Given Matrix [A] =$\begin{bmatrix} \ 4 & 2 & 1 & 3 \ \ 6 & 3 & 4 & 7 \ \ 2 & 1 & 0 & 1 \ \end{bmatrix}$, the rank of the matrix is

A box contains 10 screws, 3 of which are defective. Two screws are drawn at random with replacement. The probability that none of the two screws is defective will be

If P, Q and R are three points having coordinates (3, - 2, 01), (1, 3, 4), (2, 1, - 2) in XYZ space, then the distance from point P to plane OQR (O being the origin of the coordinate system) is given by

Muller Breslau principle in structural analysis is used for

In the design of lacing system for a built-up steel column, the maximum allowable slenderness ratio of a lacing bar is

A curved member with a straight vertical leg is carrying a vertical load at Z, as shown in the figure. The stress resultant(s) in the XY segment is/are

Which of the following elements of a pitched roof industrial steel building primarily resist lateral load parallel to the ridge?

A bar of varying square cross section is loaded symmetrically as shown in the figure. Loads shown are placed on one of the axes of symmetry of cross-section. Ignoring self weight, the maximum tensile stress in N/mm² anywhere is

The vertical hydraulic conductivity of the top soil at certain is 0.2 cm/hr. A storm of intensity 0.5 cm/hr occurs over the soil for an indefinite period. Assuming the surface drainage to be adequate, the infiltration rate after the storm has lasted for a very long time, shall be

For a two-dimensional irrotational flow, the velocity potential is defined as ^$\psi$= In(x²+y²). Which of the following is a possible stream function,^$\Psi$, for this flow?

Temperature stresses in concrete pavements may cause the slab to crack. If a slab cools uniformly, then the crack will develop at the following locations of the slab

The moisture content of soil in the root zone of an agricultural crop at a certain stage is found to be 0.05. The field capacity of the soil is 0.15. The root zone depth is 1.1 m. The consumptive use of crop at this stage is 2.5 mm/day and there is no precipitation during this period. Irrigation efficiency is 65%. It is intended to raise the moisture content to the field capacity in 8 days through irrigation. The necessary depth of irrigation is

A flat plate is kept in an infinite fluid medium. The fluid has a uniform free stream velocity parallel to the plate. For the laminar boundary layer formed on the plate, pick the correct option matching:

The speed and delay studies on a defined section of highway are conducted by

The total irrigation depth of water, required by a certain crop in its entire growing period (150 days), is 25.92 cm. The culturable command area for a distributary channel is 100,000 hectares. The distributary channel shall be designed for a discharge

If L defines the Laplace Transform of a function, L [sin (at)] will be equal to

From amongst the following sewage treatment options, largest land requirements for a given discharge will be needed for

A laboratory model of a river is built to a geometric scale of 1:00. The fluid used in the model is oil of mass density 900 kg/m³. The highest flood in the river is 10,000 m³/s. The corresponding discharge in the model shall be

Top ring beam of an Intze tank carries a hoop tension of 120 kN. The beam cross section is 250 mm wide and 400 mm deep and it is reinforced with 4 bars of 20 mm diameter of Fe 415 grade. Modular ratio of the concrete is 10. The tensile stress in N/mm² in the concrete is

In a redundant joint model, three bar members are pin connected at Q as shown in the figure. Under some load placed at Q, the elongation of the members MQ and OQ are found to be 48 mm and 35 mm respectively. Then the horizontal displacement u and the vertical displacement v of the node Q, in mm, will be respectively

A steel portal frame has dimensions, plastic moment capacities and applied loads as shown in the figure. The vertical load is always twice of the horizontal load. The collapse load P required for the development of a beam mechanism is

The results of analysis of a raw water sample are given below:

From the data given above, it can be inferred that water needs removal of

A long structural column (length = L) with both ends hinged is acted upon by an axial compressive load P. The differential equation governing the bending of column is given by ^{$Ei \frac{d^2y}{dx^2} = - py$}where y is the structural lateral deflection and EI is the flexural rigidity. The first critical load on column responsible for its buckling is given by

The state of two dimensional stress acting on a concrete lamina consists of a direct tensile stress,^$\sigma_x$= 1.5 N/mm², and shear stress _^$\tau$= 1.20 N/mm², which cause cracking of concrete. The tensile strength of the concrete in N/mm² is

