## Thursday, August 29, 2013

### (Questions with Answer Key)- GATE 2013 Civil Engineering Examination

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.....

## Monday, August 26, 2013

### GATE 2012 Questions and Answer key

Q.(1-25) Carry one marks each
Q.1 The estimate obtained of the definite integral by the Simpson's rule with three-point function evaluation exceeds the exact value by

(a) 0.235   (b) 0.068    (c) 0.024    (d) 0.012
Sol : (d)
Q.2 The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is
(a) <50%   (b) 50%    (c) 75%    (d) 100%                                        Sol: (a)

Q.3 The infinite series 1+x+x^2/2! + x^3/3! + x^4/4! +.........
(a) sec x    (b) e^x     (c) cos x    (d) 1 + sin^2 x                              Sol: (b)

Q.4 The Poisson's ratio is defined as
(a) mode[axial stress/ Lateral Stress]        (b) mode[lateral strain/ axial strain]
(c) mode[lateral stress/axial stress]          (d) mode[axial strain/lateral strain]       Sol: (b)

Q.5 The following statements are related to bending of beams:
I. The slope of the bending moment diagram is equal to the shear force
II. The slope of the shear force diagram is equal to the load intensity
III. The slope of the curvature is equal to the flexural rotation
IV. The second derivative of the deflection is equal to the curvature.
The only False statement is
(a) I        (b) II         (c) III        (d) IV                                                                         Sol. (c)

Q.6 If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is p, then the maximum shear stress developed inside the cube is
(a) 0    (b) p/2    (c) p     (d) 2p                                                                            Sol: (a)

Q.7 As per IS:456:2000, in limit state Design of a flexural member, the strain in reinforcing bars under tension at ultimate state should not be less than
(a) fy/Es      (b) fy/Es + 0.002      (c) fy/(1.15Es)      (d)  fy/1.15 Es +0.002         Sol:(d)

Q.8 Which one of the following is categorized as a long term loss of pre-stress in a  pre-stressed concrete member?
(a) Loss due to elastic shortening
(b) Loss due to friction
(c) Loss due to relaxation of strands
(d) Loss due to anchorage slip                                                                               Sol:(c)

Q.9 In a steel plate with bolted connections, the rupture of the net section is a mode of failure under
(a) Tension    (b) Compression     (c) flexure    (d) shear                                    Sol:(a)

Q.10 The ratio of theoritical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material but with pinned ends is equal to:
(a) 0.5   (b) 1.0    (c) 2.0    (d) 4.0                                                      Sol: (d)

Q.11 The effective stress friction angle of a saturated, cohesion-less soil is 38 degrees.  The ratio of shear stress to normal effective stress on the failure plane is
(a) 0.781    (b) 0.616    (c) 0.488     (d) 0.438                        Sol: (a) T= c + Eff. stress *tan(fr. ang.)

Q.12 Two series of compaction tests were performed in the laboratory on an inorganic clayey soil employing two different levels of compaction energy per unit volume of soil. With regard to the above tests, the following statements are made.
I. The optimum moisture content is expected to be more for the tests with higher energy.
II. The maximum dry density is expected to be more for the tests with higher energy.
(a) Only I is TRUE          (b)  Only II is TRUE
(c) Both I and II are TRUE  (d) Neither I and II are TRUE                                    Sol: (b)

Q.13 As per the Indian Standard soil classification system, a sample of silty clay with liquid limit of 40% and plasticity index of 28% is classified as:
(a) CH   (b) CI    (c) CL    (d) CL-ML                                                         Sol: (b) Ip= 0.73(Wl - 20)

Q.14 A smooth rigid retaining wall moves as shown in the sketch causing the back-fill material to fail. The back-fill material is homogeneous and isotropic, and obeys Mohr - Coulomb failure criterion. The major principal stress is
(a) parallel to the wall face and acting downwards
(b) normal to the wall face
(c) oblique to the wall face acting downwards
(d) oblique to the wall face acting upwards.                                                        Sol: (b)

