To control vehicular pollution from exhaust of vehicles, following is fitted:

The concentration of OH- ion in a water supply is measured as 17 mg / L at 25° C. What is the pH of the water sample?

A 50 mm × 8 mm tie bar is supposed to carry a load of 80 kN. A specimen of the quality steel of 250 mm² cross-sectional area was tested in a laboratory. The maximum load carried by the specimen was 125 kN. What is the required gauge length (mm) for specimen if the permitted yield stress is 280 N/mm²?

A sub grade soil sample was tested using standard CBR apparatus and the observations are given below.

Assuming that the load-penetration curve is convex throughout, the CBR value (%) of the sample is

For the overhanging beam shown in the figure, the magnitude of maximum bending moment (in kN-m) is _____.

A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is

The value of $\underset{x\to 1}{lim}\left(\frac{1-e^{-c\left(1-x\right)}}{1-x{e}^{-c\left(1-x\right)}}\right)$ is

The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that 45 percent of its volume is in oil while the rest is in water. The density of the body is ___________ kg/m³.

The specific gravity of oil is 0.7 and density of water is 1000 kg/m³.

Acceleration due to gravity g = 10 m/s².

A vehicle is moving with a design speed of 100 kmph on a horizontal curve of radius of 150 m. What is the length of transition curve if the width of the carriageway, W = 7.5 m, rate of superelevation, e = 0.05, and rate of introduction of superelevation, N = 1 in 150? Consider the pavement is rotated at the inner edge of the pavement.

A vane shear test was performed on saturated clay layer at the site and it is noted that a torque of 45 N-m was required to shear the soil. In order to remould the soil, the vane was rotated rapidly under the certain value of torque say “x”. If the sensitivity of the clay is 8, then calculate the value of “x” in N-m.

Assume diameter and length of the vane to be 70 mm and 130 mm respectively, consider two way shearing.

Degree of static indeterminacy of the structure as shown in the figure is

Consider a flow through a nozzle, as shown in the figure below.

The air flow is steady, incompressible and inviscid. The density of air is 1.23 kg/m³. The pressure difference, (p₁ - p_atm) is ______ kPa (round off to two decimal places).

In order to compute the airport reference temperature and the standard temperature with respect to elevation, the monthly mean of average daily temperature and the monthly mean of the maximum daily temperature of the hottest month of the year is found to be 32^o C and 41.5^o C respectively. The airport reference temperature is: 

Activities A, B, C and D from the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are independent of each other.

The probability that the project will be completed within 40 days is ______ (round off to two decimal places).

(Note: Probability is a number between 0 and 1).

A municipal wastewater flow of 5000 m³/d is to be treated using an activated sludge system. Assuming an MLSS concentration of 1500 mg/L and an underflow concentration of 5000 mg/L form the secondary clarifier. If the sludge age is 12 days and volume of the tank is 1200 m³ then the volume of solids (m³/d) that must be wasted each day is ________. 

A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is

A road requires drivers to negotiate a turn with a radius of 250 m and 12° of banking. The coefficient of side friction required to allow a car to travel at 150 km/hr along the curve is _____.

Which compound of cement is responsible for strength of cement?

The area (in percentage) under standard normal distribution curve of random variable Z within limits from –3 to +3 is ______ 

Assertion (A): Terzaghi considered only primary consolidation and neglected secondary consolidation in his theory of consolidation.

Reason (R): Secondary consolidation begins after the end of the primary consolidation.

For a 30 m diameter and 1 m deep single stage high rate trickling filter for the following data

Sewage flow = 4.5 MLD, Recirculation ratio = 1.4, BOD of raw sewage = 250 mg/l and BOD removed in primary clarifier is 25 %

For the following data Efficiency of a single stage High rate trickling filter is _________%

A soil mass ABC having C = 8 kN/m² and φ = 20° and γ = 19kN/m² is resting on an inclined impermeable clay layer as shown in figure. What is the factor of safety against wedge failure along the interface AB?

Within a boundary layer for a steady incompressible flow, the Bernoulli equation

 Which of the following statements is/are true ?

The simply supported beam shown in the figure is loaded symmetrically using two equal point loads P. The radius of curvature of the deflection curve is 15 m for the portion of the beam that is subjected to pure bending. The vertical deflection (in mm) at point M. equidistant from both the supports is ________ (up to two decimal places).

For a portion of highway the line AB meets BC. Point A is at a MSL of 2000 m and point B is at a MSL of 1999.9 m which is at a distance of 2.5 m and point C which is at a distance of 5m from A is at a MSL of 2000.025 m. A valley curve needs to be designed at a velocity of 90 kmph. Take t = 2.5 sec, f = 0.35. The length of the valley curve is _____ m

For the hydrograph analysis, the time of concentration is defined as ________

Consider the vector field F = ax (4y - c1z) + ay (4x + 2z) +az (2y +z) in rectangular coordinated system (x, y, z) with unit vectors ax, ay, and az, If the filed F is irrotational (conservative), then the constant c₁ (in integer) is _____

Find the positive real root of x³ - x - 3 = 0 using Newton-Raphson method. If the starting guess (x₀) is 2, the numerical value of the root after two iterations (x₂) is __________ (round off to two decimal places).

Choose the correct statements with respect to compaction:

 Which of the following statements is/ are correct?

An 8-meter-long simply supported beam of size 300 × 600 mm is prestressed with force of 1400 kN as shown in the figure below.

Calculate the minimum eccentrically required at the mid span, so as to achieve complete load balancing of the beam loaded with uniformly described intensity of 30 kN/m (including self-weight).

