### GATE 2011 Civil Engineering -Questions with answers Key

### CIVIL ENGINEERING - GATE 2011 (with answers)

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__Q.(1-25) carry one mark each__

__Q.(1-25) carry one mark each__

**[A] is a square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose. The sum and difference of these matrices are defined as [S] = [A] + [A]T and [D] = [A] - [A]T, respectively. Which of the following statements is true?**

__1.__
(a) Both [S] and [D] are symmetric.

(b) Both [S] and [D] are skew-symmetric

(c) [S] is skew symmetric and [D] is symmetric.

(d) [S] is symmetric and [D] is skew symmetric.

(a) x i+1 = 1/2 { xi + N/xi }

(b) x i+1 = 1/2 { xi2 + N/xi }

(c) x i+1 = 1/2 { xi + N2/xi }

(d) x i+1 = 1/2 { xi2 - N/xi }

(a) 1/7 (b) 9/49 (c) 12/49 (d) 3/7

**Sol: (d)**

**2.**The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x^2 - N = 0. If i denotes the iteration index, the correct iterative scheme will be(a) x i+1 = 1/2 { xi + N/xi }

(b) x i+1 = 1/2 { xi2 + N/xi }

(c) x i+1 = 1/2 { xi + N2/xi }

(d) x i+1 = 1/2 { xi2 - N/xi }

**Sol: (a)**

**3.**There are two containers, with one containing 4 Red and 3 Green balls and the other containing 3 Blue and 4 Green balls. One ball is drawn at random from each container. The probability that one of the balls is Red and the other is Blue will be(a) 1/7 (b) 9/49 (c) 12/49 (d) 3/7

**Sol: (c)****4.**For the fillet weld of size 's' shown in the adjoining figure the effective throat thickness is

(a) 0.61s (b) 0.65 s

(c) 0.70s (d) 0.75s

**Sol: (b)**

**5.**A 16mm thick plate measuring 650 mm* 420 mm is used as a base plate for an ISHB 300 column subjected to a factored axial compressive load of 2000 KN. As per IS 456- 2000, the minimum grade of concrete that should be used below the base plate for safely carrying the load is

(a) M15 (b) M20 (c) M30 (d) M40

**Sol: (a)**

**6.**Consider a reinforcing bar embedded in concrete. In a marine environment this bar undergoes uniform corrosion, which leads to the deposition of corrosion products on its surface and an increase in its apparent volume of the bar. This subjects the surrounding concrete to expansive pressure. As a result, corrosion induced cracks appear at the surface of concrete. Which of the following statements is TRUE?

*(a)*Corrosion cause circumferential tensile stresses in concrete and the cracks will be parallel to the corroded reinforcing bar.

*(b)*Corrosion cause radial tensile stresses in concrete and the cracks will be parallel to the corroded reinforcing bar.

*(c)*Corrosion causes circumferential tensile stresses in concrete and the cracks will be perpendicular to the direction of the corroded reinforcing bar.

*(d)*Corrosion cause radial tensile stresses in concrete and the cracks will be perpendicular to the direction of the corroded reinforcing bar.

**Sol: (c)**

**7.**The results of sieve analysis carried out for three types of sand, P, Q and R, are given in the adjoining figure. If the fineness modulus values of the three sands are given as FMp, FMq and FMr, it can be stated that

(a) FMq = (FMp*FMr)^(1/2)

(b) FMq = 0.5(FMp+FMr)

(c) FMp > FMq > FMr

(d) FMp< FMq < FMr

**Sol: (a)**

**8.**The cross section of a thermo-mechanically treated(TMT) reinforcing bar has

(a) soft ferrite- pearlite throughout

(b) hard martensite throughout

(c) a soft ferrite- pearlite core with a hard martensitic rim

(d) a hard martensitic core with a soft pearlite bainitic rim

**Sol: (c)**

**9.**Consider a simply supported beam with a uniformly distributed load having a neutral axis(NA) as shown. For points P(on the neutral axis) and Q(at bottom of the beam) the state of stress is best represented by which of the following pairs?

**Sol: (a)**

**10.**For a saturated sand deposit, the void ratio and the specific gravity of solids are 0.70 and 2.67, respectively. The critical(upward) hydraulic gradient for the deposit would be:

(a) 0.54 (b) 0.98 (c) 1.02 (d) 1.87

**sol: (b) 0.98 = (G-1)/(1+v)**

**11.**Likelihood of general shear failure for an isolated footing in sand decreases with

(a) Decreasing footing depth

(b) Decreasing inter-granular packing of the sand

(c) Increasing footing width

(d) decreasing soil grain compressibility.