Q.15 An embankment is to be constructed with a granular soil(bulk unit weight = 20kN/m^3) on a saturated clayey silt deposit (un-drained shear strength = 25kPa). Assuming un-drained general shear failure and bearing capacity factor of 5.7, the maximum height (in m) of the embankment at the point of failure is
(a) 20.0    (b) 3.5    (c) 3.0    (d) 2.5                                                                 Sol: (a)

Q.16 A trapezoidal channel is 10.0 m wide at the base and has a side slope of 4 horizontal to 3 vertical. The bed slope is 0.002. The channel is lined with smooth concrete(Manning's n =0.012). The hydraulic radius (in m) for a depth of flow of 3.0 m is
(a) 20.0       (b) 3.5    (c) 3.0    (d) 2.1                                                            Sol: (d) Rh= A/P

Q.17 A rectangular open channel of width 5.0 m is carrying a discharge of 100 m^3/Sec. The Froude number of the flow is 0.8. The depth of flow (in m) in the channel is
(a) 4    (b) 5    (c) 16    (d) 20                                                                       Sol: (a) Fr = V/ (g.d)^0.5

Q.18 The circular water pipes shown in the sketch are flowing full. The velocity of flow (in m/sec) in the branch pipe "R" is
(a) 3    (b) 4    (c) 5   (d) 6                                                 Sol: (b)  Qp = Qq+ Qr (Q=A.V)

Q.19 The ratio of evapo- transpiration to potential evapo- transpiration is in the range
(a) 0.0  to 0.4                    (b) 0.6 to 0.9
(c) 0.0 to 1.0                     (d) 1.0 to 2.0                            Sol: (c)

Q.20 A sample of domestic sewage is digested with silver sulphate, sulphuric acid, potassium dichromate and mercuric sulphate in chemical oxygen demand (COD) test. The digested sample is then titrated with standard ferrous ammonium sulphate(FAS) to determine the un-reacted amount of
(a) mercuric sulphate
(b) potassium dichromate
(c) silver sulphate
(d) sulphuric acid                                                              Sol: (b)

Q.21 Assertion [A]: At a manhole, the crown of the outgoing sewer should not be higher than the crown of incoming sewer
Reason [A]: Transition from a larger diameter incoming sewer to a small diameter outgoing sewer at a manhole should not be made.
The CORRECT option evaluating the above statement is:
(a) Both [A] and [R] are TRUE and [R] is the correct reason for [A]
(b) Both [A] and R are TRUE but [R] is not correct reason for [A].
(c) Both [A] and [R] are false.
(d)[A] is true but [R] is false.                                           Sol: (b)

Q.22 Two major roads with two lanes each are crossing in an urban area to form an un-controlled intersection . The number of conflict points when both roads are one way is 'X' and when both roads are two way is 'Y'. The ratio of X and Y is
(a) 0.25   (b) 0.33   (c) 0.50    (d) 0.75                    Sol: (a) 0.25    X = 6  Y= 24; X/Y = 0.25

Q.23 Two bitumen samples 'X' and 'Y' have softening points 45 degrees Celsius and 60 degrees Celsius respectively. Consider the following statements:
I. Viscosity of 'X' will be higher than that of 'Y' at the same temperature.
II. Penetration value of 'X' will be lesser than that of 'Y' under standard condition:
The CORRECT option evaluating the above statements is
(a) Both I and II are TRUE
(b) I is FALSE and II is TRUE
(c) Both I and II are FALSE
(d) I is TRUE and II is FALSE.                                            Sol: (c)

Q.24 Road roughness is measured using
(a) Benkelman beam
(b) Bump indicator
(c) Dynamic cone penetrometer
(d)Falling weight deflectometer.                                     Sol: (b)

Q.25 Which of the following errors can be eliminated by reciprocal measurements in differential leveling?
I. Errors due to earth's curvature
II. Error due to atmospheric refraction
(a) Both I and II     (b) I only
(c) II only               (d) Neither I or II                          Sol: (a)

Q.26 - Q.55 carry two marks each
Q.27 In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is
(a) 1/32    (b) 2/32   (c) 3/32   (d) 6/32                      Sol:(d)  P= nCr p^r q^n-r

