GATE 2017 Question Paper (CE 02) with Answer Keys for Civil Engineering (CE) - Grad Plus

# GATE 2017 Question Paper (CE 02) with Answer Keys for Civil Engineering (CE)

Q.1- Consider the following simultaneous equations ( with c1 and c2 being constants):

3 x1 + 2 x2 = c1

4 x1 + x2 = c2

The characteristic equation for these simultaneous equation is

(A) \lambda^2-4\lambda-5=0

(B) \lambda^2-4\lambda+5=0

(C) \lambda^2+4\lambda-5=0

(D) \lambda^2+4\lambda+5=0

Ans: (A) \lambda^2-4\lambda-5=0

Q.2- Let w = f (x, y), where x and y are functions of t. Then, according to the chain rule, \frac{dw}{dt} is equal to

(A) \frac{dw}{dx}\frac{dx}{dt}+\frac{dw}{dy}\frac{dt}{dt}

(B) \frac{\partial w}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial w}{\partial y}\frac{\partial y}{\partial t}

(C) \frac{\partial w}{\partial x}\frac{dx}{dt}+\frac{\partial w}{\partial y}\frac{dy}{dt}

(D) \frac{dw}{dx}\frac{\partial x}{\partial t}+\frac{dw}{dy}\frac{\partial y}{\partial t}

Ans: (C) \frac{\partial w}{\partial x}\frac{dx}{dt}+\frac{\partial w}{\partial y}\frac{dy}{dt}

Q.3- Given that the scope of the construction work is well-defined with all its drawings, specifications, quantities and estimates, which one of the following types of contract would be most preferred?

(A) EPC contract

(B) percentage rate contract

(C) Item rate contract

(D) Lump sum contract

Ans: (D) Lump sum contract

Q.4- Let G be the specific gravity of soil solids, w the water content in the soil sample,ϒw the unit weight of water, and ϒd the dry unit weight of the soil. The equation for the zero air voids line in a compaction test plot is

(A) \gamma_d=\frac{G\gamma_w}{1+Gw}

(B) \gamma_d=\frac{G\gamma_w}{Gw}

(C) \gamma_d=\frac{Gw}{1+\gamma_w}

(D) \gamma_d=\frac{Gw}{1-\gamma_w}

Ans: (A) \gamma_d=\frac{G\gamma_w}{1+Gw}

Q.5- Consider the following statements related to the pore pressure parameters, A and B:

P. A always lies between 0 and 1.0

Q. A can be less than 0 or greater than 1.0

R. B always lies between 0 and 1.0

S. B can be less than 0 or greater than 1.0

For these statements, which one of the following options is correct?

(A) P and R

(B) P and S

(C) Q and R

(D) Q and S

Ans: (C) Q and R

Q.6- Consider a rigid retaining wall with partially submerged cohensionless backfill with a surcharge. Which one of the following diagrams closely represents the Rankine’s active earth pressure distribution against this wall?

Ans: Mark to all

Q.7- If a centrifugal pump has an impeller speed of N (in rpm), discharge Q (in m3/s) and the total head H (in m), the expression for the specific speed Ns of the pump is given by

(A) N_s=\frac{NQ^{0.5}}{H^{0.5}}

(B) N_s=\frac{NQ^{0.5}}H

(C) N_s=\frac{NQ^{0.5}}{H^{0.75}}

(D) N_s=\frac{NQ}{H^{0.75}}

Ans: N_s=\frac{NQ^{0.5}}{H^{0.75}}

Q.8- As per Noise pollution (Regional and control) Rules 2000 of India, the day time noise limit for a residential zone, expressed in dB(A)Leq, is

(A) 55

(B) 65

(C) 75

(D) 85

Ans: (A) 55

Q.9- Following observations have been made for the elevation and temperature to ascertain the stability of the atmosphere:

