Q.1

1 1 3 The minimum and the maximum eigen values of the matrix 1 5 1 are -2 and 3 1 1 6, respectively. What is the other eigen value? (A) 5

(B) 3

(C) 1

d 2x + 2 x3 = 0 is 2 dt

(D) -1

Q.2

The degree of the differential equation

(A) 0

(B) 1

(C) 2

(D) 3

Q.3

The solution for the differential equation x=0 is (A) y = e

1 2x

dy = x 2 y with condition that y = 1 at dx

x3 ( B ) ln( y ) = +4 3

x2 (C ) ln( y ) = 2

(d ) y = e

x3 3

Q.4

An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is (A) 75MPa (B) 86.5MPa (C) 100MPa (D) 122.3MPa

Q.5

A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be (A) 200kN (B) 283kN (C) 400kN (D) 800kN

Q.6

The stiffness coefficient kij indicates (A) force at i due to a unit deformation at j. (B) deformation at j due to a unit force at i. (C) deformation at i due to a unit force at j. (D) force at j due to a unit deformation at i. For an isotropic material, the relationship between the Young’s modulus (E), shear modulus (G) and Poisson’s ratio (µ) is given by ( A) G = E 2(1 + µ ) ( B) E = G 2(1 + µ ) (C ) G = E (1 + 2µ ) ( D) G = E 2(1 − µ )

Q.7

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Q.8

A clay soil sample is tested in triaxial apparatus in consolidated-drained conditions at a cell pressure of 100 kN/m2. What will be the pore water pressure at a deviator stress of 40kN/m2? (A) 0kN /m2 (B) 20kN/m2 (C) 40kN/m2 (D) 60kN/m2

Q.9

The number of blows observed in a Standard Penetration Test (SPT) for different penetration depths are given as follows. Penetration of sampler Number of blows

0-150mm 150-300mm 300-450mm The observed N value is (A) 8 (B) 14 Q.10

6 8 10

(C) 18

(D) 24

The vertical stress at some depth below the corner of a 2m x 3m rectangular footing due to a certain load intensity is 100 kN / m2 below the centre of a 4m x 6m rectangular footing at the same depth and same load intensity? (A) 25 (B) 100 (C) 200 (D) 400 There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate? (A) M1 (B) M2 (C) M3 (D) S1 The consumptive use of water for a crop during a particular stage of growth is 2.0mm / day. The maximum depth of available water is the root zone is 60mm. Irrigation is required when the amount of available water is 50% of the maximum available water in the root zone. Frequency of irrigation should be (A) 10 days (B) 15days (C) 20days (D) 25days As per the Lacey’s method for design of alluvial channels, identity the true statement from the following (A) Wetted perimeter increases with an increase in design discharge (B) Hydraulic radius increases with an increase in silt factor. (C) Wetted perimeter decreases with an increase in design discharge. (D) Wetted perimeter increases with an increase in silt factor. At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. Both the points are at the same elevation. The

Q.11

Q.12

Q.13

Q.14

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fluid density is...