A truss, as shown in the figure, is carrying 180 kN load at node L₂. The force in the diagonal member M₂U₄ will be

The Fourier series expansion of a symmetric and even function, ƒ(x) where f(x) = 1 + ^{$(2x/ \pi), - \pi$}< x < 0 and = 1– ^$(2\pi/\pi)$0 < x < _^$\pi$ will be

A simply supported beam of uniform rectangular cross section of width b and depth h is subjected to linear temperature gradient, 0^o at the top and T^o at the bottom, as shown in the figure. The coefficient of linear expansion of the beam material is α. The resulting vertical deflection at the midspan of the beam is

Group I shows different loads acting on a beam and Group 2 shows different bending moment distributions. Match the load with the corresponding bending moment diagram.

Compaction of an embankment is carried out in 500 mm thick layers. The rammer used for compaction has a foot area of 0.05 sq. m and the energy imparted in every drop of rammer is 400 Nm. Assuming 50% more energy in each pass over the compacted area due to overlap, the number of passes required to develop compactive energy equivalent to Indian Standard light compaction for each layer would be

For the soil strata shown in figure, the water table is lowered by drainage by 2 m and if the top 2 m thick silty sand stratum remains saturated by capillary action even after lowering of water table, the increase in effective vertical pressure in kPa at mid-height of the clay layer will be

Group I contains some properties of concrete/cement and Group 2 contains list of some tests on concrete/cement. Match the property with the corresponding test.

For the (3 × 3) pile group shown in the figure, the settlement of pile group, in a normally consolidated clay stratum having properties as shown in the figure, will be

A braced cut, 5m wide and 7.5 m deep is proposed in a cohesionless soil deposit having effective cohesion c’=0 and effective friction angle,^$\phi$’=36⁰. The first row of struts is to be installed at a depth of 0.5 m below ground surface and spacing between the struts should be 1.5 m. If the horizontal spacing of struts is 3 m and unit weight of the deposit is 20 kN/m³, the maximum strut load will be

A hydraulic jump takes place in a triangular channel of vertex angle 90^o, as shown in figure. The discharge is 1 m³/s and the pre-jump depth is 0.5 m. What will be the post-jump? (Take g = 9.81 m/s²)

A concrete column carries an axial load of 450 kN and a bending moment of 60 kN at its base. An isolated footing of size 2 m by 3 m, with 3 m side along the plane of the bending moment, is provided under the column. Centres of gravity of column and footing coincide. The net maximum and the minimum pressures in kN/m² on soil under the footing are respectively

Group I contains some elements in design of a simply supported plate girder and Group 2 gives some qualitative locations on the girder. Match the items of two lists as per good design practice and relevant codal provisions.

At a reclamation site for which the soil strata is shown in figure, a 3 m thick layer of a fill material is to be laid instantaneously on the top surface. If the coefficient of volume compressibility, m_v for clay is 2.2 x 10^-4 m²/kN, then the consolidation settlement of the clay layer due to placing of fill material will be

A horizontal jet strikes a frictionless vertical plate (the plan view is shown in the figure). It is then divided into two parts, as shown in the figure. If the impact loss can be neglected, what is the value of ^$\theta$?

Match List I with List II and select the correct answer.

A solids sphere (diameter 6 mm) is rising through oil (mass density 900 kg/m³, dynamic viscosity 0.7 kg/ms) at a constant velocity of 1 cm/s. What is the specific weight of the material from which the sphere is made? (Take g = 9.81 m/s²)

Two pipelines, one carrying oil (mass density 900 kg/m³) and the other water, are connected to a manometer as shown in the figure. By what amount the pressure in the water pipe should be increased so that the mercury levels in both the limbs of the manometer become equal? (Mass density of mercury = 13,550 kg/m³ and g = 9.81 m/s²)

Setting test on a sample drawn from Aeration Tank liquor of ASP (MLSS = 2800 mg/I) was carried out with 1 litre sample. The test yielded a settled volume of 200 ml. The value of Sludge Volume Index shall be

While designing a hydraulic structure, the piezometric head at bottom of the floor is computed as 10 m. The datum is 3 m below floor bottom. The assured standing water depth above the floor is 2 m. The specific gravity of the floor is computed as 10 m. The datum is 3 m below floor bottom. The assured standing water depth above the floor is 2 m. The specific gravity of the floor material is 2.5. The floor thickness should be

Match the items of List-I with List-II and select the correct answer.

