Firstranker's choice
GATE 2016
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Q. 1 – Q. 5 carry one mark each.
Q.1 If I were you, I __________ that laptop. It's much too expensive.
(A) won't buy (B) shan't buy
(C) wouldn't buy (D) would buy
Q.2 He turned a deaf ear to my request.
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What does the underlined phrasal verb mean?
(A) ignored (B) appreciated
(C) twisted (D) returned
Q.3 Choose the most appropriate set of words from the options given below to complete the following sentence.
__________ is a will, __________ is a way.
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(A) Wear, there, their (B) Were, their, there
(C) Where, there, there (D) Where, their, their
Q.4 (x% of y) + (y % of x) is equivalent to
(A) 2% of xy (B) 2% of (xy/100) (C) % of 100 (D) 100% of xy
Q.5 The sum of the digits of a two digit number is __________.
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If the new number formed by reversing the digits is greater than the original number by 54, find the original number.
(A) 39 (B) 57 (C) 66 (D) 93
Q. 6 – Q. 10 carry two marks each.
Q.6 Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to year. Year-wise annual rates of interest offered by these companies are shown by the line graph provided below.
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts received after one year as interests from companies P and Q would be in the ratio:
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(A) 2:3 (B) 3:4 (C) 6:7 (D) 4:3
Q.7 Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the availability of evidence today.
Which of the following can be logically inferred from the above sentences?
(A) Emperors who do not leave significant sculpted evidence are completely forgotten.
(B) Ashoka produced stone carved edicts to ensure that later historians will respect him.
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(C) Statues of kings are a reminder of their greatness.
(D) A king's greatness, as we know him today, is interpreted by historians.
Q.8 Fact 1: Humans are mammals.
Fact 2: Some humans are engineers.
Fact 3: Engineers build houses.
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If the above statements are facts, which of the following can be logically inferred?
I. All mammals build houses.
II. Engineers are mammals.
III. Some humans are not engineers.
(A) II only. (B) III only. (C) I, II and III. (D) I only.
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Q.9 A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the lateral surface area of the pyramid?
(A) x2 (B) 0.75 x2 (C) 0.50 x2 (D) 0.25 x2
Q.10 Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages to be read by Ananth, twice that to be read by Bharath? Assume Ananth and Bharath read all the pages with constant pace.
(A) 1 (B) 2 (C) 3 (D) 4
END OF THE QUESTION PAPER
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Firstranker's choice
GATE 2016 Civil Engineering Set-2
Q. 1 – Q. 25 carry one mark each
Q.1 The spot speeds (expressed in km/hr) observed at a road section are 66, 62, 45, 79, 32, 51, 56, 60, 53, and 49. The median speed (expressed in km/hr) is
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(Note: answer with one decimal accuracy)
Q.2 The optimum value of the function f(x) = x² – 4x +2 is
(A) 2 (maximum) (B) 2 (minimum)
(C) -2 (maximum) (D) -2 (minimum)
Q.3 The Fourier series of the function,
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f(x) = 0, -p < x = 0
= p-?, 0 < x < p
in the interval [-p,p] is
f(x) = p/4 + S [ (2/p(2n-1)2) cos(2n-1)x + (1/n) sin(nx) ]
The convergence of the above Fourier series at x = 0 gives
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(?) S 1/(2n-1)2 = p2/8 (B) S (-1)n+1/(n+1) = p2/12
(C) S 1/n2 = p2/6 (D) S (-1)n+1/(2n-1) = p/4
Q.4 X and Y are two random independent events. It is known that P(X) = 0.40 and P(X?Y) = 0.7. Which one of the following is the value of P(XnY) ?
(A) 0.7 (B) 0.5 (C) 0.4 (D) 0.3
Q.5 What is the value of lim x->0 (ex - (1+x)/x2)
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(A) 1 (B) -1 (C) 0 (D) Limit does not exist
Q.6 The kinematic indeterminacy of the plane truss shown in the figure is
(A) 11 (B) 8 (C) 3 (D) 0
Q.7 As per IS 456-2000 for the design of reinforced concrete beam, the maximum allowable shear stress (Temax) depends on the
(A) grade of concrete and grade of steel (B) grade of concrete only
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(C) grade of steel only (D) grade of concrete and percentage of reinforcement
Q.8 An assembly made of a rigid arm A-B-C hinged at end A and supported by an elastic rope C-D at end C is shown in the figure. The members may be assumed to be weightless and the lengths of the respective members are as shown in the figure.
Under the action of a concentrated load P at C as shown, the magnitude of tension developed in the rope is
(A) 3P/2 (B) P/v2 (C) v2P (D) P/2
Q.9 As per Indian standards for bricks, minimum acceptable compressive strength of any class of burnt clay bricks in dry state is
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(A) 10.0 MPa (B) 7.5 MPa (C) 5.0 MPa (D) 3.5 MPa
Q.10 A construction project consists of twelve activities. The estimated duration (in days) required to complete each of the activities along with the corresponding network diagram is shown below.