The atmosphere is classified as

(A) Stable

(B) Unstable

(C) Neutral

(D) Inverse

Ans: (B) Unstable

Q.10- The most important type of species involve in the degradation of organic matter in the case of activated sludge process is

(A) autotrophs

(B) heterotrophs

(C) prototrophs

(D) photo-autotrophs

Ans: (B) heterotrophs

Q.11- For a board guage railway track on a horizontal curve of radius R (in m), the equilibrium cant e required for a train moving at a speed of V (in km per hour) is

(A) e=1.676\frac{V^2}R

(B) e=1.315\frac{V^2}R

(C) e=0.80\frac{V^2}R

(D) e=0.60\frac{V^2}R

Ans: (B) e=1.315\frac{V^2}R

Q.12- The safety within a roundabout and the efficiency of a roundabout can be increased, respectively, by

(A) increasing the entry radius and increasing the exit radius

(B) increasing the entry radius and decreasing the exit radius

(C) decreasing the entry radius and increasing the exit radius

(D) decreasing the entry radius and decreasing the exit radius

Ans: (C) decreasing the entry radius and increasing the exit radius

Q.13- The method of orientation used, when the plane table occupies not yet located on the map, is called as

(A) traversing

(B) radiation

(C) levelling

(D) resection

Ans: (D) resection

Q.14- Consider the frame shown in the figure:

If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree of kinematical indeterminacy would be equal to

(A) 5

(B) 6

(C) 7

(D) 8

Ans: (B) 6

Q.15- Let the characteristics strength be defined as that value, below which not more than 50% of the results are expected to fall. Assuming a standard deviation of 4 MPa,  the target mean strength (in MPa) to be considered in the mix design of a M25 concrete would be

(A) 18.42

(B) 21.00

(C) 25.00

(D) 31.58

Ans: (C) 25.00

Q.16- In a material under a state of plane strain, a 10×10 mm square centered at a point gets deformed as shown in the figure.

If the shear strain Υxy of this point is expressed as 0.001 K (in rad), the value of K is

(A) 0.50

(B) 0.25

(C) -0.25

(D) -0.50

Ans: A or D

Q.17- The plate load test was conducted on a clayey strata by using a plate of 0.3 m × 0.3 m dimensions, and the ultimate load per unit area for the plate was found to be 180 kPa. The ultimate bearing capacity (in kPa) of a 2 m wide square footing would be

(A) 27

(B) 180

(C) 1200

(D) 2000

Ans:  (B) 180

Q.18- For a construction project, the mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be _____

Ans: 209 to 219

Q.19- The divergence of the vector field V = x2 i + 2 y3 j + Z4 k at x = 1, y = 2, z = 3 is ______

Ans: 133.9 to 134.1

Q.20- A two-faced fair coin has its faces designated as head (H) and tale (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be _____

Ans: 0.5 to 0.5

Q.21- A sheet pile has an embedment depth of 12 m  in a homogeneous soil stratum. The coefficient of permeability of soil is 10-6 m/s. Different in the water levels between the two sides of the sheet pile is 4 m. The flow net is constructed with five number of flow lines and eleven number of equipotential lines. The quantity of seepage (in cm3/s per m, up to one decimal place) under the sheet pile is ______

Ans: 1.6 to 1.6

Q.22- The VPI ( vertical point of intersection ) is 100 m away ( when measured along the horizontal) from the VPC ( vertical point of curvature). If the vertical curve is parabolic, the length of the curve (in meters and measured along the horizontal) is _____

Ans: 199.99 to 200.01

Q.23- During a storm event in a certain period, the rainfall intensity is 3.5 cm/hour and the Φ-index is 1.5 cm/hour. The intensity of effective rainfall (in cm/hour, up to one decimal place) for this period is _____

Ans: 1.9 to 2.1

Q.24- The infiltration capacity of a soil follows the Horton’s exponential model, f = C1 + C2e -kt. During an experiment, the initial infiltration capacity was observed to be 200 mm/h. After a long time, the infiltraion capacity was reduced to 25 mm/h. If the infiltration capacity after 1 hour was 90 mm/h, the value of the decay rate constant, k (in h-1, up to two decimal places) is ______

