A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to M_P, the minimum load at which the beam would collapse is

The Young's modulus of a wire of of length L and radius r is Y Nm². If the length is reduced to L/2, and radius r/2, its Young's modulus will be

The general solution of ^{$\frac{d^2y}{dx^2} + y = o $ is}

In the design of a reinforced concrete bean the requirement for bond is not getting satisfied. The economical option to satisfy the requirement for bond is by

Group symbols assigned to silty sand and clayey sand are respectively

When a retaining wall moves away from the back-fill, the pressure exerted on the wall is termed as

The product of matrices (PQ)^–1 and P is

A person standing on the bank of a canal drops a stone on the water surface. He notices that the disturbance on the water is not traveling up-stream. This is because the flow in the canal is

A stable channel is to be designed for a discharge of Q m³/s with silt factor f as per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by

Two primary air pollutants are

The capacities of “One-way 1.5 m wide sidewalk (persons per hour)” and “One-way 2-lane urban road (PCU per hour, with no frontage access, no standing vehicles and very little cross traffic)” are respectively

The shape of the STOP sign according to IRC: 67-2001 is

A combined value of flakiness and elongation index is to be determined for a sample of aggregates. The sequence in which the two tests are conducted is

The type of surveying in which the curvature of the earth is taken into account is called

Compaction by vibratory roller is the best method of compaction in case of

The value of $\int\limits_0^3 \int\limits_0^x (6 - x - y) dx dy$ is

Three values of x and y are to be fitted in a straight line in the form y = a + bx by the method of least squares. Given: ^{$\sum x= 6, \sum y=21, \sum x^2\ and\ \sum xy = 46,$} the values of a and b are respectively

A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would be

The following simultaneous equations X + y + z = 3 X + 2y + 3z = 4 X + 4y + kz = 6 will NOT have a unique solution for k equal to

The equation ^{$k_x\frac{\partial^2h}{\partial x^2} + k_z \frac{\partial ^2h}{\partial z^2} = 0$}can be transformed to^{$\frac{\partial^2h}{\partial x_1^2} + \frac{\partial ^2h}{\partial z^2} = 0$}by substituting

The specific gravity of paving bitumen as per IS:73 – 1992 lies between

Solution of ^{$\dfrac{dy}{dx} = -\dfrac{x}{y}$}at x = 1 and y = ^{$\sqrt 3$}is

If probability density function of a random variable X is f(x) = x² for – 1_^$\le$ x_^$\le$1, and = 0 for any other value of x Then, the percentage probability ^{$p \left(}

• \dfrac{1}{3} \le x \le \dfrac{1}{3} \right) $is

The span(s) to be loaded uniformly for maximum positive (upward) reaction at support P, as shown in the figure below, is (are)

The eigen values of the matrix ^{$[P] = \begin{bmatrix} \ 4 & 5 \ \ 2 & -5 \ \end{bmatrix}$}are

Two biodegradable components of municipal solid waste are

A vertical PQ of length L is fixed at its top end P and has a flange to the bottom end Q. A weight W is dropped vertically from a height h (<L) on to the flange. The axial stress in the rod can be reduced by

The base width of an elementary profile of gravity dam of height H is b. The specific gravity of the material of the dam is G and uplift pressure coefficient is K. The correct relationship for no tension at the heel is given by

Unfactored maximum bending moments at a section of a reinforced concrete beam resulting from a frame analysis are 50, 80, 120 and 180 kNm under dead, live, wind and earthquake loads respectively. The design moment (kNm) as per IS: 456- 2000 for the limit state of collapse (flexure) is

A flood wave with a known inflow hydrograph is routed through a large reservoir. The outflow hydrograph will have

The inner (dot) product of two vectors ^{$\vec P$}and ^{$\vec Q$}is zero. The angle (degrees) between the two vectors is

A rigid bar GH of length L is supported by a hinge and a spring of stiffness K as shown in the figure below. The buckling load (P_cr) for the bar will be

The maximum shear stress in a solid shaft of circular cross section having diameter subjected to a torque T is $\tau$ . If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