Total floats (in days) for the activities 5-7 and 11-12 for the project are, respectively,
(A) 25 and 1 (B) 1 and 1 (C) 0 and 0 (D) 81 and 0
Q.11 A strip footing is resting on the surface of a purely clayey soil deposit. If the width of the footing is doubled, the ultimate bearing capacity of the soil
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(A) becomes double (B) becomes half (C) becomes four-times (D) remains the same
Q.12 The relationship between the specific gravity of sand (G) and the hydraulic gradient (i) to initiate quick condition in the sand layer having porosity of 30% is
(A) G = 0.7i + 1 (B) G = 1.43i- 1 (C) G = 1.43i + 1 (D) G = 0.7i – 1
Q.13 The results of a consolidation test on an undisturbed soil, sampled at a depth of 10 m below the ground level are as follows:
Saturated Unit Weight: 16 kN/m³
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Pre-consolidation pressure: 90 kPa
The water table was encountered at the ground level. Assuming the unit weight of water as 10 kN/m³, the over-consolidation ratio of the soil is
(A) 0.67 (B) 1.50 (C) 1.77 (D) 2.00
Q.14 Profile of a weir on permeable foundation is shown in figure I and an elementary profile of 'upstream pile only case' according to Khosla's theory is shown in figure II. The uplift pressure heads at key points Q, R and S are 3.14 m, 2.75 m and 0 m, respectively (refer figure II).
What is the uplift pressure head at point P downstream of the weir (junction of floor and pile as shown in the figure I)?
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(A) 2.75 m (B) 1.25 m (C) 0.8 m (D) Data not sufficient
Q.15 Water table of an aquifer drops by 100 cm over an area of 1000 km². The porosity and specific retention of the aquifer material are 25% and 5%, respectively. The amount of water (expressed in km³) drained out from the area is
Q.16 Group I contains the types of fluids while Group II contains the shear stress rate of shear relationship of different types of fluids, as shown in the figure.
Group I Group II
P. Newtonian fluid 1. Curve 1
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Q. Pseudo plastic fluid 2. Curve 2
R. Plastic fluid 3. Curve 3
S. Dilatant fluid 4. Curve 4
5. Curve 5
The correct match between Group I and Group II is
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(A) P-2, Q-4, R-1, S-5 (B) P-2, Q-5, R-4, S-1
(C) P-2, Q-4, R-5, S-3 (D) P-2, Q-1, R-3, S-4
Q.17 The atmospheric layer closest to the earth surface is
(A) the mesosphere (B) the stratosphere (C) the thermosphere (D) the troposphere
Q.18 A water supply board is responsible for treating 1500 m³/day of water. A settling column analysis indicates that an overflow rate of 20 m/day will produce satisfactory removal for a depth of 3.1 m. It is decided to have two circular settling tanks in parallel. The required diameter (expressed in m) of the settling tanks is
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Q.19 The hardness of a ground water sample was found to be 420 mg/L as CaCO3. A softener containing ion exchange resins was installed to reduce the total hardness to 75 mg/L as CaCO3 before supplying to 4 households. Each household gets treated water at a rate of 540 L/day. If the efficiency of the softener is 100%, the bypass flow rate (expressed in L/day) is
Q.20 The sound pressure (expressed in µPa) of the faintest sound that a normal healthy individual can hear is
(A) 0.2 (B) 2 (C) 20 (D) 55
Q.21 In the context of the IRC 58-2011 guidelines for rigid pavement design, consider the following pair of statements.
I: Radius of relative stiffness is directly related to modulus of elasticity of concrete and inversely related to Poisson's ratio
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II: Radius of relative stiffness is directly related to thickness of slab and modulus of subgrade reaction.
Which one of the following combinations is correct?
(A) I: True; II: True (B) I: False; II: False (C) I: True; II: False (D) I: False; II: True
Q.22 If the total number of commercial vehicles per day ranges from 3000 to 6000, the minimum percentage of commercial traffic to be surveyed for axle load is
(A) 15 (B) 20 (C) 25 (D) 30
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Q.23 Optimal flight planning for a photogrammetric survey should be carried out considering
(A) only side-lap (B) only end-lap (C) either side-lap or end-lap (D) both side-lap as well as end-lap
Q.24 The reduced bearing of a 10 m long line is N30°E. The departure of the line is
(A) 10.00 m (B) 8.66 m (C) 7.52 m (D) 5.00 m
Q.25 A circular curve of radius R connects two straights with a deflection angle of 60°. The tangent length is
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(A) 0.577 R (B) 1.155 R (C) 1.732 R (D) 3.464 R
Q. 26 – Q. 55 carry two marks each
Q.26 Consider the following linear system.
x + 2y - 3z = a
2x + 3y + 3z = b
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5x + 9y - 6z = c
This system is consistent if a, b and c satisfy the equation
(A) 7a-b-c = 0 (B) 3a + b - c = 0 (C) -a - b + c = 0 (D) 7a - b + c = 0
Q.27 If f (x) and g(x) are two probability density functions
f(x) = (x/a2)+1/a : -a=x<0
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g(x) = (-x/a2)+1/a : 0=x=a
= 0 : otherwise
= 0 : otherwise
Which one of the following statements is true?