While applying the Rational formula for computing the design discharge, the rainfall duration is stipulated as the time of concentration because

The plan area of a reservoir is 1 km². The water level in the reservoir is observed to decline by 20 cm in a certain period. During this period the reservoir receives a surface inflow of 10 hectare-meters, and 20 hectare-meters are abstracted from the reservoir for irrigation and power. The pan evaporation and rainfall recorded during the same period at a near by meteorological station are 12 cm and 3 cm respectively. The calibrated pan factor is 0.7. The seepage has from the reservoir during this period in hectare-meters is

A traffic stream in a particular direction of a two lane road is moving with a constant speed of 50 kmph, with an average headway of .52 seconds. The longitudinal distance between two consecutive vehicles is

The design speed for a National Highway is 100 kmph. If the maximum permissible superelevation is 0.10 and the coefficient of lateral friction is 0.15, the ruling minimum radius of horizontal curve on the highway should be

The plate load test conducted with a 75 cm diameter plate on soil subgrade yielded a deflection of 2.5 mm under a stress of 800 N/cm². The modulus of elasticity of the subgrade soil, in kN/cm², is

An ideal horizontal flow setting basin is 3 m deep having surface area 900 m². Water flows at the rate of 8000 m³/d, at water temperature 20^oC (m = 10^-3 kg/m.s) and p = 1000 kg/m³). Assuming Stokes law to be valid, the proportion (percentage) of spherical sand particles (0.01 mm in diameter with specific gravity 2.65), that will be removed, is

In the Marshall method of mix design, the coarse aggregates, fine aggregates, filler and bitumen, having respective specific gravities of 2.62, 2.72, 2.70 and 1.02, are mixed in the ratio of 55, 34.6, 4.8. The specific gravity of the mix would be

A beam PQRS is 18 m long and is simply supported at points Q and R 10 m. Overhangs PQ and RS are 3 m and 10 m part. Overhangs PQ and RS are 3 m and 5 m respectively. A train of two point loads of 150 kN and 100 kN, 5 m apart, crosses this beam from left to right with 100 kM load leading.

The maximum sagging moment under the 150 kN load anywhere is

Match the following:

A beam PQRS is 18 m long and is simply supported at points Q and R 10 m. Overhangs PQ and RS are 3 m and 10 m part. Overhangs PQ and RS are 3 m and 5 m respectively. A train of two point loads of 150 kN and 100 kN, 5 m apart, crosses this beam from left to right with 100 km load leading.

During the passage of the loads, the maximum and the minimum reactions at support R, in kN, are respectively

A beam PQRS is 18 m long and is simply supported at points Q and R 10 m. Overhangs PQ and RS are 3 m and 10 m part. Overhangs PQ and RS are 3 m and 5 m respectively. A train of two point loads of 150 kN and 100 kN, 5 m apart, crosses this beam from left to right with 100 kM load leading.

The maximum hogging moment in the beam anywhere is

Match the following:

Results of a water sample analysis are as follows:

(milliequivalent weight of CaCO₃ = 50 mg/meq). Hardness of the water sample in mg/l as CaCO₃ is

A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm² and 2.2 N/mm² respectively.

The theoretical failure load of the beam for attainment of limit state of collapse in flexure is

A reinforced concrete beam, size 200 mm wide and 300 mm deep overall is simply supported over a span of 3 m. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm bottom face and nominal shear reinforcement. The characteristics compressive strength and the bending tensile strength of the concrete are 20.0 N/mm² and 2.2 N/mm² respectively.

Ignoring the presence of tension reinforcement, find the value of load P in kN when the first flexure crack will develop in the beam.

A truss tie consisting of 2 ISA 75 x 75 x 8 mm carries a pull of 150 kN. At ends the two angles are connected, one each on either side of a 10 mm thick gusset plate, by 18 mm diameter rivets arranged in one row. The allowable stresses in rivet are f_s = 90.0 N/mm² and f_br = 250 N/mm².

Maximum tensile stress in the tie in N/mm² is

A truss tie consisting of 2 ISA 75 x 75 x 8 mm carries a pull of 150 kN. At ends the two angles are connected, one each on either side of a 10 mm thick gusset plate, by 18 mm diameter rivets arranged in one row. The allowable stresses in rivet are f_s = 90.0 N/mm² and f_br = 250 N/mm².