**Sol: (b)**

**12.**For a sample of dry, cohesion less soil with friction angle @, the failure plane will be inclined to the major principal plane by an angle equal to

(a) @ (b) 45 degree (c) 45 - @/2 (d) 45 + @/2

**Sol: (d)**

**13.**Two geometrically identical isolated footings, X(Linear elastic) and y(rigid), are loaded identically(shown alongside). The soil reaction will

(a) be uniformly distributed for Y but not for X

(b) be uniformly distributed for X but not for Y

(c) be uniformly distributed for both X and Y

(d) not the uniformly distributed for both X and Y.

**Sol: (a)**

**14.**A soil is composed of solid spherical grains of identical specific gravity and diameter between 0.075 mm to 0.0075 mm. If the terminal velocity of the largest particle falling through water without flocculation is 0.5 mm/sec, that for the smallest particle would be:

(a) 0.005 mm/sec (b) 0.05 mm/sec (c) 5 mm/sec (d) 50 mm/sec

**Sol: (a)**

**15.**A watershed got transformed from rural to urban over a period of time. The effect of urbanization on storm runoff hydro-graph from the watershed is to

(a) decrease the volume of runoff

(b) increase the time to peak discharge

(c) decrease the time base

(d) decrease the peak discharge

**Sol: (c)**

**16.**For a given discharge, the critical flow depth in an open channel depends on

(a) channel geometry only

(b) channel geometry and bed slope

(c) channel geometry, bed slope and roughness

(d) Channel geometry, bed slope, roughness and Reynolds number.

**Sol: (a)**

**17.**For a body completely submerged in a fluid, the centre of gravity(G) and centre of Buoyancy(O) are known. The body is considered to be in stable equilibrium if

(a) O does not coincide with the centre of mass of the displaced fluid.

(b) G coincides with the centre of mass of the displaced fluid.

(c) O lies below G

(d) O lies above G.

**Sol: (d)**

**18.**The flow in a horizontal, friction less rectangular open channel is super critical. A smooth hump is built on the channel floor. As the height of hump is increased, choked condition is attained. With further increase in the height of the hump, the water surface will

(a) rise at a section upstream of the hump

(b) drop at a section upstream of the hump

(c) drop at the hump

(d) rise at the hump

**Sol: (b)**

**19.**Consider the following unit processes commonly used in water treatment: rapid mixing(RM), flocculation(F), primary sedimentation(PM), secondary sedimentation(SS), chlorination(C) and rapid sand filtration(RSF). The order of these unit processes(First to last) in a conventional water treatment plant is

(a) PS ->RSF -> F-> RM-> SS-> C

(b) PS-> F-> RM -> RSF -> SS -> C

(c) PS -> F -> SS -> RSF -> RM -> C

(d) PS -> RM -> F -> SS -> RSF -> C

**Sol: (d)**

**20.**Anaerobically treated effluent has MPN of total coliform as 10^6/ 100 mL. After chlorination, the MPN value declines to 10^2/100 mL. The percent removal (%R) and log removal (logR) of total coliform MPN is

(a) %R = 99.90; log R =4

(b) %R = 99.90, log R =2

(c) %R = 99.99; log R = 4

(d) %R = 99.99; log R =2

**Sol: (d)**

**21.**Consider four common air pollutants found in urban environments, NO, SO2, Soot and O3. Among these which one is the secondary air pollutant?

(a) O3 (b) NO (c) SO2 (d) Soot

**So: (a)**

**22.**The probability that k number of vehicle arrive( i.e. cross a predefined line) in time t is given as (y.t)^k ( e^(-yt)/k!), where y is the average vehicle arrival rate. What is the probability that the time headway is greater than or equal to time t1?

