GATE Mock Test -1

The BOD₅ if the temperature of the sample and seeded solution water are 20⁰C(saturation is 9.07 mg/l), the initial DO₅ at saturation and sample dilution is 1:30 with seeded solution . The final DO of seeded dilution water is 8mg/l and the final DO of seeded dilution water is 2mg/l assuming volume of BOD bottle is 300ml

• 181mg/l

• 281mg/l

• 251mg/l

• 290mg/l

Rainfall depth over a watershed is monitored through six no. of well distributed rain gauges. Gauged data is given below    Rain gauge no.  1 2  3  4 5 6 Rainfall depth(mm) 470 465 435 525 480 510 Area of thiessen polygon (*104 m²) 95 100 98 80 85 92 The thiessen mean value (in mm, up to one decimal place) of the rainfall is 

A sample of water has been analyzed for common ions and results are presented in the form of an bar diagram as shown  The non carbonate hardness(expressed in mg/l as CaCO₃ ) of the sample is  

• 40

• 165

• 195

• 205

How many four digit numbers can be formed with 10 digit 0,1,2,3...9 if no number can start with 0 and if repetitions are not allowed?

Match list -1 (curve identification in the figure) with list-2 (nature of fluid) and select answer using the codes given below:             X-axis -strain rate             Y-axis-shear stress  LIST-1                    LIST-2 A) Curve A                  1.Newtonian B) Curve B                  2.Dilatant C) Curve C                  3.Ideal bingham plastic D) Curve D                  4.pseudo-plastic codes:               A       B       C        D

• 3    4   1   2

• 2   4    1    3

• 3   1   4    2

• 2   1   4   3

R.L of a floor level is 200.490m. Staff reading on the floor is 1.695m, the staff held upside down against the bottom of the roof is 3.305m. height of the ceiling is:

• 3.5m

• 4.0m

• 5.0m

• 6.0m

If E=10;J=20;O=30; and T=40, what will be P+E+S+T?

• 82

• 164

• 120

• 51

If duty(D) is 1428 hectares/cumec and base period (B) is 120 days for an irrigated crop , then delta (Δ)in meters is given by

• 102.8

• 0.73

• 1.38

• 0.01

A sand stratum and a clay stratum have the same thickness at 2m .The coefficient of compressibility of sand is 1/3 rd of the coefficientof compressibility of clay and permeability of sand is 5000 times that of clay. Assuming the same void ratio, the ratio of consolidation time for the clay that of sand is

• 10,000

• 15,000

• 5,000

• 30,000

A test plate 30cm square ,settles by 12mm under a load of 4.5kN in a sandy soil. By how much will a footing 2m*2m subjected to a load of 200kN settle?

• 36.3mm

• 20.87mm

• 75.75mm

• 18.15mm

The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q.How many units should be produced to minimize the total cost (V+F)?

• 5

• 4

• 7

• 6

Two machine M1 and M2 are able to execute any of four jobs P, Q, R, and S. The machine can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects. Job Q on 3 objects, job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?

• 2 hours

• 2.5 hours

• 3 hours

• 3.5 hours

The infiltration capacity of a catchment is represented by horton's equation as tp=0.5+1.2e^-0.5t,where t_p is in cm/h and t is in hours . Assuming the infiltration to take place at capacity rates in a storm of 4 hours duration, estimate the average rate of infiltration for the duration of the storm in (cm/h)

• 1.02

• 2

• 3.56

• 3.14

Consider the case where noise level of 90 dBA exists for 5 min and is followed by reduced noise level of 60dBA for 50 min . The equivalent continuous energy level (L_eq) for 55 min period is

• 70dB

• 79.63dB

• 59.26dB

•    84.21dB

Two points A and B are 1530 m apart across a river. The reciprocal levels measured are           Level at  Readings on A (in m) B A 2.165 3.810 B 0.910 2.355         The true difference in level between A and B would be

• 1.255m

• 1.355m

• 1.545m

• 1.845m

Knowledgeable dog owners recommend obtaining a purebred dog from a ______ breeder, one who is ______ and respected by customers and breeders alike.

• Discerning … equivocal

• Demanding … flexible

• Churlish … charming

• Reputable … admired

Given that logP/(y-z)=logQ/(z-x) =logR/(x-y) =10,for x≠y≠z, What is the value of PQR?