Q.28 The eigen values of matrix [9  5 ; 5  8] (where 9  5 is first row and 5  8 is second) are
(a)  -2.42 and 6.86
(b) 3.48  and 13.53
(c) 4.70  and 6.86
(d) 6.86 and 9.50                                                                      Sol: (b)

Q.29 For the parallelogram OPQR shown in the sketch,  vect.OP = ai + bj  and vetc.OR = ci + dj. i and j are unit vectors. The area of the parallelogram is
(a) ad - bc        (b) ac - bd         (c) ad - ba         (d) ab - cd        Sol: (a)

Q.30 The solution of the ordinary differential equation  dy/dx + 2y = 0 for the boundary condition, y=5 at x = 1 is
(a) y = e ^(-2x)    (b) y = 2.e^(-2x)     (c) y = 10.95.e^(-2y)    (d) y = 36.95.e^(-2x)
Sol: (d)  y = c.e^(-2x)
Q.31 A simply supported beam is subjected to a uniformly distributed load of intensity w per unit length, on half of the span from one end. The length of the span and the flexural stiffness are denoted as l and EI respectively. The deflection at mid span of the beam is
(a) 5/6144. wl^2/EI    (b) 5/768. w.l^4/ EI
(c) 5/384.wl^4/EI        (d) 5/192. wl^4/EI                              Sol: (b)

Q.32 The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force P and a moment M at mid height. The reaction(s) at R is/are:
(a) A vertical force equal to P
(b) A force equal to P/2
(c) A vertical force equal to P and a horizontal force equal to M/h
(d) A vertical force equal to P/2 and a horizontal force equal to M/h   Sol: (c)

Q.33 A concrete beam pre-stressed with a parabolic tendon is shown in the sketch. The eccentricity of the tendon is measured from the centroid of the cross section. The applies pre-stressing force at service is 1620 kN. The uniformly distributed load of 45 kN/m includes the self weight.
The stress (in N/mm2) in the bottom fibre at mid-span is
(a) tensile 2.90   (b) compressive 2.90
(c) tensile 4.32   (d) compressive 4.32                                Sol: (b)  stress= -P/A-P.e/z+M/z

Q.34 A symmetric frame PQR consists of two inclined members PQ and QR, connected at 'Q' with a rigid joint, and hinged at 'P' and 'R'. The horizontal length PR is l. If a weight W is suspended at 'Q', the bending moment at 'Q' is
(a) Wl/2    (b) Wl/4     (c) Wl/8      (d) zero                            Sol: (d)

Q.35 Two plates are connected by fillet welds of size 10mm and subjected to tension as shown in the figure. The thickness of each plate is 12mm. The yield stress and the ultimate tensile stress of steel are 250 MPa and 410 MPa respectively. The welding is done in the workshop (Ymw= 1.25). As per the Limit State Method of IS 800: 2007, the minimum length(rounded off to the nearest higher multiple of 5 mm) of each weld to transmit a force P equal to 270 kN is
(a) 100 mm    (b) 105 mm    (c) 110 mm    (d) 115 mm                    Sol: (b)

Q.36 Two soil specimens with identical geometric dimensions were subjected to falling head permeability tests in the laboratory under identical conditions. The fall of water head was measured after an identical time interval. The ratio of initial to final water heads for the test involving the first specimen was 1.25. If the co-efficient of permeability  of the specimen is 5 times that of the first, the ratio of initial to final water heads in the test involving the second specimen is
(a) 3.05  (b) 3.80   (c) 4.00    (d) 6.25                                  Sol: (a)   k = aL/At.[ln(h1/h2)]

Q.37 A layer of normally consolidated, saturated silty clay of 1 m thickness is subjected to one dimensional consolidation under a pressure increment of 20 kPa. The properties of the soil are: specific gravity = 2.7, natural moisture content = 45%, compression index = 0.45, and recompression index = 0.05. The initial average effective stress within the layer is 100 kPa. Assuming Terzaghi's theory to be applicable, the primary consolidation settlement(rounded off to the nearest mm) is
(a) 2 mm   (b) 9 mm    (c) 14 mm    (d) 16 mm                    Sol: (d)

