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# GATE CE 2021 : Topper's Mini Mock 5 (App update required to attempt this test)

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Question 1

The function at x = 4 attains

Question 2

Consider the given matrix .

Find the principle sub matrix of matrix A

Question 3

The eigen values of the matrix are?

Question 4

The price of a wire made of a superalloy material is proportional to the square of its length. The price of 10 m length of the wire is Rs. 1600. What would be the total price (in Rs.) of two wires of lengths 4 m and 6 m?

Question 5

A monkey is trying to reach the top of a tree. He climbs 3 feet in a minute but slides down by 1.5 feet after each climb. If he reaches the top of the tree in 58 minutes, then the maximum possible height of the tree is ________ feets.

Question 6Multiple Correct Options

Which of the following differential equation is/are non homogenous differential equations?

Question 7

Consider the following statements relating to the level of poker play of four players P, Q, R and S.
I. P always beats Q
II. R always beats S
III. S loses to P only sometimes
IV. R always loses to Q
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set

Question 8

The head of a newly formed government desires to appoint five of the six selected members P, Q, R, S, T and U to portfolios of Home, Power, Defence, Telecom and Finance. U does not want any portfolio if S gets one of the five. R wants either Home or Finance or no portfolio. Q says that if S gets either Power or Telecom, then she must get the other one. T insists on a portfolio(any) if P gets one.
Which is the valid distribution of portfolio?

Question 9

Anuj, Bhola, Chandan, Dilip, Easwar and Faisal live on different floor 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?

Question 10

Let where then F(e) equals

Question 11

Agonic line is the line joining the points having

Question 12

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 + 50.000 m contour cuts the line PQ is

Question 13

If the Euler load for a column is 800 kN and crushing load is 1200 kN,then the Rankine load in kN will be….

Question 14

The Atterberg limits of a soil are LL = 68% and PL = 34% and it contains 85% by weight of clay. The water content of a sample is 45%. Determine the predominant clay mineral.

Question 15Multiple Correct Options

Consider the following statements and select the correct option(s) among them.

Question 16Multiple Correct Options

Which of the following statements holds for the Influence line diagram (ILD)?

Question 17Multiple Correct Options

For the elementary profile of Gravity dam the height of the water level from the base is 20 m. Assuming the unit weight of water as 10 kN/m3 and unit weight of concrete as 24 kN/m3.Assume uplift to have developed fully. Which of the following statements are true?

Question 18

The x and y components of the velocity field for a 2-D fluid flow is given by u=3y-y2 and v=3x-x2.What would be the rate of shear deformation and angular velocity of fluid flow in z direction respectively at point (2,3)?

Question 19

If total hardness and alkalinity of a water sample are 200 mg/l as CaCO3 and 260 mg/l as CaCO3 respectively, what are the values of carbonate hardness and non – carbonate hardness?

Question 20Multiple Correct Options

Three plates (1), (2) and (3) are welded together as shown in the figure below. Which of the following statements is/are correct about welding?

Question 21

The radius of a horizontal circular curve on a highway is 120 m. The design speed is 60
km/hour, and the design coefficient of lateral friction between the tyre and the road surface is 0.15. The estimated value of superelevation required (if full lateral friction is assumed to
develop), and the value of coefficient of friction needed (if no superelevation is provided) will, respectively, be

Question 22

A survey was made with a chain 0.5 link two short and plotted to a scale of 1 cm = 300m. the plan now found to have shrunk so that a line originally 6 cm long was found 5.4 cm. If the area of the plan was measured and is 24.5 sq. cm. find the true area of the survey.

Question 23

A beam with equal overhangs as shown below have supports adjusted such that the maximum bending moment is the minimum possible. The supports are positioned such that a = _____ L.

Question 24

A 6m sand layer lies above clay layer of thickness 8m, the saturated unit weight of sand and clay are 19 and 22 KN/m3 respectively. Initially the water is at 4m below the ground level but due to capillary action the sand gets saturated up to 1.5m above the existing water table. The change in the effective stress due to capillary action at middle of the clay layer is ______ N/m3.

(unit weight of sand above GWT is 18.5 KN/m3)

Question 25

A pre-tensioned rectangular concrete beam 150 mm wide and 300 mm depth is prestressed with three straight tendons, each having a cross-sectional area of 50 mm2, to initial stress of . The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6, the loss of prestressing force (in kN, up to one decimal place) due to the elastic deformation of concrete only is ______

Question 26

A concrete column carries on axial load of 450 kN and a bending moment of 60 kN m at its base. An isolated footing of size 2 m by 3m, with 3m side along the plane of the bending moment, is provided under the column. Centres of gravity of column and footing coincide. The net maximum and the minimum pressures in kN/m2 on soil under the footing are respectively.

Question 27Multiple Correct Options

The concentration of Na, Ca and Mg are 21, 3 and 1.5 meq respectively and the electrical conductivity is 200 micro mho/cm at 25C .

Question 28

If the slope of infiltration capacity curve as shown in figure is -0.4605, the value of the constant k (i.e the rate of decay of the difference between initial and final infiltration rate) in the Horton's equation of infiltration capacity curve will be equal to _______time-1. Question 29

A pile of 0.50 m diameter and of length 10 m is embedded in a deposit of clay. The undrained strength parameters of the clay are cohension = 60 kN/m2 and the angle of internal friction = 0. The skin friction capacity (kN) of the pile for an adhesion factor of 0.6 , is

Question 30

A square footing (2 m × 2m) is subjected to an inclined point load P as shown in the figure below. The water table is located well below the base of the footing. Considering one–way eccentricity, the net safe load carrying capacity of the footing for a factor of safety of 3.0 is _________ kN.
The following factor may be used:
Bearing capacity factors: Nq = 33.3, Nï= 37.16; Shape factor: Fqs =FYs = 1.314 ; Depth factors : Fqd = FYd = 1.113; Inclination factors : Fqi = 0.444, FYi = 0.02 Question 31

A sleeve 10 cm long encases a vertical metal rod of 3 cm diameter with radial clearance of 0.02 mm. If when immersed in oil viscosity 6.0 poise, the effective weight of sleeve is 7.5 N. Calculate the speed of sleeve while sliding down in cm/s.

Question 32

A landfill is to be designed for the population of 2,00,000. The solid waste generation is 1 kg/person/day. The density of uncompacted fill is 100 kg/m3. The compaction ratio is 3 and volume of landfill is 0.020 km3. The ratio of cover to compacted fill is 0.4. Calculate the number of years this landfill can be used.

Question 33Multiple Correct Options

Consider the following statements regarding time – cost model. Which of the following statements are correct.

Question 34

Which of the following statement is correct?

1) If 1500 g of cement is required to have 1875 g cement paste of normal consistency, the percentage of water is 25%.

2) If P is the percentage of water required for normal consistency, water to be added for determination of tensile strength test is .

3) The raw materials used for manufacture of high alumina cement are 40% bauxite, 40% lime and 15% iron oxide with a little % of ferric oxide, silica, magnesia etc.

Question 35

A rectangular concrete beam of width 120 mm and depth 200 mm is prestressed by pretensioning to a force of 150 kN at an eccentricity of 20 mm. The cross sectional area of the prestressing steel is 187.5 mm2. Take modulus of elasticity of steel and concrete as 2.1 × 105 MPa and 3.0 × 104 MPa respectively. The percentage loss of stress is the prestressing steel due to elastic deformation of concrete is
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