A circular metallic rod of length 250 mm is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of 0.2 mm between the rod and the wall on the right side. If the temperature of the rod is increased by 200° C, the magnitude of axial stress developed in the rod is _____ MPa.

Young’s modulus of the material of the rod is 200 GPa and the coefficient of thermal expansion is 10^-5 per °C.

For a two dimensional, incompressible flow having velocity components u and v in the x and y directions, respectively, the expression $\frac{\delta (u^2)}{\delta x}+\frac{\delta (uv)}{\delta y}$ can be simplified to

A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a massless and inextensible string PQ. If the coefficient of static friction for all surfaces is 0.4, the minimum force F (in kN) needed to move the block S is

A circular column is subjected to an un-factored load of 1600 kN. The effective length of the column is 3.5 m, the concrete is M 25, and the value of ${\rho }_g=\frac{A_{SC}}{A_g}=2\mathrm{\%}$ for Fe 415 steel. The design diameter of the column will be nearly

Flow depth and bed slope of a wide rectangular alluvial canal are 3.8 m and 1.5 × 10^-4 respectively. The velocity is found out to be 1.9 m/s. The mean size of the sediment particles is 1.6 mm. What is the ratio (corrected up to three decimal point) of rugosity coefficient given by Strickler’s formula to the actual rugosity coefficient?

The permeability of sand in horizontal and vertical directions are 3 × 10-3 cm/sec and 1 × 10-3 cm/sec and the permeability of clay in horizontal and vertical directions are 9 × 10-7 cm/sec and 3 × 10-9 cm/sec, then the ratio of seepage loss per meter length of dam in sand to clay is:

A wastewater sample is experimented for 5-day BOD at 20°C and it is found to be 120 mg/L. If the reaction rate constant is 0.414 (base e) per day then the amount of BOD remaining in the sample after 8 days is ______

Statement (I): Air-entraining cement has a higher initial setting time than O.P.C and resists frost action better.

Statement (II): Air-entraining cement has a longer final setting time compared to O.P.C 

A parametric curve defined by $x=\cos \left(\frac{\pi u}{2}\right),y=\sin \left(\frac{\pi u}{2}\right)$in the range of 0 ≤ u ≤ 1 is rotated about the X – axis by 360 degrees. Area of the surface generated is

An embankment of formation width 10 m and side slope 1.5 H: 1 V is to be constructed. The depth at center at different chainages is shown in the table below. Width at top of embankment is 30 m.

If the ground is levelled in transverse direction to center line of the road, calculate the total volume (in m³) of earth required for the embankment by trapezoidal method.

A 10 m wide rectangular channel has a bed slope of 3.33 × 10^-3 and the Manning's coefficient 0.015. Water in the channel is flowing at a uniform depth of 3 m. At a particular section gradually varied flow (GVF) is observed and the flow depth is measured as 3.1 m. The GVF profile at that section is classified as

 A 300 mm long copper wire of uniform cross-section is pulled in tension so that a maximum tensile stress of 270 MPa is developed within the wire. The entire deformation of the wire remains linearly elastic. The elastic modulus of copper is 100 GPa. The resultant elongation (in mm) is ________.

The vertical photograph was exposed with a 60 cm focal length camera at a flying height of 3,000 meters above datum. What is the photo scale at point a if the elevation of point A on the ground is 300 m above datum?

The rotational stiffness coefficient indicated as K₁₁ for the frame with details as shown is

A slope of infinite extent is made in a dense sand layer at angle of 30° to the horizontal. Determine the factor of safety of the slope against shear failure if the angle of internal friction of the soil be 26° 

At a particular site location, sampling is performed, length of sample before withdrawal is 700 mm and penetration of the samples in the soil mass is 500 mm. Calculate the recovery ratio of the sample?

Consider a stepped shaft subjected to a twisting moment applied at B as shown in the figure. Assume shear modulus, G = 77 GPa. The angle of twist at C (in degrees) is _____ (Give answer up to three decimal places)

A frame is being shown in the figure below, where a load P is acting horizontally. The support A is a fixed support while support D is a hinged support.

All the members are axially rigid. Based on this choose the correct statements out of the following:

Consider the initial value problem below. The value of y at x = In 2, (rounded off to 3 decimal places) is

$\frac{dy}{dx}=2x-y,y\left(0\right)=1$

An RC square footing of the side length of 2 m and uniform overall depth of 300 with an effective cover of 40 mm is provided on a 200 × 200mm column. As per IS 456: 2000, the critical section for one-way shear from the center of column (in mm) is ______.

A loamy soil with the dry unit weight of 1.3 g/cc has the root zone depth of 80 cm. The field capacity is 30 percent and the plant start wilting if the moisture content falls below 10 percent. If it is given that the minimum water depth required for the optimum growth of the plant is the half of the field capacity moisture, then the water required to raise the water level from wilting point to optimum moisture is ______

A valley curve which is formed by a descending grade of 1 in 30 meeting an ascending grade 1 in 40 for a design speed of 100 kmph. Assume: Driver’s reaction time = 2.5 sec, Coefficient of friction = 0.35 and Allowable Rate of Change of centrifugal Acceleration = 0.6 m/sec³ respectively. Then which of the following is true?

In a water treatment plant, bleaching power is used for the disinfection of the water. The facility serving a rural area has the water supply rate of 80 lpcd with population of 5000. If the daily requirement of the bleaching powder is 3.5 kg and the available chlorine needed to chlorinate the water supply is 1.5 ppm, then the efficiency of bleaching powder dosage is ______