(A) Mean of f (x) and g(x) are same; Variance of f (x) and g(x) are same
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(B) Mean of f (x) and g(x) are same; Variance of f (x) and g(x) are different
(C) Mean of f (x) and g(x) are different; Variance of f(x) and g(x) are same
(D) Mean of f (x) and g(x) are different; Variance of f(x) and g(x) are different
Q.28 The angle of intersection of the curves x² = 4y and y² = 4x at point (0, 0) is
(A) 0° (B) 30° (C) 45° (D) 90°
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Q.29 The area between the parabola x² = 8y and the straight line y = 8 is
Q.30 The quadratic approximation of f(x) = x³ – 3x² – 5 at the point x = 0 is
(A) 3x² - 6x -5 (B) -3x² -5 (C) -3x² + 6x – 5 (D) 3x² -5
Q.31 An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson's ratio?
(A) 0.00 (B) 0.25 (C) 0.50 (D) 1.00
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Q.32 For the stress state (in MPa) shown in the figure, the major principal stress is 10 MPa.
The shear stress t is
(A) 10.0 MPa (B) 5.0 MPa (C) 2.5 MPa (D) 0.0 MPa
Q.33 The portal frame shown in the figure is subjected to a uniformly distributed vertical load w (per unit length).
The bending moment in the beam at the joint 'Q' is
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(A) zero (B) wL²/24 (hogging) (C) wL²/12 (hogging) (D) wL²/8 (sagging)
Q.34 Consider the structural system shown in the figure under the action of weight W. All the joints are hinged. The properties of the members in terms of length (L), area (A) and the modulus of elasticity (E) are also given in the figure. Let L, A and E be 1 m, 0.05 m² and 30 × 10º N/m², respectively, and W be 100 kN.
Which one of the following sets gives the correct values of the force, stress and change in length of the horizontal member QR?
(A) Compressive force = 25 kN; Stress = 250 kN/m²; Shortening = 0.0118 m
(B) Compressive force = 14.14 kN; Stress = 141.4 kN/m²; Extension = 0.0118 m
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(C) Compressive force = 100 kN; Stress = 1000 kN/m²; Shortening = 0.0417 m
(D) Compressive force = 100 kN; Stress = 1000 kN/m²; Extension = 0.0417 m
Q.35 A haunched (varying depth) reinforced concrete beam is simply supported at both ends, as shown in the figure. The beam is subjected to a uniformly distributed factored load of intensity 10 kN/m.
The design shear force (expressed in kN) at the section X-X of the beam is
Q.36 A 450 mm long plain concrete prism is subjected to the concentrated vertical loads as shown in the figure. Cross section of the prism is given as 150 mm × 150 mm. Considering linear stress distribution across the cross-section, the modulus of rupture (expressed in MPa) is
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Q.37 Two bolted plates under tension with alternative arrangement of bolt holes are shown in figures 1 and 2. The hole diameter, pitch, and gauge length are d, p and g, respectively.
Which one of the following conditions must be ensured to have higher net tensile capacity of configuration shown in Figure 2 than that shown in Figure 1?
(A) p² > 2gd (B) p² < 4gd (C) p² > 4gd (D) p > 4gd
Q.38 A fixed-end beam is subjected to a concentrated load (P) as shown in the figure. The beam has two different segments having different plastic moment capacities (Mp, 2Mp) as shown.
The minimum value of load (P) at which the beam would collapse (ultimate load) is
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(A) 7.5Mp/L (B) 5.0Mp/L (C) 4.5Mp/L (D) 2.5Mp/L
Q.39 The activity-on-arrow network of activities for a construction project is shown in the figure. The durations (expressed in days) of the activities are mentioned below the arrows.
The critical duration for this construction project is
(A) 13 days (B) 14 days (C) 15 days (D) 16 days
Q.40 The seepage occurring through an earthen dam is represented by a flownet comprising of 10 equipotential drops and 20 flow channels. The coefficient of permeability of the soil is 3 mm/min and the head loss is 5 m. The rate of seepage (expressed in cm³/s per m length of the dam) through the earthen dam is
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Q.41 The soil profile at a site consists of a 5 m thick sand layer underlain by a c-f soil as shown in figure. The water table is found 1 m below the ground level. The entire soil mass is retained by a concrete retaining wall and is in the active state. The back of the wall is smooth and vertical. The total active earth pressure (expressed in kN/m²) at point A as per Rankine's theory is
Q.42 OMC-SP and MDD-SP denote the optimum moisture content and maximum dry density obtained from standard Proctor compaction test, respectively. OMC-MP and MDD-MP denote the optimum moisture content and maximum dry density obtained from the modified Proctor compaction test, respectively. Which one of the following is correct?