(a) y.e ^(yt1) (b) Y. e ^(-t1) (c) e^(yt1) (d) e^(-yt1)

**Sol: (d)**

**23.**A vehicle negotiates a transition curve with uniform speed v. If the radius of the horizontal curve and the allowable jerk are R and J, respectively, the minimum length of the transition curve is

(a) R^3/ (vJ) (b) J^3 /(Rv) (c) Rv^2/J (d) v^3 / (RJ)

**sol: (d)**

**24.**In Marshall testing of bituminous mixes, as the bitumen content increases the flow value

(a) remains constant

(b) decreases first and then increases

(c) increases monotonically

(d) increases first and then decreases

**Sol:(c)**

**25.**Curvature correction to a staff reading in a differential leveling survey is

(a) always subtractive

(b) always zero

(c) always additive

(d) dependent on latitude

**Sol:(a)**

__Q.(26 -55) carry two marks each__

**26.**For an analytic function, f(x +iy) = u(x, y) + iv(x,y) , u is given by u= 3x^2 - 3 y^2. The expression for v, considering K to be a constant is

(a) 3.y^2 - 3 .x^2 + K (c) 6.y - 6.x + K

(b) 6.x - 6.y + K (d) 6.x.y + K

**Sol: (d)**

**27.**What should be the value of lambda such that the function defined below is continuous at x = pi/ 2?

(a) 0 (b) 2/pi (c) 1 (d) pi/2

**Sol: (c)**

**28.**What is the value of the definite integral,

(a) 0 (b) 2/pi (c) 1 (d) pi/2

**Sol : (b)**

**29.**If A and B are two arbitrary vectors with magnitudes as a and b, respectively, IA*BI^2 will be equal to

(a) (ab)^2 - (A.B)^2

(b) a.b - A.B

(c) (ab)^2 + (A.B)^2

(d) a.b + A.B

**Sol: (a)**

**30. Please see the question in the pic.**

**Sol: (d)**

**31.**

**Sol: (d) 13/21 Mp**

**32.**For the cantilever bracket, PQRS, loaded as shown in the adjoining figure (PQ = RS = L, and, QR = 2L), which of the following statements is FALSE?

(a) The portion RS has a constant twisting moment with a value of 2WL.

(b) The portion QR has a varying twisting moment with a maximum value of WL.

(c) The portion P has a varying bending moment with a maximum value of WL.

(d) The portion PQ has no twisting moment.

**Sol: (b)**

**33.**

**Sol: (c)**

**34.**Consider two RCC beams, P and Q, each having the section 400 mm*750 mm(effective depth d =750 mm) made with concrete having a Tmax= 2.1 N/mm2. For the reinforcement provided and the grade of concrete used; it may be assumed that the Tc= 0.75N/mm2. The design shear in beam P is 400 kN and in beam Q is 750 kN. Considering the provisions of IS 456 - 2000, which of the following statements is TRUE?

(a) Shear reinforcement should be designed for 175 kN for beam P and the section for beam Q should be revised.

(b) Nominal shear reinforcement is required for beam P and the shear reinforcement should be designed for 120 kN for beam Q.

(c) Shear reinforcement should be designed for 175 kN for beam P and the shear reinforcement should be designed for 525 kN for beam Q.

(d) The sections for both beams P and Q need to be revised.

**35.**The adjoining figure shows a schematic representation of a steel plate girder to be used as a simply supported beam with a concentrated load. For stiffeners, PQ(running along the beam axis) and RS (Running between the top and bottom flanges) which of the following pairs of the statements is TRUE?

(a) (i) RS should be provided under the concentrated load only.

(ii) PQ should be placed in the tension side of the flange.

(b) (i) RS helps to prevent local buckling of the web.

(ii) PQ should be placed in the compression side of the flange.

(c) (i) RS should be provided at the supports.

(ii) PQ should be placed along the neutral axis.

(d) (i) RS should be provided away from the points of action of concentrated loads.

(ii) PQ should be provided on the compression side of the flange.

**Sol: (b)**

**36.**A single under-reamed, 8 m long, RCC pile (shown in the adjoining figure) weighing 20 KN with 350 mm shaft diameter and 750 mm under -ream diameter is installed withing stiff, saturated silty clay(undrained shear strength is 50 kPa, adhesion factor is 0.3, and the applicable bearing capacity factor is 9) to counteract the impact of soil swelling on a structure constructed above. Neglecting suction and the contribution of the under-ream to the adhesive shaft capacity(rounded off to the nearest integer value of kN) of the pile?

**Sol: (b)**

**37.**Identical surcharge are placed at ground surface at sites X and Y, with soil conditions shown alongside and water table at ground surface. The silty clay layers at X and Y are identical. The thin sand layer at Y is continuous and free-draining with a very larger discharge capacity. If primary consolidation at X is estimated to complete in 36 months, what would be the corresponding time for completion of primary consolidation at Y?