Q.38 Steady state seepage is taking place through a soil element at Q,  2 m below the ground surface immediately downstream of the toe of an earthen dam as shown in the sketch. The water level in a piezometer installed at P, 500 mm above Q, is at the ground surface. The water level in a piezometer installed at R, 500 mm below Q, is 100 mm above the ground surface. The bulk saturated unit weight of the soil is 18 kN/m^3 and the unit weight of water is 9.81 kN.m3. The vertical effective stress (in kPa) at Q is
(a) 14.42   (b) 15.89   (c) 16.38    (d) 18.34                  Sol: (b)  Eff Stres = Ysat.h - Yw.hw

Q.39 The top width and depth of flow in a triangular channel were measured as 4 m and 1 m, respectively. The measured velocities on the centre line at the water surface, 0.2 m and 0.8 m below the surface are 0.7 m/sec, 0.6 m/sec and 0.4 m/sec, respectively. Using two- point method of velocity measurement, the discharge (in m^3/sec) in the channel is
(a) 1.4     (b) 1.2   (c) 1.0    (d) 0.8                      Sol: (c)  Vmean = (V0.2+V0.8)/2; Q= A.Vmean

Q.40 Group I contains parameters and Group II lists methods/instruments.
Group I                                                            Group II
P. Stream flow velocity                                                 1. Anemometer
Q. Evapo-transpiration rate                                           2. Penman's method
R. Infiltration rate                                                          3. Horton's method
S. Wind velocity                                                           4. Current meter
The CORRECT match of Group I with Group II is
(a) P-1, Q-2, R-3, S-4
(b) P-4, Q-3, R-2, S-1
(c) P-4, Q-2, R-3, S-1
(d) P-1, Q-3, R-2, S-4                                              Sol: (c)

Q.41 Wheat crop requires 55 cm of water during 120 days of base period. The total rainfall during this period is 100mm. Assume the irrigation efficiency to be 60%. The area(in ha) of the land which can be irrigated with a canal flow of 0.01 m^3/sec is
(a) 13.82     (b) 18.85    (c) 23.04     (d) 230.40             Sol:(a)

Q.42  A water sample has pH of 9.25. The concentration of hydroxyl ions in the water sample is
(a) 10^(-9.25) moles/L     (b) 10^(-4.75) moles/L   (c) 0.302 mg/L   (d) 3.020 mg/L
Sol: (c)
Q.43 A town is required to treat 4.2 m^2/min of water for daily domestic supply. Flocculating particles are to be produced by chemical coagulation. A column analysis indicated that an overflow rate of 0.2 mm/sec will produce satisfactory particle removal in a settling basin at a depth of 3.5 m. The required surface area (in m^2) for settling is
(a) 210   (b) 350     (c) 1728   (d) 21000                  Sol: (b) A= Q/V; Q=4.2 m^2/min;V=0.2mm/s

Q.44 A pavement designer has arrived at a design traffic of 100 million standard axles for a newly developing national highway as per IRC: 37 guidelines using the following data:
Design life = 15 years; commercial vehicle count before pavement construction = 4500 vehicles/day ; annual traffic growth rate = 8%. The vehicle damage factor used in the calculation was
(a) 1.53    (b) 2.24    (c) 3.66     (d) 4.14              Sol: (b) mSA= 365.A[(1+r)^n-1]*Vdf/r

Q.45 The following data are related to a horizontal curved portion of a two-lane highway: length of curve= 200 m, radius of curve = 300 m and width of pavement = 7.5 m. In order to provide a stopping sight distance(SSD) of 80 m, the set back distance (in m) required from the centre line of the inner lane of the pavement is
(a) 2.54   (b) 4.55   (c) 7.10   (d) 7.96                      Sol: (*)

Q.46 A two-lane urban road with one-way traffic has a maximum capacity of 1800 vehicles/hour. Under the jam condition, the average length occupied by the vehicles is 5.0 m. The speed versus density relationship is linear. For a traffic volume of 1000 vehicles/hour, the density (in vehicles/km) is
(a) 52   (b) 58   (c) 67   (d) 75                                 Sol: (c)

