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# GATE CE 2021 : Topper's Mini Mock 3 (App update required to attempt this test)

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Question 1

Find a word that is the synonym of -

ENDEAVOUR

Question 2

If

**NDTV**is coded as**4404**and**ABP**is coded as**126**, then how will**NEWS**be coded as?Question 3

The probability of drawing a card which is atleast a spade or a king from a pack of 52 cards is

Question 4

Identify the best way to improve the underlined part of the given sentence. If there is no improvement required, select ‘no Improvement’.

The Artist co-operates with God in making increasingly larger numbers of people see the beauty of the world which these people could never

**themselves.**__see for__Question 5

The trace and determinant of a 2 × 2 matrix are –2 and –35 respectively. It’s Eigen values are

Question 6

Which one of the following figures are equal to one acre?

1) 43560 sq.ft

2) 40 gunthas

3) 10 sq. gunters chain

4) 4850 sq. yard

Select the correct answer using codes given below:

1) 43560 sq.ft

2) 40 gunthas

3) 10 sq. gunters chain

4) 4850 sq. yard

Select the correct answer using codes given below:

Question 7

If the modulus of sub-grade reaction of standard plate of 30 cm diameter is 20 kg/cm

^{3}, the value of modulus of sub-grade reaction for a standard plate is --------- kg/cm^{3}.Question 8

A solid cylindrical shaft of 50 mm diameter transmits a torque of 1200 Nm. Find the value of shear stress developed.

Question 9

As per IS : 456 : 2000, as long as the stress in concrete does not exceed times of its characteristic strength, creep may be assumed to be proportional to the stress. The value of

*x*isQuestion 10

Consider the U-tube manometer. What is the pressure(N/m

^{2}) difference between A & B ? (Take g=10)

Question 11

A watershed has four precipitation stations A, B, C and X. The station X was inoperative during a storm. The stations A, B and C recorded precipitations of 6.80 cm, 4.50cm and 3.60cm respectively. The average annual precipitation at A, B, C and X are 71.6cm, 51.8cm, 65.6cm and 48.2cm. Estimate the missing storm precipitation at station X , using arithmetic average method.

Question 12

What is the reaction at support D of the rigid-jointed structure shown below?

Question 13

A square footing of 2.5m× 2.5m size has been founded at 1.2m below the ground level in a cohesion soil having bulk density of 1.8t/m

^{3}and unconfined compressive strength of 6.0 t/m^{2}. Determine the ultimate bearing capacity of footing for a FOS of 3.0 by Skempton’s Method. (In t/m^{2})Question 14

A solid circular shaft is required to transmit 200 kW while turning at 1.5 rev/second. The allowable shearing stress is 42 MPa, then the required diameter of the shaft is ________cm.

Question 15

The spot speeds (expressed in km/hr) observed at a road section are 66, 62, 45, 79, 32, 51, 56, 60, 53, and 39. The median speed (expressed in km/hr) is ________.

(

(

*Note: answer with one decimal accuracy*)Question 16

Find the Laplace transform of

Question 17

what can be the value of the product of p, q and r?

Question 18

What is the probability of getting a sum of 9 from two throws of a dice?

Question 19

The Value of

is________.

is________.

Question 20

If x is real, the maximum value of is __________.

Question 21

Two identical rigid bars AB and BC are pinned at B and C supported at A by a pin in a frictionless roller that can only displace vertically, then determine the critical load of the system.

Question 22

The following data were recorded in a constant head permeability test:

(i) Internal diameter of permeameter = 7.5 cm

(ii) Head loss over a sample length of 18 cm = 24.7 cm

(iii) Quantity of water collected in 60 sec = 626 ml

(iv) Void ratio of the soil sample = 78.6%

What will be the coefficient of permeability (in cm/s) of the soil and seepage velocity (in cm/s) during the test?

(i) Internal diameter of permeameter = 7.5 cm

(ii) Head loss over a sample length of 18 cm = 24.7 cm

(iii) Quantity of water collected in 60 sec = 626 ml

(iv) Void ratio of the soil sample = 78.6%

What will be the coefficient of permeability (in cm/s) of the soil and seepage velocity (in cm/s) during the test?