**Sol: (c) Tv = (Cv . t)/ H^2**

**A field vane testing instrument was inserted completely into a deposit of soft, saturated silty clay with the cane rod vertical such that the top of the blades were 500 mm below the ground surface. Upon application of a rapidly increasing torque about vane rod, the soil was found to fail when the torque reached 4.6 Nm. Assuming mobilization of un-drained shear strength on all failure surfaces to be uniform and the resistance mobilized on the surface of the vane rod to be negligible, what would be the peak un-drained shear strength(rounded off to the nearest integer value of kPa) of the soil?**

38.

38.

**Sol: (b)**

**39.**A single pipe of length 1500 m and diameter 60 cm connects two reservoirs having a difference of 20 m in their water levels. The pipe is to be replaced by two pipes of the same length and equal diameter d to convey 25% more discharge under the same head loss. If the friction factor is assumed to be the same for all the pipes, the value of d is approximately equal to which of the following options?

(a) 37.5 cm (b) 40.0 cm (c) 45.0 cm (d) 50.0 cm

**Sol : (d)**

**40.**A spillway discharge flood at a rate of 9 m^3/sec per meter width. If the depth of flow on the horizontal apron at the toe of the spillway is 46 cm, the tail water depth needed to form a hydraulic jump is approximately given by which of the following options?

(a) 2.54 m (b) 4.90 m (c) 5.77 m (d) 6.23 m

**Sol: (c)**

**41.**In an aquifer extending over 150 hectare, the water table was 20 m below ground level. Over a period of time the water table dropped to 23 m below the ground level. If the porosity of aquifer is 0.40 and the specific rentention is 0.15, what is the change in the ground water storage of the aquifer?

(a) 67.5 ha-m (b) 112.5 ha-m (c) 180.9 ha-m (d) 450.0 ha-m

**Sol: (b)**

**42.**Total suspended particulate matter(TSP) concentration in ambient air is to be measured using a high volume sampler. The filter used for this purpose had an initial dry weight of 9.787 gm. The filter was mounted in the sampler and the initial air flow rate through the filter was set at 1.5 m3/min. Sampling continued for 24 hours. The airflow after 24 hours was measured to be 1.4m3/min. The dry weight of the filter paper after 24 hour sampling was 10.283 gm. Assuming a linear decline in the air flow rate during the sampling, what is the 24 hours average TSP concentration in the ambient air?

(a) 59.2 Ug/m3 (b) 118.6 Ug/m3 (c) 237.5 Ug/m3 (d) 574.4 Ug/m3, here U means 'micro'

**Sol:(c)**

**43.**Chlorine gas( 8 mg/L as Cl2) was added to a drinking water sample. If the free chlorine residual and pH was measured to be 2 mg/L(as Cl2) and 7.5 respectively, what is the concentration of residual OCl-(negative) ions in the water? Assume that the chlorine gas added to the water is completely converted to HOCl and OCl-(negative). Atomic Weight of Cl: 35.5

Given: OCl-

**+**H+ <=> HOCl , K = 10^(7.5)

(a) 1.408 * 10^(-5) moles/ L

(b) 2.817 * 10^(-3) moles/L

(c) 5.634*10^(-5) moles/L

(d) 1.127 * 10^(-4) moles/L

**Sol: (b)**

**44.**If the jam density is given as Kf and free flow speed is given as Uf, the maximum flow for a linear traffic speed- density model is given by which of the following options?

(a) 1/4*Kf* Uf (b) 1/3*Kf* Uf (c) 3/5* Kf* Uf (d) 2/3* Kf * Uf

**Sol: (a)**

**45.**If v is the initital speed of a vehicle, g is the gravitational acceleration, G is the upward longitudinal slope of the road and f if co-efficient of rolling friction during braking, the braking distance(measured horizontally) for the vehicle to stop is

(a) v^2/ [g(G+f)]
(b) v^2/[2g(G+f)] (c) v.g/[G+f] (d) v.f/ [G+f]

**Sol: (b)**

**46.**The cumulative arrival and departure curve of one cycle of an approach lane of a signalized intersection is shown in the adjoining figure. The cycle time is 50s and the effective red time is 30s and the effective green time is 20s. What is the average delay?

(a) 15 sec (b) 25 sec (c) 35 sec (d) 45 sec

**47.**The observation from a closed loop transverse around an obstacle are

What is the value of the missing measurement(rounded off to nearest 10 mm)?