Q.47 The horizontal distance between two stations P and Q is 100 m. The vertical angles from P and Q to the top of a vertical tower at T are 3 Deg. and 5 Deg. above horizontal, respectively. The vertical angles from P and Q to the base of the tower are 0.1 D and 0.5 D below horizontal, respectively. Stations P, Q and the tower are in the same vertical plane with P and Q being on the same side of T. Neglecting earth's curvature and atmospheric refraction, the height (in m) of the tower is
(a) 6.972     (b) 12.387     (c) 12.540     (d) 128.745                Sol:(b)

Directions(Q.48- 49) : The flow net around a sheet pile wall is shown in the sketch. The properties of the soil are: permeability co-efficient = 0.09 m/day(isotropic), specific gravity = 2.70 and void ratio =0.85. The sheet pile wall and the bottom of the soil are impermeable.

Q.48 The seepage loss( in m^3 per day per unit length of the wall) of water is
(a) 0.33   (b) 0.38    (c) 0.43    (d) 0.54                                 Sol: (b)

Q.49 The factor of safety against occurrence of piping failure is
(a) 3.55   (b) 2.93     (c) 2.60     (d)  0.39                                  Sol:(c)

Directions(Q.50- 51): An activated sludge system(sketched below) is operating at equilibrium with the following information.
Waste water related data: flow rate = 500 m^3/hour, influent BOD = 150 mg/L, effluent BOD = 10 mg/L. Aeration tank related data: hydraulic retention time = 8 hours, mean-cell-residence time = 240 hours, volume = 4000 m^3, mixed liquor suspended solids = 200 mg/L

Q.50 The food to biomass (F/M) ratio (in kg BOD per kg biomass per day) for the aeration tank is
(a) 0.015    (b) 0.210    (c) 0.225    (d) 0.240                   Sol: (c) F/M = 500*150/ (200*4000) kg/hr

Q.51 The mass (in kg/day) of solids wasted from the system is
(a) 24000    (b) 10000   (c) 800    (d) 33                          Sol: (a) M= 200*500*1000*24 kg/day

Directions (Q.52-53) : The cross section at mid span of a beam at the edge of a slab is shown in the sketch. A portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are M25 and Fe415 respectively. The total area of reinforcing bars (A) is 4000 mm^2. At the ultimate limit state, xu denotes the depth of the neutral axis from the top fibre. Treat the section as under reinforced and flanged (xu>100 mm).

Q.52 The value of xu(in mm) computed as per the Limit State Method of IS:456:2000 is
(a) 200.0  (b) 223.3   (c) 236.3    (d) 273.6                Sol: (c)

Q.53 The ultimate moment capacity (in kNm) of the section as per the Limit State Method of IS:456:2000 is
(a) 475.2    (b) 717.0    (c) 756.4    (d) 762.5           Sol: (b)

Directions (Q.54-55): The drainage area of a watershed is 50 km^2. The phi index is 0.5 cm/hour and the base flow at the outlet is 10 m^3/sec. One hour unit hydrograph (unit depth = 1cm) of the watershed is triangular in shape with a time base of 15 hours. The peak ordinate occurs at 5 hours.

Q.54 The peak ordinate (in m^3/s/cm) of the unit hydro-graph is
(a) 10.00    (b) 18.52    (c) 37.03    (d) 185.20                Sol: (b)

Q.55 For a storm of depth of 5.5 cm and duration of 1 hour, the peak ordinate (in m^3/sec) of the hydro graph is

(a) 55.00    (b) 82.60     (c) 92.60       (d) 102.60           Sol: (c)

GENERAL APTITUDE (GA) QUESTIONS
Q.56-Q.60 carry one mark each
Q.56 Choose the most appropriate alternative from the options given below to complete  the following sentence:
Suresh's dog is the one ............ was hurt in the stampede.
(a) that   (b) which    (c) who    (d) whom                   Sol:(*)

Q.57 The cost function for a product in a firm is given by 5.q^2, where q is the amount of production. The firm can sell the product at a market price of Rs. 50 per unit. The number of units to be produced by the firm such that the profit is maximized is
(a) 5    (b) 10    (c) 15    (d) 25                            Sol: (a)