Ans: 0.98 to 1.00

Q.25- While aligning a hill road with a ruling gradient of 6%, a horizontal curve of radius 50 m is encountered. The grade compensation (in percentage, up to two decimal places) to be provided for this case would be ____

Ans: 1.49 to 1.51

Q.26- The tangent to the curve represented by y=x\;\ln\;x is required to have 450 inclination with the x-axis. The coordinates of the tangent point would be

(A) (1,0)

(B) (0,1)

(C) (1,1)

(D) \left(\sqrt{2\;}\sqrt2\right)

Ans: (A) (1,0)

Q.27- Consider the following definite integral:

I=\int_0^1\frac{\left(\sin^{-1}x\right)^2}{\sqrt{1-x^2}}dx

The value of the integral is

(A) \frac{\pi^3}{24}

(B) \frac{\pi^3}{12}

(C) \frac{\pi^3}{48}

(D) \frac{\pi^3}{64}

Ans: (A) \frac{\pi^3}{24}

Q.28- If A=\begin{bmatrix}1&5\\6&2\end{bmatrix} and B=\begin{bmatrix}3&7\\8&4\end{bmatrix}, ABT is equal to

(A) \begin{bmatrix}38&28\\32&56\end{bmatrix}

(B) \begin{bmatrix}3&40\\42&8\end{bmatrix}

(C) \begin{bmatrix}43&27\\34&50\end{bmatrix}

(D) \begin{bmatrix}38&32\\28&56\end{bmatrix}

Ans: (A) \begin{bmatrix}38&28\\32&56\end{bmatrix}

Q.29- Consider the following second-order differential equation:

y” – 4y’ + 3y = 2t – 3t2

The particular solution of the differential equation is

(A) -2 -2t -t2

(B) – 2t – t2

(C) 2t – 3t

(D) -2 -2t – 3t2

Ans: (A) -2 -2t -t2

Q.30- Group I gives a list of test methods and test apparatus for evaluating some of the properties of Ordinary Portland Cement (OPC) and concrete. Group II gives the list of these properties.

The correct match of the items in Group I with the items in Group II is

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

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

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

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

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

Q.31- Two prismatic beams having the same flexural rigidity of 1000 kN-m2 are shown in the figures.

If the mid-span deflections of these beams are denoted by δ1 and δ2 (as indicated in the figures), the correct option is

(A) δ1 = δ2

(B) δ1 < δ2

(C) δ1 > δ2

(D) δ1 >> δ2

Ans: (A) δ1 = δ2

Q.32- Consider the three prismatic beams with the clamped supports, P, Q, and R as shown in the figures.

Given that the modulus of elasticity, E is 2.5×104 MPa; and the moment of inertia, I is 8×108 mm4, the correct comparison of the magnitudes of the shear force S and the bending moment M developed at the supports is

(A) SP < SQ < SRMP =MQ =MR

(B) SP =SQ >SR;    MP =MQ >MR

(C) SP <SQ >SRMP =MQ =MR

(D) SP <SQ <SRMP <MQ <MR

Ans: (C) SP <SQ >SRMP =MQ =MR

Q.33- Consider the following statements:

P. Wall of one brick thick are measured in square meters.

Q. Walls of one brick thick are measured in cubic meters.

R. No deduction in the brickwork quantity is made for openings in walls up to 0.1 m2 area.

S. For the measurement of excavation from the borrow pit in a fairly uniform ground, deadmen are left at suitable intervals.

For the above statements, the correct option is

(A) P-False;  Q-True;  R-False;  S-True

(B) P-False;  Q-True;  R-False;  S-False

(C) P-True;  Q-False;  R-True;  S-False

(D) P-True;  Q-False;  R-True;  S-True

Ans: (D) P-True;  Q-False;  R-True;  S-True

Q.34- Two identical concrete piles having the plan dimensions 50 cm × 50 cm are driven into a homogeneous sandy layer as shown in the figures. Consider the being capacity factor Nq for \phi=30^0 as 24.