(a) 396.86 m (b) 396.79 m (c) 396.05 m (d) 396.94 m

**Sol : (b)**

__Common Data Questions (48-49)__
A sand layer found at sea floor under 20 m water depth is characterized with relative density = 40%, maximum void ratio = 1.0, minimum void ratio = 0.5, and specific gravity of soil solids = 2.67. Assume the specific gravity of sea water to be 1.03 and the unit weight of fresh water to be 9.91 kN/m3.

**48.**What would be the effective stress(rounded off to the nearest integer value of kPa) at 30 m depth into the sand layer?

(a) 77 kPa (b) 273 kPa (c) 268 kPa (d) 281 kPa

**Sol: (b)**

**49.**What would be the change in the effective stress(rounded off to the nearest integer value of kPa) at 30 m depth into the sand layer if the sea water level permanently rises by 2 m?

(a) 19 kPa (b) O kPa (c) 21 kPa (d) 22 kPa

The ordinates of a 2-h unit hydro-graph at 1 hour intervals starting from time t = 0, are 0, 3, 8, 6, 3, 2 and 0 m3/sec. Use trapezoidal rule for the numerical integration, if required.

(a) 1.00 km^2 (b) 2.00 km^2 (c) 7.92 km^2 (d) 8.64 km^2

(a) 41.0 m^3/sec (b) 43.4 m^3/sec (c) 53.0 m^3/sec (d) 56.2 m^3/sec

A rigid beam is hinged at one end and supported on linear elastic spring(both having a stiffness of 'k') at points '1' and '2', and an inclined load acts at '2', as shown

(a) d1= 2/5(2P/k) and d2 = 4/5(2P/k)

(b) d1= 2/5(P/k) and d2 = 4/5(P/k)

(c) d1= 2/5[P/(2k)^(1/2)] and d2 = 4/5[P/(1.414k)]

(d) d1 = 2/5 [(1.414 P)/k] and d2 = 4/5[(1.414P)/k]

(a) R1 = 20 kN and R2 = 40 kN

(b) R1 = 50 kN and R2 = 50 kN

(c) R1 = 30 kN and R2 = 60 kN

(d) R1 = 40 kN and R2 = 80 kN

The sludge from the aeration tank of the activated sludge process(ASP) has solids(by weight) of 2%. This sludge is put in a sludge thickener, where sludge volume is reduced to half. Assume that the amount of solids in the supernatant from the thickener is negligible, the specific gravity of sludge solids is 2.2 and the density of water is 1000 kg/m^3.

(a)990 kg/m^3 (b) 1000 kg/m^3 (c) 1011 kg/m^3 (d) 1022 kg/m^3

(a) 3.96 % (b) 4.00 % (c) 4.04% (d) 4.10%

(a) P^2 = Q^3.R^2 (b) Q^2 = P.R

(c) Q^2 = R^3.P (d) R= P^2.Q^2

(a) Incomprehensible

(b) Indelible

(c) Inextricable

(d) Infallible

(a) Merge (b) Split (c) Collect (d) Separate

If you are trying to make a strong impression on your audience, you can not do so by being understand, tentative or .....................

(a) hyperbolic (b) restrained (c) argumentative (d) indifferent

I contemplated ......... Singapore for my vacation but decided against it.

(a) to visit (b) having to visit (c) visiting (d) for a visit

A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

(a) P (b) Q (c) R (d) S

Based on the above passage which topic would not be included in a unit on bereavement?

(a) How to write a letter of condolence

(b) What emotional stages are passed through in the healing process

(c) What the leading cause of death are

(d) How to give support to grieving friend

(a) 7.58 Liters. (b) 7.84 Liters (c) 7 Liters (d) 7.29 Liters

(a) 4 (b) 5 (c) 6 (d) 7

(a) 5 (b) 4 (c) 7 (d) 6

**Sol: (b)**__Common Data Questions (50-51) :__The ordinates of a 2-h unit hydro-graph at 1 hour intervals starting from time t = 0, are 0, 3, 8, 6, 3, 2 and 0 m3/sec. Use trapezoidal rule for the numerical integration, if required.