• 0

• 1

• Xyz

• 10^xyz

The observed bearings of a traverse  are given below   Line Bearing  Line Bearing PQ 46⁰15' QP 226⁰15' AR 108⁰15'  RQ  286⁰15' RS 201⁰30' SR 20⁰30' ST 321⁰45'  TS 141⁰45' The station(s) most likely to be affected by local attraction is/are

• Only R

• Only S

• R and S

• P and Q

The critical height of an unsupported vertical cut in a cohesive soil is given by    where c= unit cohesion              Φ= angle of internal friction              γ=unit weight of soil

• (4c/γ)tan(45⁰+Φ/2)

• (2c/γ)tan(45⁰+Φ/2)

• (4c/γ)cot(45⁰+Φ/2)

• (2c/γ)cot(45⁰+Φ/2)

  Given f(t) =L^-1[(3s+1)/(s³+4s²+(k-3)s)] if Lim _t->∞ f(t) =1, then the value of K is

• 1

• 2

• 3

• 4

Due to rise in temperature the viscosity and unit weight of percolating fluid are reduced to 70% and 90% resp. other things being constant , the change in coefficient of permeability will be

• 20.0%

• 28.6%

• 63.0%

• 77.8%

In a rectangular strain gauge rosette , the strain recorded are ε_0⁰=400 µ strain,  ε_45⁰=300 µ strain,  ε_90⁰=200 µstrain, What is the maximum principal strain at that point

• 500 µstrain

• 400 µstrain

• 300 µstrain

• 200 µstrain

The muskingum method of flood routing gives θ₂=c₀I₂+c₁I₁+c₂θ₁.The coefficients in this equation will have values such that

• C₀+c₁=c₂

• C₀-c₁-c₂=1

• C₀+c₁+c₂=0

• C₀+c₁+c₂=1

A square footing has dimensions of 2m by 2m and a depth of 2m . What will be its ultimate bearing capacity in pure clay with an unconfined compressive strength of 0.15N/mm² ,Φ=0⁰,γ=1.7g/cm³  by using Terzaghi's bearing capacity equation?

• 589kN/mm²

• 602kN/mm²

• 704kN/mm²

• None of these

A canal 6m deep runs through a soil having Cu=1818kN/(m2), Φu=10°,e=0.80, and Gs=2.72.The angle of slope of bank is 45°.If sudden drawdown takes place up to the bed level of the canal. The factor of safety is  (For β=angle of slope of bank =45°, Φu=10°, Sn=0.108, Φu=4.88°, stability number=0.137)  

• 2.96

• 2.14

• 1.41

• 1.14

Find out the mean proportion of 3 & 27 also find out their third proportion

• 9,243

• 10,81

• 15,19683

• 12,810

X and y are integers and if x^2/y^3 is even integer then which of the following must be an even integer?

• X-y

• Y+1

• X^2/y^4

• Xy

Activated sludge is the

• Aerated sludge in the aeration unit

• Sludge settled in the humus tank.

• Sludge in the secondary tank after aeration and rich in microbial mass.

• Sludge in the secondary tank after aeration and rich in nutrients

The sequent depth ratio in a hydraulic jump formed in a horizontal rectangular channel is 16.48 . the froude number of super critical stream is

• 4

• 8

• 12

• 120

A consolidated undrained triaxial compression test was performed on a saturated sand at a cell  pressure of 80kPa.The ultimate deviator stress was 270kPa and the pore pressure at peak stress was  -50kPa. The effective angle of internal friction of soil will be

• 30.63⁰

• 45⁰

• 63.43⁰

• 0⁰

Assume that a large stream has reoxygenation constant ,K₂ of 0.4/days ,a flow velocity of 5 miles / hour and at point of pollutant discharge,the stream is saturated with oxygen at 10mg/l.The waste water flow rate is very small compared with stream flow. So the mixture is assumed to be saturated with dissolved oxygen and to have an oxygen demand of 20mg/l.The deoygenating constant K₁ Is 0.2 /day.The DO level 30 miles downstream is (e^-0.05=0.951 & e^-0.1=0.905)

• 8mg/l

• 9mg/l

• 10mg/l

• 7mg/l

A surface water flow of 28000m³/day is coagulated by  adding 75mg/l of ferrous sulphate and an equivalent dose of lime. How much lime is required at a purity of 90%CaO.