Q.58 Choose the most appropriate alternative from the options given below to complete the following sentence:
Despite several ........ the mission succeeded in its attempt to resolve the conflict.
(a) Alternative   (b) setbacks    (c) meetings     (d) delegations   Sol: (b)

Q.59 Which one of the following options is closest in meaning to the word given below?
Mitigate
(a) Diminish      (b) Divulge     (c) Dedicate   (d) Denote             Sol:(a)

Q.60 Choose the grammatically INCORRECT sentence:
(a) They gave us the money back less the service charges of Three Hundred rupees.
(b) This country's expenditure is not less than that of Bangladesh.
(c) The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser sum.
(d) This country's expenditure on educational reforms is very less. Sol: (d)

Q. 61 - Q. 65 carry two marks each.

Q.61 Given the sequence of terms, AD CG FK JP, the next term is
(A) OV (B) OW (C) PV (D) PW                                     Sol: (a)

Q.62 Wanted Temporary, Part-time persons for the post of Field Interviewer to conduct personal
interviews to collect and collate economic data. Requirements: High School-pass, must be
available for Day, Evening and Saturday work. Transportation paid, expenses reimbursed.
Which one of the following is the best inference from the above advertisement?
(A) Gender-discriminatory
(B) Xenophobic
(C) Not designed to make the post attractive

(D) Not gender-discriminatory                                             Sol: (d)

Q.63 A political party orders an arch for the entrance to the ground in which the annual convention is
being held. The profile of the arch follows the equation y = 2x – 0.1x2 where y is the height of the
arch in meters. The maximum possible height of the arch is
(A) 8 meters (B) 10 meters (C) 12 meters (D) 14 meters        Sol:(b)

Q.64  An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies
60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.
The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable.
Of Y’s shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y
is
(A) 0.288 (B) 0.334 (C) 0.667 (D) 0.720   Sol: (b)

Q.65 Which of the following assertions are CORRECT?
P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged
(A) P, Q (B) Q, R (C) P, R (D) R, S               Sol:(c)

(* )means marks to all
END OF THE QUESTIONS
(References:  GATE 2013  by GK Publishers)

## Saturday, August 24, 2013

### Tacheometry (Surveying)

Hi,

Tacheometry is the branch of Surveying in which we determine the horizontal and vertical distances with the angular measurements with an instrument , Tacheometer.

It is not so accurate method of finding the horizontal distances as the Chaining is, but it is most suitable for carrying out the surveys to find the distances in the hilly area where other methods are quite difficult being carried out. It is generally used to locate contours, hydrographic surveys and laying out routes of highways, railways etc.

The instruments required for carrying out the Tacheometric survey are:
(1) A Tacheometer (2) A Stadia Rod.

• Tacheometer: Tacheometer is more or less a Theodolite installed with  a stadia diaphragm. Stadia diaphragm is equiped with three horizontal hairs and one vertical hair. So we can take three vertical staff reading at the same instruments setting, lower most hair reading, central hair reading and the top hair reading. The difference between the lower hair reading and the upper hair reading gives the staff intercept(s).

The Tacheometer with the analactic lens are famous because their additive constant is 0. There is one concave lens introduced between the eye piece and the object piece to eliminate the additive constant of the instrument. It simplifies the calculations.
Methods of Tacheometric Survey:
(A) Stadia Hair Method

1. Fixed Hair Method
2. Movable Hair Method

(B) Tangential Method

### (A)Stadia Hair Method:

• As the name suggests in this method theodolite with the stadia diaphragm is used to find out the staff intercept between the lower and upper hairs and also the central hair reading is noted.

Principle of Stadia hair method is that the ratio of the length of perpendicular to the base is constant in case of similar triangles.

1. Fixed Hair Method: In the fixed hair method the cross hairs of the diaphragm are kept at a constant distance apart and the staff intercept varies with the horizontal and vertical position of the staff with respect to the Theodolite.
2. Movable Hair Method: In this method the staff intercept between the lower hair and the upper hair is kept constant by moving the horizontal cross hairs in the vertical plane.

