GATE CE exam:gate PYQs & Answers — Page 73

Questions 721–730 of 1300. Imported answers require independent review unless marked reviewed.

The solution of the second-order differential equation

with boundary conditions

and

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is a constant, the general solution of

will be in the form of

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The value of

using the trapezoidal rule with four equal subintervals is

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1.718

1.727

2.192

2.718

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The smallest eigenvalue and the corresponding eigenvector of the matrix

, respectively, are

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1.55 and

2.00 and

1.55 and

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A 50 mL sample of industrial wastewater is taken into a silica crucible. The empty weight of the crucible is 54.352 g. The crucible with the sample is dried in a hot air oven at 104 °C till a constant weight of 55.129 g. Thereafter, the crucible with the dried sample is fired at 600 °C for 1 h in a muffle furnace, and the weight of the crucible along with residue is determined as 54.783 g. The concentration of total volatile solids is ______.

Your answerChoose one option.

1540 μg/L

8620 mg/L

6920 mg/L

1700 mg/L

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A prismatic steel beam is shown in the figure. The plastic moment,

, calculated for the collapse mechanism using static method and kinematic method is

Diagram for Civil Engineering question 28

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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 (

) along the inclined surface between the wedge and the block is 0.2. All other surfaces are frictionless. The wedge angle is 30°.

Diagram for Civil Engineering question 29

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

. The value of the coefficient ‘

’ (round off to one decimal place) is

Your answerChoose one option.

0.6

0.5

2.0

0.9

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A frame EFG is shown in the figure.

All members are prismatic and have equal flexural rigidity. The member FG carries a uniformly distributed load

per unit length. Axial deformation of any member is neglected. Considering the joint F being rigid, the support reaction at G is

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Contractor X is developing his bidding strategy against Contractor Y. The ratio of Y’s bid price to X’s cost for the 30 previous bid in which Contractor X has competed against Contractor Y is given in the Table

Ratio of Y’s bid price to X’s cost	Number of bids
1.02	6
1.04	12
1.06	3
1.10	6
1.12	3

Based on the bidding behaviour of the Contractor Y, the probability of winning against Contractor Y at a mark up of 8% for the next project is

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more than 0% but less than 50%

more than 50% but less than 100%

100%

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A clay layer of thickness

has a preconsolidation pressure

and an initial void ratio

. The initial effective overburden stress at the mid-height of the layer is

. At the same location, the increment in effective stress due to applied external load is

. The compression and swell indices of the clay are

and

, respectively. If

, then the correct expression to estimate the consolidation settlement (

) of the clay layer is

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GATE CE exam:gate PYQs

Question 26

Question 26

Question 27

Question 27

Question 28

Question 28

Question 29

Question 29

Question 30

Question 30