Minimum number of rivets required at each end is

Figure shows the geometry of a strip footing supporting the load bearing walls of a three storied building and the properties of clay layer.

If the pressure acting on the footing is 40 kPa, the consolidation settlement of the footing will be

Match the following:

sewage discharged into inland waters)| (Allowable limit, mg/I)| | P BOD₅| 1. 50| | Q COD| 2. 30| | R Oil and Grease | 3. 20| | S Total Suspended Solids| 4. 10| | | 5. 5| | | 6. 3|

A canal having side slopes 1:1 is proposed to be constructed in a cohesive soil to a depth of 10 m below the ground surface. The soil properties are: ^$\phi_u$=150, C_n = 12 kPa, e = 1.0, Gs = 2.65.

If Taylor’s Stability Number, Sn is 0.08 and if the canal flows full, the factor of safety with respect to cohesion against failure of the canal bank slopes will be

Figure shows the geometry of a strip footing supporting the load bearing walls of a three storied building and the properties of clay layer.

If the elastic modulus and the Poisson’s ratio of the clay layer are respectively 50×10³ kPa and 0.4 and if the influence factor for the strip footing is 1.75, the elastic settlement of the footing will be

A very wide rectangular channel carries a discharge of 8m³/s per m width. The channel has a bed slope of 0.004 and Manning’s roughness coefficient, n = 0.015. At a certain section of the channel, the flow depth is 1 m.

What Gradually Varied Flow profile exists at this section?

A canal having side slopes 1:1 is proposed to be constructed in a cohesive soil to a depth of 10 m below the ground surface. The soil properties are: ^$\phi_u$=150, C_n=12 kPa, e = 1.0, Gs = 2.65.

If there is a sudden drawdown of water in the canal and if Taylor’s Stability Number for the reduced value of ^$\phi_u$is 0.126, the factor of safety with respect to cohesion against the failure of bank slopes will be

A very wide rectangular channel carries a discharge of 8 m³/s per m width. The channel has a bed slope of 0.004 and Manning’s roughness coefficient, n = 0.015. At a certain section of the channel, the flow depth is 1 m.

At what distance from this section the flow depth will be 0.9 m? (Use the direct step method employing a single step)

Column I below gives a list of physical properties of aggregates which should be determined to judge their suitability in road construction. Column II gives a list of laboratory tests which are conduced to determine these properties.

Which of the following matches is correct?

A pipeline (diameter 0.3 m, length 3 km) carries water from point P to point R (see figure). The piezometric heads at P and R are to be maintained at 100 m and 80 m, respectively. To increase the discharge, a second pipe is added in parallel to the existing pipe from Q to R. The length of the additional pipe is also 2 km. Assume the friction factor, f = 0.04 for all pipes and ignore minor losses.

What is the increase in discharge if the additional pipe has same diameter (0.3 m)?

A pipeline (diameter 0.3 m, length 3 km) carries water from point P to point R (see figure). The piezometric heads at P and R are to be maintained at 100 m and 80 m, respectively. To increase the discharge, a second pipe is added in parallel to the existing pipe from Q to R. The length of the additional pipe is also 2 km. Assume the friction factor, f = 0.04 for all pipes and ignore minor losses.

If there is no restriction on the diameter of the additional pipe, what would be the maximum increase in discharge theoretically possible from this arrangement?

An average rainfall of 16 cm occurs over a catchment during a period of 12 hours with uniform intensity. The unit hydrograph (unit depth = 1 cm, duration = 6 hours) of the catchment rises linearly from 0 to 30 cumecs in six hours and then falls linearly from 30 to 0 cumecs in the next 12 hours. ^$\psi$index of the catchment is known to be 0.5 cm/hr. Base flow in the river is known to be 5 cumecs.

Peak discharge of the resulting direct runoff hydrograph shall be

An average rainfall of 16 cm occurs over a catchment during a period of 12 hours with uniform intensity. The unit hydrograph (unit depth = 1 cm, duration = 6 hours) of the catchment rises linearly from 0 to 30 cumecs in six hours and then falls linearly from 30 to 0 cumecs in the next 12 hours. ^$\psi$index of the catchment is known to be 0.5 cm/hr. Base flow in the river is known to be 5 cumecs.