**50.**What is the catchment area represented by the unit hydro-graph?(a) 1.00 km^2 (b) 2.00 km^2 (c) 7.92 km^2 (d) 8.64 km^2

**Sol: (c)**

**51.**A storm of 6.6 cm occurs uniformly over the catchment in 3 hours. If phi- index is equal to 2 mm/h and base flow is 5 m^3/sec, what is the peak flow due to the storm?(a) 41.0 m^3/sec (b) 43.4 m^3/sec (c) 53.0 m^3/sec (d) 56.2 m^3/sec

**Sol: (c)**

__Linked Answer Questions (52-53):__A rigid beam is hinged at one end and supported on linear elastic spring(both having a stiffness of 'k') at points '1' and '2', and an inclined load acts at '2', as shown

**52.**Which of the following options represents the deflections d1 and d2 at point '1' and '2'?(a) d1= 2/5(2P/k) and d2 = 4/5(2P/k)

(b) d1= 2/5(P/k) and d2 = 4/5(P/k)

(c) d1= 2/5[P/(2k)^(1/2)] and d2 = 4/5[P/(1.414k)]

(d) d1 = 2/5 [(1.414 P)/k] and d2 = 4/5[(1.414P)/k]

**Sol:(b)****53.**If the load P equals 100 KN, which of the following options represents forces R1 and R2 in the springs at points '1' and '2'?(a) R1 = 20 kN and R2 = 40 kN

(b) R1 = 50 kN and R2 = 50 kN

(c) R1 = 30 kN and R2 = 60 kN

(d) R1 = 40 kN and R2 = 80 kN

__Statement for Linked Answer Questions (54 - 55) :__The sludge from the aeration tank of the activated sludge process(ASP) has solids(by weight) of 2%. This sludge is put in a sludge thickener, where sludge volume is reduced to half. Assume that the amount of solids in the supernatant from the thickener is negligible, the specific gravity of sludge solids is 2.2 and the density of water is 1000 kg/m^3.

**54.**What is the density of the sludge removed from the aeration tank?(a)990 kg/m^3 (b) 1000 kg/m^3 (c) 1011 kg/m^3 (d) 1022 kg/m^3

**55.**What is the solids content(by weight) of the thickened sludge?(a) 3.96 % (b) 4.00 % (c) 4.04% (d) 4.10%

__GENERAL APTITUDE(GA) QUESTIONS__**Q. (56-60) carry one mark each.****56.**If log(P) = (1/2)Log(Q) = (1/3)Log.(R), then which of the following option is TRUE?(a) P^2 = Q^3.R^2 (b) Q^2 = P.R

(c) Q^2 = R^3.P (d) R= P^2.Q^2

**Sol: (b)****57.**Which of the following options is the closest in the meaning to the word below:**Inexplicable**(a) Incomprehensible

(b) Indelible

(c) Inextricable

(d) Infallible

**Sol : (a)****58.**Choose the word from the options given below that is most nearly opposite in meaning to the given word:**Amalgamate**(a) Merge (b) Split (c) Collect (d) Separate

**Sol: (b)**

**59.**Choose the most appropriate word from the options given below to complete the following sentences.If you are trying to make a strong impression on your audience, you can not do so by being understand, tentative or .....................

(a) hyperbolic (b) restrained (c) argumentative (d) indifferent

**Sol : (b)**

**60.**Choose the most appropriate word(s) from the options given below to complete the following sentence.I contemplated ......... Singapore for my vacation but decided against it.

(a) to visit (b) having to visit (c) visiting (d) for a visit

**Sol: (c)**

__Q.(61-65) carry two marks each.__**61.**P, Q , R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below:A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

(a) P (b) Q (c) R (d) S

**Sol: (d)**

**62.**Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting.Based on the above passage which topic would not be included in a unit on bereavement?

(a) How to write a letter of condolence

(b) What emotional stages are passed through in the healing process

(c) What the leading cause of death are

(d) How to give support to grieving friend

**Sol: (c)**

**63.**A container originally contains 10 liters of pure spirit. From this container 1 liters of spirit is replaced with 1 liter of water. Subsequently, 1 liter of the mixture is again replaced with 1 liter of water and this process is repeated one more time. How much spirit is now left in the container?(a) 7.58 Liters. (b) 7.84 Liters (c) 7 Liters (d) 7.29 Liters

**Sol: (d)**

**64.**A transporter receives same numbers of orders each day. Currently, he has some pending orders(backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?(a) 4 (b) 5 (c) 6 (d) 7

**Sol: (c)**

**65.**The variable cost(V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost(F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost(V+F)?(a) 5 (b) 4 (c) 7 (d) 6

**Sol:(a)**

**END of GATE 2013 Questions and Answer key**

**(Ref: GK Publishers - GATE 2013)**