(A) OMC-SP < OMC-MP and MDD-SP < MDD-MP (B) OMC-SP > OMC-MP and MDD-SP< MDD-MP
(C) OMC-SP < OMC-MP and MDD-SP > MDD-MP (D) OMC-SP > OMC-MP and MDD-SP > MDD-MP
Q.43 Water flows from P to Q through two soil samples, Soil 1 and Soil 2, having cross sectional area of 80 cm² as shown in the figure. Over a period of 15 minutes, 200 ml of water was observed to pass through any cross section. The flow conditions can be assumed to be steady state. If the coefficient of permeability of Soil 1 is 0.02 mm/s, the coefficient of permeability of Soil 2 (expressed in mm/s) would be
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Q.44 A 4 m wide strip footing is founded at a depth of 1.5 m below the ground surface in a c-f soil as shown in the figure. The water table is at a depth of 5.5 m below ground surface. The soil properties are: c' = 35 kN/m², f' = 28.63°, ?sat = 19 kN/m³, ?bulk = 17 kN/m³ and ?w = 9.81 kN/m³. The values of bearing capacity factors for different f' are given below.
Using Terzaghi's bearing capacity equation and a factor of safety Fs = 2.5, the net safe bearing capacity (expressed in kN/m²) for local shear failure of the soil is
Q.45 A square plate is suspended vertically from one of its edges using a hinge support as shown in figure. A water jet of 20 mm diameter having a velocity of 10 m/s strikes the plate at its mid-point, at an angle of 30° with the vertical. Consider g as 9.81 m/s² and neglect the self-weight of the plate. The force F (expressed in N) required to keep the plate in its vertical position is
Q.46 The ordinates of a one-hour unit hydrograph at sixty minute interval are 0, 3,3, 12, 8, 6, 3 and 0 m³/s. A two-hour storm of 4 cm excess rainfall occurred in the basin from 10 AM. Considering constant base flow of 20 m³/s, the flow of the river (expressed in m³/s) at 1 PM is
Q.47 A 3 m wide rectangular channel carries a flow of 6 m³/s. The depth of flow at a section P is 0.5 m. A flat-topped hump is to be placed at the downstream of the section P. Assume negligible energy loss between section P and hump, and consider g as 9.81 m/s². The maximum height of the hump (expressed in m) which will not change the depth of flow at section P is
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Q.48 A penstock of 1 m diameter and 5 km length is used to supply water from a reservoir to an impulse turbine. A nozzle of 15 cm diameter is fixed at the end of the penstock. The elevation difference between the turbine and water level in the reservoir is 500 m. Consider the head loss due to friction as 5% of the velocity head available at the jet. Assume unit weight of water = 10 kN/m³ and acceleration due to gravity (g) = 10 m/s². If the overall efficiency is 80%, power generated (expressed in kW and rounded to nearest integer) is
Q.49 A tracer takes 100 days to travel from Well-1 to Well-2 which are 100 m apart. The elevation of water surface in Well-2 is 3 m below that in Well-1. Assuming porosity equal to 15%, the coefficient of permeability (expressed in m/day) is
(A) 0.30 (B) 0.45 (C) 1.00 (D) 5.00
Q.50 A sample of water has been analyzed for common ions and results are presented in the form of a bar diagram as shown.
The non-carbonate hardness (expressed in mg/L as CaCO3) of the sample is
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(A) 40 (B) 165 (C) 195 (D) 205
Q.51 A noise meter located at a distance of 30 m from a point source recorded 74 dB. The reading at a distance of 60 m from the point source would be
Q.52 For a wastewater sample, the three-day biochemical oxygen demand at incubation temperature of 20°C (BOD3day, 20°C) is estimated as 200 mg/L. Taking the value of the first order BOD reaction rate constant as 0.22 day-1, the five-day BOD (expressed in mg/L) of the wastewater at incubation temperature of 20°C (BOD5day, 20°C) would be
Q.53 The critical flow ratios for a three-phase signal are found to be 0.30, 0.25, and 0.25. The total time lost in the cycle is 10 s. Pedestrian crossings at this junction are not significant. The respective Green times (expressed in seconds and rounded off to the nearest integer) for the three phases are
(A) 34, 28, and 28 (B) 40, 25, and 25 (C) 30, 30, and 30 (D) 50, 25, and 25
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