__GATE 2013 Questions and answer key for CIVIL ENGG.__

__Q. 1 – Q. 25 carries one mark each.__**Q.1**There is no value of x that can simultaneously satisfy both the given equations.Therefore, find the

‘least squares error’ solution to the two equations, i.e., find the value of x that minimizes the sum of

squares of the errors in the two equations. __________

**2x = 3**

**4x =1**

**Q.2**What is the minimum number of multiplications involved in computing the matrix product PQR?

Matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and

1 column. _______

**_Sol:_**_

**16 multiplications**

**Q.3**A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that

a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:

(A) 0.04 (B) 0.2 (C)0.02 (D) 0.0004

**Sol: (D) p = 1/50*1/50**

**Q.4**Maximum possible value of Compacting Factor for fresh (green) concrete is:

(A) 0.5 (B) 1.0 (C) 1.5 (D) 2.0

**Sol: (B)**

**Q.5**As per IS 800:2007, the cross-section in which the extreme fiber can reach the yield stress, but

cannot develop the plastic moment of resistance due to failure by local buckling is classified as

(A) plastic section (B) compact section

(C) semi-compact section (D) slender section

**Sol:(C)**

**Q.6**The creep strains are

(A) caused due to dead loads only

(B) caused due to live loads only

(C) caused due to cyclic loads only

(D) independent of loads

**Sol: (A)**

**Q.7**As per IS 456:2000 for M20 grade concrete and plain bars in tension the design bond stress

Tbd = 1.2 MPa. Further, IS 456:2000 permits this design bond stress value to be increased by 60 %

for HSD bars. The stress in the HSD reinforcing steel bars in tension, Ts= 360 MPa. Find the

required development length, Ld, for HSD bars in terms of the bar diameter, Phi. __________

**46.875.phi**

**Q.8**The ‘plane section remains plane’ assumption in bending theory implies:

(A) strain profile is linear

(B) stress profile is linear

(C) both strain and stress profiles are linear

(D) shear deformations are neglected

**Sol:(A)**

**Q.9**Two steel columns P (length L and yield strength fy= 250MPa) and Q (length 2L and yield

strength fy= 500 MPa) have the same cross-sections and end-conditions. The ratio of buckling

load of column P to that of column Q is:

(A) 0.5 (B) 1.0 (C) 2.0 (D) 4.0

**Sol: (D)**

**Q.10**The pin-jointed 2-D truss is loaded with a horizontal force of 15kN at joint S and another 15 kN

vertical force at joint U, as shown.Find the force in member RS (in kN) and report your answer

taking tension as positive and compression as negative.

**Sol: Zero**

**Q.11**A symmetric I-section (with width of each flange = 50 mm, thickness of each flange = 10 mm,

depth of web = 100 mm, and thickness of web = 10 mm) of steel is subjected to a shear force of

100 kN. Find the magnitude of the shear stress(in N/mm^2) in the web at its junction with the top

flange. _______

**Sol: 70 to 72**___

**Q.12**In its natural condition, a soil sample has a mass of 1.980 kg and a volume of 0.001 m^3. After

being completely dried in an oven, the mass of the sample is 1.800 kg. Specific gravity G is 2.7.

Unit weight of water is 10 kN/m^3. The degree of saturation of the soil is:

(A) 0.65 (B) 0.70 (C) 0.54 (D) 0.61

**Sol:(c) Yd=Y/(1+w); Yd=G. Yw/(1+e); eS=w.G**

**Q.13**The ratio Nf/Nd is known as shape factor, where Nf is the number of flow lines and Nd is the

number of equi-potential drops. Flow net is always drawn with a constant b/a ratio, where b and a

are distances between two consecutive flow lines and equi-potential lines, respectively. Assuming

that b/a ratio remains the same, the shape factor of a flow net will change if the

(A) upstream and downstream heads are interchanged

(B) soil in the flow space is changed

(C) dimensions of the flow space are changed

(D) head difference causing the flow is changed

**Sol:(b)**

**Q.14**Following statements are made on compacted soils, wherein DS stands for the soils compacted on dry side of optimum moisture content and WS stands for the soils compacted on wet side of

optimum moisture content. Identify the incorrect statement.

(A) Soil structure is flocculated on DS and dispersed on WS.

(B) Construction pore water pressure is low on DS and high on WS.

(C) On drying, shrinkage is high on DS and low on WS.

(D) On access to water, swelling is high on DS and low on WS.