Formula to carry out calculation works:
Case:

### (a) Staff held vertical:

 Tacheometry -Staff held vertical

D = (f/i).s+ (f+d)
where, f/i = multiplying constant
s = staff intercept between the bottom and top hair
f+d = Additive constant
D = Horizontal distance between the staff station and the observer's position

### (b) Inclined sights staff held vertical:

D = (f/i).s. cos^2A + (f+d) cosA
V = {(f/i).s.} .[{sin(2A)}/2] + (f+d) sinA
Where A is the angle of elevation or angle of depression.

### (c) Inclined sights upwards, staff held normal:

D = [(f/i).s+ (f+d)]cosA - h.sinA  ;    V= [(f/i).s+ (f+d)].sinA
h= central hair reading.
R.L. of staff = H.I. + [(f/i).s+ (f+d)].sinA - hcosA

### (d) Inclined sights downwards, staff held normal:

D = [(f/i).s+ (f+d)]cosA - h.sinA  ;  V= [(f/i).s+ (f+d)].sinA
R.L. of staff = H.I. + [(f/i).s+ (f+d)].sinA - hcosA

### (B)Tangential Method:

In Tangential method only central hair reading is noted down and generally two angular observations are taken to calculate the horizontal and vertical distances.

Thanks!

Reference: Surveying Vol-1  Dr. B.C.Punmia

Check these books.

## Friday, August 23, 2013

### Contours - Characteristics and Uses

Hello,

You can walk along the spaced contours much more easily, as compared to the crowded contours. Do yo know what is a contour?
Here are certain terms which are useful in understanding the contours.
• Contour -  Contour is an imaginary line on ground joining points of equal or constant elevations. contours are important to draw the topographical maps in which vertical distances are also shown using the contour lines.

• Contour interval: Vertical distance between any two consecutive contours is known as the contour interval. It depends upon the scale of the map, nature of the ground and availability of the fund  and time.

• Horizontal equivalent/ horizontal interval:  It is the shortest horizontal distance between the two consecutive contours.

• Contour Gradient: Imaginary line on the surface of the earth, maintains a constant angle to the horizontal.

### Characteristics of the contours:

1. Two contours of different elevation do not cross each other with only exception in the contours of a overhanging cliff.
2. Contours of different elevations do not combine or overlap to each other with exception in the contours of a vertical cliff.
3. When contours are drawn closer to each other, it shows a steep slope on the ground and when they are far apart it shows the gentle slope on the ground.
4. When contours are equally spaced they represent a uniform slope, and when they are parallel straight and equivalent they represent a plane surface.
5. A contour is perpendicular to a line of the steepest slope.
6. A contour must close itself in the map or must go out of the boundaries of the map.
7. A set of ring contours with higher values of contour inside and lower values outside represents a hill and if the higher values are outside and lower values inside then it represents a depression like a pond.
8. When contours cross a ridge they form a V- shape across them. While if they cross a valley they form a u-shape or may a V shape also difference being, the concavity of the contour lines lies towards the lower contours in case of valley while it is convexity lying towards the another lower value in case of contours of a ridge.

Uses of Contours:

1.  To study the general character of the tract of the country without visiting the ground. With the knowledge of characteristics of contours, it is easy to visualize whether country is flat, undulating or mountainous.
2. To decide the sites for engineering works such as reservoirs, canals, roads and railways etc. on the basis of the economy.
3. To determine the catchment area of the drainage basin and hence capacity of the proposed reservoir.
4. To compute the earth work required for filling or cutting along the linear alignment of the projects such as canals, roads, etc.
5. To find out the inter-visibility of the points.
6. To trace out a contour gradient for road alignments.
7. To draw longitudinal and cross- sections to ascertain nature of  the ground.
Thank you!!

References:
Surveying Vol-I  by Dr. B. C. Punmia

## Thursday, August 22, 2013

### Theodolite and Useful Terms

Hi,

• Theodolite: Theodolite is the most precise instrument designed for the measurement of the horizontal and vertical angles.