If QP1 and QP2 represent the ultimate point bearing resistances of the piles under dry and submerged conditions, respectively, which one of the following statements is correct?

(A) QP1 >QP2 by about 100%

(B) QP1 <QP2 by about 100%

(C) QP1 >QP2 by about 5%

(D) QP1 <QP2 by about 5%

Ans: (A) QP1 >QP2 by about 100%

Q.35- Following are the statemetns related to the stress paths in a triaxial testing of soils:

P. If \sigma_1=\sigma_3, the stress point lies at the origin of the p-q plot.

Q. If \sigma_1=\sigma_3, the stress point lies on the p-axis of the p-q plot.

R. If \sigma_1>\sigma_3, both the stress points p and q are positive.

For the above statements, the correct combination is

(A) P-False;  Q-True;  R-True

(B) P-True;  Q-False;  R-True

(C) P-False;  Q-True;  R-False

(D) P-True;  Q-False;  R-False

Ans: (A) P-False;  Q-True;  R-True

Q.36- Two cars P and Q are moving in a racing track continuously for two hours. Assume that no other vehicles are using the track during this time. The expressions relating the distance travelled d (in km) and time t (in hour) for both the vehicles are given as

P:d = 60t

Q:d = 60t2

Within the first one hour, the maximum space headway would be

(A) 15 km at 30 minutes

(B) 15 km at 15 minutes

(C) 30 km at 30 minutes

(D) 30 km at 15 minutes

Ans: (A) 15 km at 30 minutes

Q.37- For the construction of a highway, a cut is to be made as shown in the figure.

The soil exhibits c’ = 20 kPa, ∅’ = 180, and the undrained shear strength = 80 kPa. The unit weight of water is 9.81 kN/m3. The unit weights of the soil above and below the ground water table are 18 and 20 kN/m3, respectively. If the shear stress at point A is 50 kPa, the factors of safety against the shear failure at this point, considering  the undrained and drained conditions, respectively, would be

(A) 1.6 and 0.9

(B) 0.9 and 1.6

(C) 0.6 and 1.2

(D) 1.2 and 0.6

Ans: (A) 1.6 and 0.9

Q.38- Two towers, A and B, standing vertically on a horizontal gorund, appear in a vertical aerial photograph as shown in the figure.

The length of the image of the tower A on the photograph is 1.5 cm and of the tower B is 2.0 cm. The distance of the top of the tower A (as shown by the arrowhead) is 4.0 cm and the distance of the top of the tower B is 6.0 cm, as measured from the principal point p of the photograph. If the height of the tower B is 80 cm, the height (in meters) of the tower A is _____

Ans: 89 to 91

Q.39- A hollow circular shaft has an outer diameter of 100 mm inner diameter of 50 mm. If the allowable shear stress is 125 MPa, the maximum torque (in kN-m) that the shaft can resist is _____

Ans: 20 to 25

Q.40- A simply supported rectangular concrete beam of span 8 m has to be prestressed with a force of 1600 kN. The tendon is of parabolic profile having zero eccentricity at the supports. The beam has to carry an external uniformly distributed load of intensity 30 kN/m. Neglecting the self-weight of the beam, the maximum dip (in meters, up to two decimal places) of the tendon at the mid-span to balance the external load should be _____

Ans: 0.14 to 0.16

Q.41- Two plates of 8 mm thickness each are connected by a fillet weld of 6 mm thickness as shown in the figure.

The permissible stress in the plate and the weld are 150 MPa and 110 MPa, respectively. Assuming the length of the shown in the figure to be the effective length, the permissible load P (in kN) is

Ans: 59 to 61

Q.42- Consider the portal frame shown in the figure and assume the modulus of elasticity, E=2.5×104 MPa and the moment of inertia, I=8×108 mm4 for all h=the members of the frame.