Question 23

A soil sample has a void ratio of 0.75, moisture content = 15%, G

_{S}= 2.6 and γ_{w}= 9.81 kN/m^{3}. The amount of water (in kN) required to be added per m^{3}to make it saturated isQuestion 24

An activated sludge system is operating at equilibrium with the following information:

Waste water related data:

Flow rate = 750 m

Aeration tank related data:

Hydraulic retention time = 6 hours, mean-cell-residence time = 300 hour, volume = 5000 m

Food-to-biomass (F/M) ratio for the aeration tank is ________ day–1.

Waste water related data:

Flow rate = 750 m

^{3}/hour, influent BOD = 120 mg/*l*, effluent BOD = 8 mg/*l*.Aeration tank related data:

Hydraulic retention time = 6 hours, mean-cell-residence time = 300 hour, volume = 5000 m

^{3}, mixed liquor suspended solids = 2500 mg/l. Mixed liquor volatile suspended solids = 1500 mg/l.Food-to-biomass (F/M) ratio for the aeration tank is ________ day–1.

Question 25

An ideal horizontal flow settling basin is 2.5 m deep having surface area 1200 m

^{2}. Water flows at the rate of 15000 m^{3}/day at water temperature 20 °C, dynamic viscosity, μ = 1 × 10^{–3}kg/m-sec and density of water, ρ = 1000 kg/m^{3}. Assuming Stoke’s law to be valid, the approximate percentage of spherical sand particles (0.01 mm in diameter with specific gravity 2.6) that will be removed isQuestion 26

The design speed for a two-lane road is 70 kmph. When a design vehicle with a wheel base of 7 m is negotiating a horizontal curve on the road, the off-tracking is measured as 0.12 m. The required widening ( in m) of carriageway of the two-lane road on the curve is approximately.

Question 27

A reinforced concrete beam of rectangular cross section width 250 mm and effective depth 450 mm is subjected to a factored shear force of 150 kN. The grade of concrete, main steel and stirrups are M20, Fe 415 and Fe250 respectively. For the area of main steel provided the design shear stress of concrete is 0.48 N/mm

^{2}, the beam is designed for collapse limit state. What is the spacing (in mm), of 2 legged 8 mm stirrups?Question 28

A bore is a hydraulic jump which propagates into a still or slower moving fluid as shown in the figure below. Assume that the still water is 2 m deep and the water behind the bore is 3 m deep. What will be the induced water velocity (in m/s)?

Question 29

Total suspended particulate matter (TSP) concentration in ambient air is to be measured using a high volume sampler. The filter used for this purpose had and initial dry weight of 10.574g. The filter was mounted in the sampler and the initial air flow rate through the filter was set at 2 m

^{3}/min. Sampling continued for 24 hours. The airflow after 24 hours was measured to be 1.2 m^{3}/min. The dry weight of the filter paper after 24 hour sampling was 12.345g. Assuming a linear decline in the air flow rate during sampling, what is the 24 hour sampling, what is the 24 average TSP concentration (in μg/m^{3}) in the ambient air?Question 30

The velocity along the centre line of a nozzle of length

*L=0.8 m*is given by*V*=2t where*V*= velocity in m/s, t= time in seconds from commencement of flow; x =distance from inlet to the nozzle. The total acceleration (in ) of fluid at*t =*3 sec and x = 0.5 m, L= 0.8 m will beQuestion 31

A rectangular foundation of size 4m x 3m exerts a pressure of 25 kN/m

^{2}. The vertical stress at a point X located below 3m as shown in the figure isQuestion 32

Consider the frame ABCD

The horizontal deflection of B to the left is _______mm.

The horizontal deflection of B to the left is _______mm.

Question 33

Consider a 6m concrete beam of rectangular cross section 200 mm × 450 mm. The beam is prestressed by 4 wires of diameter 5 mm located 125 mm above the soffit. The prestress induced in the wires is 1.5 kN/mm

If a concentrated load acts at the midpoint of the load, then the maximum load that can be applied without producing tension at the bottom of the beam is

^{2}.If a concentrated load acts at the midpoint of the load, then the maximum load that can be applied without producing tension at the bottom of the beam is

Question 34

A pipe of 50 mm diameter is 6 m long and the velocity of flow of water in the pipe is 2.4 m/s. What power (in W) would be saved if the central 2 m length of pipe was replaced by 75 mm diameter pipe, the change of section being sudden?

[Take f = 0.04 for the pipes of both diameter]

[Take f = 0.04 for the pipes of both diameter]

Question 35

Find Resultant Reaction at the left support for the given parabolic 3 -hinged Arch.

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