**Sol:(c)**

**Q.15**Four columns of a building are to be located within a plot size of 10 m x 10 m. The expected load

on each column is 400 kN. Allowable bearing capacity of the soil deposit is 100 kN/m2. The type

of foundation best suited is

(A) isolated footing (B) raft foundation

(C) pile foundation (D) combined footing

**Sol:(a)**

**Q.16**For sub-critical flow in an open channel, the control section for gradually varied flow profiles is

(A) at the downstream end (B) at the upstream end

(C) at both upstream and downstream ends (D) at any intermediate section

**Sol:(a)**

**Q.17**Group-I contains dimensionless parameters and Group- II contains the ratios.

Group-I Group -II

P. Mach Number 1. Ratio of inertial force and gravitational force

Q. Reynolds Number 2. Ratio of fluid velocity and velocity of sound

R. Weber Number 3. Ratio of inertial force and viscous force

S. Froude Number 4. Ratio of inertial force and surface tension force

The correct match of dimensionless parameters in Group- I with ratios in Group-II is:

(A) P-3, Q-2, R-4, S-1 (B) P-3, Q-4, R-2, S-1

(C) P-2, Q-3, R-4, S-1 (D) P-1, Q-3, R-2, S-4

**Sol:(c)**

**Q.18**

For a two dimensional flow field, the stream function W is given as W=3/2(y^2-x^2). The

magnitude of discharge occurring between the stream lines passing through points (0,3) and (3,4)

is:

(A) 6 units (B) 3 units (C) 1.5 units (D) 2 units

**Sol: (b)**

**Q.19**An isohyet is a line joining points of

(A) equal temperature (B) equal humidity

(C) equal rainfall depth (D) equal evaporation

**Sol: (c)**

**Q.20**Some of the water quality parameters are measured by titrating a water sample with a titrant.

Group-I gives a list of parameters and Group-II gives the list of titrants.

**Group-I**

**Group-II**

P.Alkalinity 1. N/35.5 AgNO3

Q. Hardness 2. N/40 Na2S2O3

R. Chloride 3. N/50 H2SO4

S. Dissolved oxygen 4. N/50 EDTA

The correct match of water quality parameters in Group-I with titrants in Group-II is:

(A) P-1, Q-2, R-3, S-4 (B)P-3, Q-4, R-1, S-2

(C)P-2, Q-1, R-4, S-3 (D) P-4, Q-3, R-2, S-1

**Sol:(B)**

**Q.21**A water treatment plant is designed to treat 1 m3/s of raw water. It has 14 sand filters. Surface area of each filter is 50 m2. What is the loading rate (in m^3/day.m^2) with two filters out of service for routine back washing? ___

**Sol: 144 m^3/ day.m^2**

**Q.22**Select the strength parameter of concrete used in design of plain jointed cement concrete pavements from the following choices:

(A) Tensile strength

(B) Compressive strength

(C) Flexural strength

(D) Shear strength

**Sol: (c)**

**Q.23**It was observed that 150 vehicles crossed a particular location of a highway ina duration of 30

minutes. Assuming that vehicle arrival follows a negative exponential distribution, find out the

number of time head ways greater than 5 seconds in the above observation? __________

**Q.24**For two major roads with divided carriageway crossing at right angle,a full clover leaf interchange with four indirect ramps is provided. Following statements are made on turning movements of vehicles to all directions from both roads. Identify the correct statement:

(A) Merging from left is possible,but diverging to left is not possible.

(B) Both merging from left and diverging to left are possible.

(C) Merging from left is not possible,but diverging to left is possible.

(D) Neither merging from left nor diverging to left is possible.

**Q.25**The latitude and departure of a line AB are +78 m and -45.1 m, respectively. The whole circle

bearing of the line AB is:

(A) 30° (B) 150° (C) 210° (D) 330°

**Sol: (A)**

__Q. 26 to Q. 55 carry two marks each.__**Q.26**The state of 2D-stress at a point is given by the following matrix of stresses:

{ n1 s1; s2 n2 } = {100 30, 30 20}

What is the magnitude of maximum shear stress in MPa?

(A) 50 (B) 75 (C) 100 (D) 110

**Sol: (A)**

**Q.27**Find the magnitude of the error (correct to two decimal places) in the estimation of following

integral using Simpson’s 1/3 rule. Take the step length as 1. Integral[0 to 4] (x^4+10)dx.

**Sol: 8.53**

**To be continued.....**