The rotation (in degrees, up to one decimal place) at the rigid joint Q would be ____

Ans: 0.9 to 1.1

Q.43- A 2 m long, axially loaded mild steel rod of 8 mm diameter exhibits the load-displacement (p-δ) behavior as shown in the figure.

Assume the yield stress of steel as 250 MPa. The complementary strian energy (in N-mm) stored in the bar up to its linear elastic behavior will be ____

Ans: Mark to all

Q.44- Consider a square-shaped area ABCD on the ground with its centre at M as shown in the figure. Four concentrated vertical loads of P= 5000 kN are applied on this area, one at each corner.

The vertical stress increment (in kPa, up to one decimal place) due to these loads according to the Boussinesq’s equation, at a point 5 m right below m, is ______

Ans: 187.0 to 192.0

Q.45- The figure shows a U-tube having a 5 mm × 5 mm square cross-section filled with mercury (specific gravity=13.6) up to a height of 20 cm in each limb (open to the atmosphere).

If 5 cm3 of water is added to the right limb, the new height (in cm, up to two decimal places) of mercury in the LEFT limb will be ____

Ans: 20.70 to 20.76

Q.46- A 1 m wide rectangular channel carries a discharge of 2 m3/s. The specific energy-depth diagram is prepared for the channel. It is observed in this diagram that corresponding to a particular specific energy, the subcritical depth is twice the supercritical depth. The subcritical depth (in meters, up to two decimal places) is equal to ____

Ans: 1.06 to 1.08

Q.47- A catchment is idealized as a 25 km × 25 km square. It has five rain gauges, one at each corner and one at the center, as shown in the figure.

During a month, the precipitation at these gauges is measured as G1 = 300 mm, G2 = 285 mm, G3 =272 mm, G4 =290 mm and G5 =288 mm. The average precipitation (in mm, up to one decimal place) over the catchment during this month by using the Thiessen polygon method is _____

Ans: 286.9 to 287.9

Q.48-  The culturable command area of a canal is 10,000 ha. The area grows only two crops–rice in the Kharif season and wheat in the Rabi season. The design discharge of the canal is based on the rice requirements, which has an irrigated area of 2500 ha, base period of 150 days and delta of 130 cm. The maximum permissible irrgated area (in ha) for wheat, with a base period of 120 days and delta of 50 cm, is ____

Ans: 5150 t0 5250

Q.49- Water is pumped at a steady uniform flow rate of 0.01 m3/s through a horizontal smooth circular pipe of 100 mm diameter. Given that the Reynolds number is 800 and g is 9.81 m2/s, the head loss (in meters, up to one decimal place) per km length due to friction would be ____

Ans:65.0 to 69.0

Q.50- The composition of a municipal solid waste sample is given below:

The difference between the energy content of the waste sample calculated on dry basis and as-discarded basis (in kJ/kg) would be _____

Ans: 3850 to 3900

Q.51- For a given water sample, the ratio between BOD5day, 200C and the ultimate BOD is 0.68. The value of the reaction rate constant k (on base e) (in day-1, up to two decimal places) is _____

Ans: 0.22 to 0.24

Q.52- A municipal corporation is required to treat 1000 m3/day of water. It is found that on overflow rate of 20 m/day will produce a satisfactory removal of the discrete suspended particles at a depth of 3 m. The diameter (in meters, rounded to the nearest integer) of a circular setting tank designed for the removal of these particles would be ______

Ans: 8 to 8

Q.53- The analysis of a water sample produces the following results:

The total hardness (in mg/L as CaCO3) of the water sample is _____

Ans: 300 to 300

Q.54- The radii of relative stiffness of the rigid pavements P and Q are denoted by lp and lQ, respectively. The geometric and material properties of the concrete slab and underlying soil are given below:

The ratio (up to one decimal place) of lp/lQ is _____

Ans: 1.9 to 2.1

Q.55- An observer standing on the deck of a ship just sees the top of a lighthouse. The top of the lighthouse is 40 m above the sea level and height of the observer’s eye is 5 m above from the lighthouse is ______

Ans: 32.5 to 33.5

Q.56-  The event would have been successful if you _____ able to come.