Commonly used terms in a Theodolite Survey:

• (a) Centering: It means setting the Theodolite exactly over an instrument station so that its vertical axis passes through the station mark. It is done with the help of a Plumb bob suspended from the vertical axis of the Theodolite.
• (b) Transiting: It is the process of reversing the telescope/line of sight about the horizontal axis in the vertical plane.
• (c)Face Left and Face Right : If the vertical circle of the Theodolite is on the left side of the observer, then the observation taken are known as Face Left observations. Similarly if the vertical circle is on the right, the observation taken such as are known as Face Right observations.
• (d) Line of collimation : Line of collimation or also known as the line of sight is the imaginary line joining the center of the cross hairs and the center of the object glass and its continuation.
• (e)Axis of level Tube: It is a line tangential to the longitudinal curve of the level tube at the center of the tube, it is also known as the bubble line. When the instrument is level in horizontal plane, i.e. bubble is central this axis is horizontal.
• Classification of Theodolite:

There are two broad classification of Theodolite
(a) Transit Theodolite   (b) Non Transit Theodolite

• (a) Transit Theodolite: In this type of theodolite the line of sight can be revolved about trunion  axis/ horizontal axis through 180 degrees in the vertical plane.
• (b) Non- Transit Theodolite: It can not be transited as in the case of a transit Theodolite.
Another classification of the Theodolite can be done on the basis of the type of the scale fitted to the Theodolite i.e. vernier or micrometer.
(i) Vernier Theodolites.
(ii) Micrometer Theodolites.

Diameter of the lower plate of the graduated circle determines the size of the Theodolite. Commonly they are available in 8 cm or 12 cm sizes while 14 cm and 25 cm instruments are used for triangulation work.

Thanks for your kind visit!

## Monday, August 19, 2013

### Plane Table Survey - Surveying(Civil Engineering)

Hello,

A short introduction to plane tabling- A graphical method of Surveying.

Plane Table Survey:

Plane Table Survey is a method of Surveying in which field work and the office work are done simultaneously. It is also known as the graphical method of Surveying. A manuscript map is made in the field and the topographic details can be filled in later.

 Plane-Table Cut-a-way, shows a part of the table and the tripod stand

List of Instruments used in Surveying:

• (1) Plane Table
• (3) Plumbing fork and Plumb bob
• (4) Spirit Level
• (5) Chain or Tape
• (6) Rain roof cover for the plane table
• (7) Compass
• (8) Ranging Rods
• (9) Drawing Sheets
• (10) Drawing equipment.

Procedure: To do the plane tabling one has to follow the following procedure at every plane table set-up:

• (a) Fixing the plane table to the tripod stand
• (b)Setting up and temporary adjustments:

1.     Leveling the plane table with the help of spirit level
2.    Centering with the help of plumbing fork
3.     Orientation by trough compass or by back sighting

• (c) Sighting the points with the help of Alidade

Methods of plane tabling:

1. For locating details:

(a) Radiation Method: A ray is drawn towards the point with the help of the Alidade.  With the help of Chain or Tape the horizontal distance is measured from the Plane Table to the point and this point is located on the sheet by plotting it into the scale of the map.

(b) Intersection Method: In this method two instrument stations are used but no chain or tape is required. Intersecting rays are drawn from these two stations whose location is already plotted (by measuring the distance between them), the point of intersection is the location of the point.

2. For locating Plane Table Stations:
(a) Traversing: In this method the location of the Plane Table station is located in the following manner:
(1) At previous station a ray is drawn in the forward direction(Toward next station) and point is plotted by measuring the horizontal distance and plotting it to scale.
(2) Instrument is shifted to next station(which is just located in first step) and the previous station is back-sighted to orient the plane table.

(b) Resection: Resection the process of finding the position of a station where plane table, is placed, with the help of sights taken towards known and visible points whose location has already been plotted.

First of all the plane table is oriented correctly by one of the four given methods:
(1) Orientation by trough compass
(2) Orientation by back sighting
(3) Orientation by two point problem
(4) Orientation by three point problem

Then afterwards point is located.

Thank You!