If the per capita contribution of suspended solids and BOD is 90 gm and 55 gm, find the population equivalents of

1. A combined system serving 1000 persons and having 75 gm per capita daily of BOD.
2. 40,000 litres daily of industrial wastewater containing 1800 mg/l of suspended solids. Respectively,

Consider the following statements.

1. Hydraulic gradient required to initiate " quick" condition is independent of the ratio of volume of voids to volume of solids in a soil mass. 

2. Initiation of piping under hydraulic structures can be prevented by increasing the length of flow path of water.

3. Seepage pressure is independent of the coefficient permeability.

In a certain irrigation project and in a given year, 72% and 56% of the culturable command area remained unirrigated in Kharif and Rabi season, then the intensity of irrigation for that year and for that project, will be

A cantilever beam AB of length ‘l’ and subjected to a U.D.L. of intensity ‘w’ KN/m over a length ‘b’ is over a in the figure. If EI is constant, then what is the deflection at C?

Which one of the statements is/are correct?

The pH values of two samples A and B are 7.2 and 8.4 respectively. Assume the variation of [H]⁺ with time to be linear. The average pH value of water is _______

A steel bar is subjected to an axial pull of 84 kN. Stress-induced into the bar is 140 N/mm². If Young's modulus is 2 x 10⁵ N/mm², then the longitudinal strain produced will be

Which one of the following is correct ILD for the Shear force just left to 'C' as shown in the figure.

A cylindrical container that is 50 cm in height and 10 cm in radius is filled with water up to the top. The vessel is open at the top. The quantity ______ × 10^-3 m³ of water left in the container when it is rotated at a speed of 420 rpm.

A rectangular column 300 x 550 mm effective is reinforced with 4 – 32 mm & 2 – 16 mm diameter bars. Lateral ties of diameter ______ should be provided at a spacing of  ________.

What is the ratio of the shape factors for beam cross-sections having rectangular, circular and triangular shapes and of same area?

A smooth circular pipe of a diameter of 50 cm carrying water with an average velocity of 25 cm/s and dynamic viscosity of 0.2 poise. The thickness of the laminar sublayer is ______mm.

Consider the following statements:

In the water supply distribution network,

1) The gridiron system requires more lengths of pipelines and a larger number of cut-off valves.

2)  Employing a gridiron system, Repair works can be easily done without affecting the other users.

3) In a dead-end system, the pressure is almost constant and very high at remote parts.

4) Dead end system requires less number of cut-off valves and more number of & scour valves.

Which of these statements are correct?

Consider the given matrix, $A=\left[\begin{array}{ccc}2& 3& 7\\ 0& 5& 1\\ 0& 0& 0\end{array}\right]$, Then the minimum number of eigenvalues of matrix A.adj(A) that are zero is _______. 

The integral $\underset{1}{\overset{3}{\int }}\frac{1}{x}dx$ is evaluated using Simpson rule on two equal intervals with length 1.

For a specific material, the modulus of rigidity is 40 % of the young’s modulus. Then 

A CU test was conducted on a soil sample with a cell pressure of 100 kN/m². The deviator stress at failure was observed to be 60 kN/m². The soil is known to have cohesion C'=0 and the angle of shearing resistance is 30^o and undrained cohesion is 0 and the undrained angle of shearing resistance is 13.3^o. What was the pore pressure (kN/m2) at failure? 

A 5^o branch curve deviated from a n^o main track in the reverse direction. If the speed in the branch track and main track is restricted to 35 Kmph and 80 Kmph respectively, then calculate the value of ‘n’ (to the nearest integer) if both the track are B.G.

Directions : Select your answer to following question using the codes given below :

Codes :

Assertion A : The load carrying capacity of bored cast in - situ pile in a sandy soil is much less than that of a driven pile of similar dimension.

Reason R : A drive pile generates much more point bearing resistance than a bored pile

The in-situ density of an embankment, compacted at a water content of 12% was determined with the help of a core cutter. The empty mass of the cutter was 1286 grams and the cutter full of soil had a mass of 3195 grams, the volume of the cutter being 1000 cm³. Calculate the degree of saturation (in percent, up to two decimal places) of the embankment. (Take G = 2.7)

Find out the critical path and duration of following project network:

For the beam as shown, the value of the maximum bending moment can be written as $\frac{w{L}^2}{C}$, Then what will be the value of C?

What would be the specific force (in kN m ³ / kN, up to two decimal places) for a triangular channel of apex angle 90° and top width of 2 m if the water is flowing at the rate of 10 m ³ / s in the channel? Take g = 10 m / s ² .

Two coins are tossed one after another. The probability of the first coin and the second coin to get the head, is x and y respectively. If the P [Both the coins show up heads] = P [first coin shows up tail and the second coin show up head]. Then the value of x is ________

The divergence of the vector field $3xz\hat{i}+2xy\hat{j}-y{z}^2\hat{k}$ at a point (1,1,1) is equal to

A circle of 100 mm in diameter is inscribed in a steel plate before it is stressed and the plate is loaded as shown in the figure.

Determine the major axis of the ellipse formed in mm [up to 2 decimal]. Take E = 2.1 × 10⁶ kg/cm² and Poisson's ratio is 0.28 

Consider the following statements regarding slip/failure surface 

1) Planer failure commonly occurs in soil deposits with the specified plane of weakness

2) Circular failure is also known as composite failure

3) Noncircular failure occurs in non-homogeneous soil

Which of the above statement is/are true?