Area of the catchment in hectares is

A water treatment plant treating 10 mld of water requires 20 mg/I of filter Alum, Al₂ (SO₄)₃.18 H₂O. The water has 6 mg/l of alkalinity as CaCo₃ (Al = 26.97, S = 32, O = 16, H = 1, Ca = 40, and C = 12).

Total alkalinity requirement (10⁶ mg per day as CaCO₃) matching filter Alum, shall be

A water treatment plant treating 10 mld of water requires 20 mg/I of filter Alum, Al₂ (SO₄)₃. 18 H₂O. The water has 6 mg/l of alkalinity as CaCo₃ (Al = 26.97, S = 32, O = 16, H = 1, Ca = 40, and C = 12).

Quantity of Quick Lime required (10⁶ mg per year as CaO) shall be

A conventional Activated Sludge Plant treating 1000 m³/d of municipal waste water disposes of its anaerobically digested sludge on relatively impervious farmland. Use the following data:

BOD = 190 mg/I (Excess activated sludge returned to primary) | | 2. Primary Setting| SS-50% removal BOD-30% removal| | 3. Excess Activated Sludge applied (80% Volatile of total)| 0.4 g VSS produced per g BOD| | 4. Anaerobic Digester| VSS reduced 50% Digested Sludge Concentration – 60% Sludge Specific Gravity-1| | 5. Application on farmland| 2 m³ /ha.d|

Total volatile suspended solids to be anaerobically digested (kg/d, VSS) shall be

A conventional Activated Sludge Plant treating 1000 m³/d of municipal waste water disposes of its anaerobically digested sludge on relatively impervious farmland. Use the following data:

BOD = 190 mg/I (Excess activated sludge returned to primary) | | 2. Primary Setting| SS-50% removal BOD-30% removal| | 3. Excess Activated Sludge applied (80% Volatile of total)| 0.4 g VSS produced per g BOD| | 4. Anaerobic Digester| VSS reduced 50% Digested Sludge Concentration – 60% Sludge Specific Gravity-1| | 5. Application on farmland| 2 m³ /ha.d|

Area requirements (ha) for disposal of the sludge on farmland shall be

Which of the following sewage treatment methods has inherent problem of odour, ponding, and fly nuisance?

Zero hardness of water is achieved by

Maximum strains in an extreme fibre in concrete and in the tension reinforcement (Fe - 415 grade and Es = 200 kN/mm²) in a balanced section at limit state of flexure are respectively

The effective length of a column in a reinforced concrete building frame, as per IS: 456-2000, is independent of the

The working stress method of design specifies the value of modular ratio, m = 280/ ^{$(3\sigma_{cbc})$}, where ^{$\sigma_{cbc}$}is the allowable stress in bending compression in concrete. To what extent does the above value of m make any allowance for the creep of concrete?

A masonry dam is found on previous sand having porosity equal to 45% and specific gravity of sand particles is 2.65. For a desired factor of safety of 3 against sand boiling, the maximum permissible upward gradient will be

Water is pumped from a well tapping an unconfined aquifer at a certain discharge rate and the steady state drawdown (X) in an observation well is monitored. Subsequently, the pumping discharge is doubled and the steady state drawdown in the same observation well is found to be more than double (i.e. more than 2X). This disproportionate drawdown is caused by

A double draining clay layer, 6 m thick, settles by 30 mm in three years under the influence of a certain loads. Its final consolidation settlement has been estimated to be 120 mm. If a thin layer of sand having negligible thickness is introduced at a depth of 1.5 m below the top surface, the final consolidation settlement of clay layer will be

A 25 kN point load acts on the surface of an infinite elastic medium. The vertical pressure intensity in kN/m² at a point 6.0 m below and 4.0 m away from the load will be

In a plate load test conducted on cohesionless soil, a 600 mm square test plate settles by 15 mm under a load intensity of 0.2 N/mm². All conditions remaining the same, settlement of a 1 m square footing will be

A granular soil possesses saturated density of 20 kN/m³. Its effective angle friction is 35 degrees. If the desired factor of safety is 1.5, the safe angle of slope for this soil, when seepage occurs at and parallel to the surface, will be

A “H” shaped frame of uniform flexural rigidity EI is loaded as shown in the figure. The relative outward displacement between points K and O is

The stiffness K of a beam deflecting in a symmetric mode, as shown in the figure, is