• 500kg/day

• 470kg/day

• 550kg/day

• 450kg/day

The value of line integral  ∫(2xy²dx+2x²ydy+dz) c along  a path joining the origin (0,0,0) and the point (1,1,1) is

• 0

• 2

• 4

• 6

With a(n) ______ grin, the boy quickly slipped the candy into his pocket without his mother’s knowledge.

• Jaundiced

• Nefarious

• Stereotypical

• Sentimental

Each of the letters in the figure below represents a unique integer from 1 to 9. The letters are positioned in the figure such that each of (A+B+C), (C+D+E), (E+F+G) and (G+H+K) is equal to 13. Which integer does E represent?                        | A | B | C |                                 | D |                                 | E | F | G |                                           | H |                                           | K |

• 1

• 4

• 6

• 7

For wheel loads 3kN,4kN,5kN,6kN spaced 2m,3m,3m apart are moving on a simply supported beam of span 24m with 3kN load loading from left to right. To find maximum BM at 18m from left support , the load that must be placed at the section is 

• 3kN

• 4kN

• 5kN

• 6kN

Design the rate of super elevation for a horizontal  highway curve of radius 500m and speed 100kmph

The limiting neutral axis depth for a rectangular section of effective depth d. For SAIL-MA:300 HY grade steel is_____d

The dimension of a symmetrical welded I-section are shown in the figure.  All dimensions are in mm. The plastic section modulus about the weaker axis (in cm³) up to one decimal place is______  

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

• .

• .

• .

• .

For a linear elastic isotropic material the no. of independent elastic constants is/are

• 1

• 2

• 3

• 4

For the bracket connection shown inthe following fig. Which bolt will have the maximum resultant force?

• Bolt 1

• Bolt 2

• Bolt 3

• Bolt 4

A numerical solution of the equation f(x)=x+√x -3=0 can be obtained using newton raphson method. If the starting value is x=2 for  the iteration , the value of x that is to be used in the next step is

• 0.306

• 0.739

• 1.694

• 2.306

The allowable Net Positive Suction Head (NPSH) for a pump provided by the  manufacturer for a flow of 0.05 m³ /s  is 3.3 m. The temperature of water is  30⁰C (vapour pressure head absolute  = 0.44 m), atmosphere pressure is 100 kPa  absolute and the head loss from the reservoir to pump is 0.3 N-m/N. The maximum  height of the pump above the suction reservoir is

• 10.19m

• 6.89m

• 6.15m

• 2.86m

A uniformly distributed load of 2kN/m covers left half of the span of a three hinged parabolic arch , span 40m and central rise 10m . Which of the following statements relating to different function at the loaded quarter point are correct? 1.The slope is tan^-1(1/2) 2.The normal thrust is 6√ 3 kN. 3.The shear force is not zero. 4.The bending moment is zero. select the correct answer using the codes given below:

• 1,2 and 4

• 2 and 3

• 1 and 3

• 3 and 4

Consider the following statements:     1. Effective length of a battened column is usually increased to account for the additional load on battens due to the lateral expansion of columns. 2.As per IS 800:1984, permissible stress in bending compression depends on both euler buckling stress and the yield stress of steel. 3.As per IS 800:1984,the effective length of a column effectively held in position at both ends but not restrained against rotation , is taken to be greater than that in the ideal end conditions. THE TRUE statements are

• 1 and 2

• 2 and 3

• 1 and 3

• 1,2 and 3

A column 300mm*300mm is provided an footing 1m*1m supported on soil having allowable bearing pressure of 360kN/m² at depth 1m below ground . The minimum thickness of footing assuming M20 concrete and Fe 4,5 steel;

• 430mm

• 490mm

• 530mm

• 590mm

On a national highway pavement section mean value of Benkelman beam deflection was obtained as 1.45mm with standard deviation σ of 0.107 cm. Pavement temperature measured was 37°and moisture correction was obtained as 1.6. What is the value of characteristic deflection considering the value of 2σ ?

• 1.94mm

• 2.64mm

• 2.72mm

• 2.69mm