(A) are

(B) had been

(C) have been

(D) would have been

Ans: (B) had been

Q.57- There was no doubt that their work was through.

Which of the words below is closet in meaning to the underlined word above?

(A) pretty

(B) complete

(C) sloppy

(D) haphazard

Ans: (B) complete

Q.58- Four cards lie on a table. Each card has a number printed on one side a colour on the other. The faces visible on the cards are 2, 3, red, and blue.

Proposition: If a card has an even value on one side, then its opposite face is red.

The cards which MUST be turned over to verify the above proposition are

(A) 2, red

(B) 2, 3, red

(C) 2, blue

(D) 2, red, blue

Ans: (C) 2, blue

Q.59- What is the value of x when 81\times\left(\frac{16}{25}\right)^{x+2}\div\left(\frac35\right)^{2x+4}=144?

(A) 1

(B) -1

(C)-2

(D) cannot be determined

Ans: (B) -1

Q.60- Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

(A) 1/9

(B) 2/9

(C) 1/3

(D) 4/9

Ans: (B) 2/9

Q.61- Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in a matter of minutes while for others it took much longer.

From this, what can one conclude?

(A) The centre operates on a first-come-first-served basis, but with variable service times, depending on specific customer needs.

(B) Customers were served in an arbitrary order, since they took varying amounts of time for service completion in the centre.

(C) Since some people came out within a few minutes of entering the centre, the system is likely to operate on a last-come-first-served basis.

(D) Entering the centre early ensured that one would have shorter service times and most people attempted to do this.

Ans:  (A) The centre operates on a first-come-first-served basis, but with variable service times, depending on specific customer needs.

Q.62- A map shows the elevations of Darjeeling, Gangtok, Kalimpong, Pelling, and Siliguri. Kalimpong is at a lower elevation than Gangtok. Pelling is at a lower elevation than Gangtok. Pelling is at a higher elevation than Siliguri. Darjeeling is at a higher elevation than Gangtok.

Which of the following statements can be inferred from the paragraph above?

i.  Pelling is at a higher elevation than Kalimpong

ii.  Kalimpong is at a lower elevation than Darjeeling

iii.  Kalimpong is at a higher elevation than Siliguri

iv.  Siliguri is at a lower elevation than Gangtok

(A) Only i

(B) Only ii and iii

(C) Only ii and iv

(D) Only iii and iv

Ans: (C) Only ii and iv

Q.63- P, Q, R, S, T and U are seated a circular table. R is seated two places to the right of Q. P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats, which of the following must necessarily be true?

(A) P is immediately to the right of R

(B) T is immediately to the left of P

(C) T is immediately to the left of P or P is immediately to the right of Q

(D) U is immediately to the right of R or P is immediately  to the left of T

Ans: (C) T is immediately to the left of P or P is immediately to the right of Q

Q.64- Budhan covers a distance of 19 km in 2 hours by cycling one fourth of the time and walking the rest. The next day he cycles (at the same speed as before) for half the time and walks the rest (at the same speed as before) and covers 26 km in 2 hours. The speed in km/h at which Budhan walks is

(A) 1

(B) 4

(C) 5

(D) 6

Ans: (D) 6

Q.65- The points in the graph below represent the halts of a lift for durations of 1 minute, over a period of 1 hour.

Which of the following statements are correct?

i. The elevator never moves directly from any non-ground floor to another non-ground floor over the one hour period

ii. The elevator stays on the fourth floor for the longest duration over the one hour period

(A) Only i

(B) Only ii

(C) Both i and ii

(D) Neither i nor ii

Ans: (D) Neither i nor ii

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