Calculate the length of the transition curve on a plain terrain using the following data:

Design speed = 65 kmph

The radius of the circular curve = 220 m

Allowable rate of introduction of superelevation (pavement rotated about the center line) = 1 in 150

Pavement width including extra widening = 7.5m

A block of negligible mass rests on a surface that is inclined at 30° to the horizontal plane as shown in the figure. When a vertical force of 900 N and a horizontal force of 750 N are applied, the block is just about to slide.

The coefficient of static friction between the block and surface is _______ (round off to two decimal places).

Four rain gauges A, B, C, and D are placed at the corners of a square region of side 4 km and the fifth rain gauge E is placed at the center of the region. The precipitation measured at each station is given below.

P_A = 4.8 cm, P_B = 13 cm, P_C = 8 cm, P_D = 5.4 cm, P_E = 9.4 cm

What is the mean precipitation of the region?

An aerial photograph of a terrain is taken at a scale of 1:8500, For 3000 m altitude of the flight above mean sea level and 20 cm focal length of the camera, the expected average elevation of the terrain will be____meter.

Calculate the coefficient a₀ of Fourier series for

$f\left(t\right)=\{\begin{array}{c}{t}^2,0\le t\le 2\\ -t+6,2\le t\le 6\end{array}$

General solution of the Cauchy-Euler equation $x^2\frac{d^{2}y}{d{x}^2}-7x\frac{dy}{dx}+16y=0$ is

For the differential equation $\frac{dy}{dx}=x^{2}y-1,y\left(0\right)=1,$ the value of y at x = 0.1, using the Taylors series method, is given by:

A wastewater sample subjected to standard BOD₅ test yields a test result of 200 mg/L. The rate constant is 0.18/day at 20°C (to the base ‘e’)

Another sample of the same wastewater is tested at a temperature of 30°C. The time in days after which the BOD yielded is 200 mg/L is ______ (up to 2 decimal places).

Two tube wells each of 200 mm diameter penetrate fully in a confined aquifer and are spaced at 150 m. find the ratio of discharge from one well (done independently) to the discharge from both wells under the same drawdown. Take the radius of influence as 200 m.

Which of the following is/are correct? 

For an earth retaining structure loaded with surcharge as shown the total thrust due to active earth pressure per metre length of the wall is__(in kN up to 2 decimal places)

Consider the following statements regarding disposal in the ocean or sea.

1. The sewage must be disposed of at the time of low tides.
2. The sewage should be released at least 3-5 m below the water level.
3. The sewage should be disposed of at least 1.5 - 2 km away from the shore.

Which of the above statements are correct?

A prismatic bar of cross-sectional area 1 mm2 and E = 200 GPa is fastened between two rigid walls at A and B and are subjected to loads as shown.

The support reactions at B and A (in kN) are

The load from the strip foundation as shown below is assumed to be distributed over the soil stratum at 2V:1H, the value of m_v varies with depth of clay stratum as

m_v = (64 + z³) × 10^-5 m²/kN

Where z is the distance from the top of the clay layer.

Assuming one-dimensional consolidation, what is the consolidation (in mm) of the clay stratum?

A wooden pile is driven with a drop hammer weighing 20 kN and in the second trial it was driven with a single-acting steam-hammer of the same weight. In both cases, the free fall was 1.0 m. The penetration in the last blow was 5 mm. What is the ratio of pile carrying capacity of drop hammer to single-acting steam-hammer according to Engineering News Formula ________

Calculate equivalent single-wheel load (ESWL) of dual wheel assembly carrying 2044 kg each at a depth of 200mm. Centre to Centre spacing b/w the two tyres = 270mm and the clear gap between the wall of the tyres = 110 mm.

(Consider the influence angle to be 45^o for the linear dispersion of stress with depth).

Which of the following statements is/are correct?

A traffic engineer needs to find AADT on a road based on data on Wednesday during the month of June.

The daily expansion factor is 7.9 and the monthly expansion factor for June is 1.5. DEF is given for 7 days.

Which of the following is/are correct?

A cast-in-situ bored pile 0.50 m diameter and 10 m deep is placed in a purely cohesive soil. If the cohesion of the soil is 4t/m² and adhesion between the pile and the soil is half the value of cohesion, then the ultimate bearing capacity of the pile is given by 

If staff readings taken on B and C by a tacheometer placed at A are

Calculate the sum of multiplying and additive constants of the tacheometer(in integer).

An equipment has been purchased at an initial cost of Rs. 600000 and has an estimated salvage value of Rs.100000. The equipment has an estimated life of 5 years. The difference between the book values (in Rs.) obtained at the end of 4^th year using sum of years digit method and the constant percentage method is ______

In a cultivated area, the soil has void ratio of 0.82 and field capacity of 40% for a particular crop root zone depth is 1.1 m. If permanent wilting point is 10%, then what will be the maximum depth (in mm) of water extracted by plants from root zone such that moisture does not fall below 25% of the maximum available moisture? Assume soil is fully saturated at field capacity.

A column as shown in the figure is hinged at both ends. Find the maximum temperature that can be raised so that buckling does not occur. Take α of column 5 × 10^-6/ °C

(answer up to 2 decimals)

The longitudinal section of the runway provides the following data:

Calculate the effective gradient of the section.

Which of the following statements are true regarding the structure shown below:

Which of the following is/are correct?

Determine the thickness (in mm, round to next even integer) of a bearing plate at the support for ISMB 600 resting on a concrete masonry wall 250 mm thick for the following data.

Reaction = 200 kN

Grade of concrete: M20

Properties of ISMB 600 @ 1202.71 N/m are:

b_f = 210 mm, t_f = 20.8 mm, t_w = 12 mm, Radius at root = 20 mm