in these buckets are denoted as W₁, W₂, and W₃ respectively. Also, let the force of water on the base of the bucket be denoted as F₁, F₂, and F₃ respectively. The option giving an accurate description of the system physics is

An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d₁ and d₂ (where d₁ = 4d₂) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _________

16 MLD of water is flowing through a 2.5 km long pipe of diameter 45 cm. The chlorine at the rate of 32 kg/d is applied at the entry of this pipe so that disinfected water is obtained at the exit. There is a proposal to increase the flow through this pipe to 22 MLD from 16 MLD. Assume the dilution coefficient, n = 1. The minimum amount of chlorine (in kg per day) to be applied to achieve the same degree of disinfection for the enhanced flow is

The potable water is prepared from turbid surface water by adopting the following treatment sequence.

For a sample of water with the ionic composition shown in the figure below, the carbonate and noncarbonate hardness concentrations (in mg/l as CaCO₃), respectively are:

A straight 100 m long raw water gravity main is to carry water from an intake structure to the jack well of a water treatment plant. The required flow through this water main is 0.21 m³/s. Allowable velocity through the main is 0.75 m/s. Assume f = 0.01, g = 9.81 m/s². The minimum gradient (in cm/100 m length) to be given to this gravity main so that the required amount of water flows without any difficulty is ___________

A traffic survey conducted on a road yields an average daily traffic count of 5000 vehicles. The axle load distribution on the same road is given in the following table:

The design peroid of the road is 15 years, the yearly traffic growth rate is 7.5% and the load safety
factor (LSF) is 1.3. If the vehicle damage factor (VDF) is calculated from the above data, the design
traffic (in million standard axle load, MSA) is ____________

The perception-reaction time for a vehicle travelling at 90 km/h, given the coefficient of longitudinal friction of 0.35 and the stopping sight distance of 170 m (assume g = 9.81 m/s²), is _____________ seconds.

The speed-density (u−k) relationship on a single lane road with unidirectional flow is u = 70 − 0.7k, where u is in km/hr and k is in veh/km. The capacity of the road (in veh/hr) is ___________

An isolated three-phase traffic signal is designed by Webster's method. The critical flow ratios for three phases are 0.20, 0.30, and 0.25 respectively, and lost time per phase is 4 seconds. The optimum cycle length (in seconds) is ___________

A levelling is carried out to establish the Reduced Levels (RL) of point R with respect to the Bench Mark (BM) at P. The staff readings taken are given below.

If RL of P is +100.000 m, then RL (in m) of R is

Group I lists tool/instrument while Group II lists the method of surveying. Match the tool/instrument with the corresponding method of surveying.

Group I                                      Group II
P. Alidade                                 1. Chain surveying
Q. Arrow                                   2. Levelling
R. Bubble tube                         3. Plain table surveying
S. Stadia hair                           4. Theodolite surveying