The members EJ and IJ of a steel truss (shown in the figure below) are subjected to a temperature rise of 30^oC. The coefficient of thermal expansion of steel is 0.000012 per ^oC per unit length. The displacement (mm) of joint E relative to joint H along the direction HE of the truss is

A reinforced concrete column contains longitudinal steel equal to 1 percent of net cross sectional area of the column. Assume modular ratio as 10. The loads carried (using the elastic theory) by the longitudinal steel and the net area of concrete are P_s and P_c respectively. The ratio P_s/P_c expressed as percent is

Cross section of a column consisting of two steel strips, each of thickness t and width b is shown in the figure below. The critical loads of the column with perfect bond and without bond between the strips are P and P₀ respectively. The ratio P/P_o is

The stepped cantilever is subjected to movements, M as shown in the figure below. The vertical deflection at the free end (neglecting the self weight) is

The maximum tensile stress at the section X-X shown in the figure below is

The liquid limit (LL), plastic limit (PL) and shrinkage limit (SL) of a cohesive soil satisfy the relation

A pile of 0.50 m diameter and length 10 m is embedded in a deposit of clay. The undrained strength parameters of the clay are cohesion = 60 kN/m² and the angle in internal friction = 0. The skin friction capacity (kN) of the pile for an adhesion factor of 0.6, is

A footing 2 m x 1 m exerts a uniform pressure of 150 kN/mm² on the soil. Assuming a load dispersion of 2 vertical to 1 horizontal, the average vertical stress (kN/m²) at 1.0 m below the footing is

A saturated clay stratum draining both at the top and bottom undergoes 50 percent consolidation in 16 years under an applied load. If an additional drainage layer were present at the middle of the clay stratum, 50 percent consolidation would occur in

A weir on a permeable foundation with down stream sheet pile is shown in the figure below. The exit gradient as per Khosla’s method is

A test plate 30 cm x 30 cm resting on a sand deposit settles by 10 mm under a certain loading intensity. A footing 150 cm x 200 cm resting on the same sand deposit and loaded to the same load intensity settles by

Water emerges from an ogee spillway with velocity = 13.72 m/s and depth = 0.3 m at its toe. The tail water depth required to form a hydraulic jump at the toe is

A volume of 3.0 x 10⁶ m³ of groundwater was pumped out from an unconfined aquifer, uniformly from an area of 5 km². The pumping lowered the water table from initial level of 102 m to 99 m. The specific yield of the aquifer is

A river reach of 2.0 km long with maximum flood discharge of 10000 m³/s is to be physically modeled in the laboratory where maximum available discharge is 0.20 m³/s. For a geometrically similar model based on equality of Froude number, the length of the river reach (m) in the model is

Rivets and bolts subjected to both shear stress $\tau_{vf_{cal}}$ and axial tensile stress $\tau_{tf_{cal}}$shall be so proportioned that the stresses do not exceed the respective allowable stresses ^$\tau_{vf}$and $\sigma_{tf}$and the value of $\left( \dfrac{\tau_{vf_{cal}}}{\tau_{vf}} + \dfrac{\sigma_{vf_{cal}}}{\sigma_{vf}} \right)$does not exceed

The flow of water (mass density = 1000 kg/m³ and kinematic viscosity = 10^-6 m²/s) in a commercial pipe, having equivalent roughness k_s as 0.12 mm, yields an average shear stress at the pipe boundary = 600 N/m² . The value of k_s / _^$\delta$ (_^$\delta$ being the thickness of aminar sub-layer) for this pipe is

An outlet irrigates an area of 20 ha. The discharge (I/s) required at this outlet to meet the evapotranspiration requirement of 20 mm occurring uniformly in 20 days neglecting other field losses is

Determine the correctness or otherwise of the following Assertion [a] and Reason [r] Assertion: The crown of the outgoing larger diameter sewer is always matched with the crown of incoming smaller diameter sewer. Reason: It eliminates backing up of sewage in the incoming smaller diameter sewer.

The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. the area of the reduced plan is measured as 81 cm², the actual (m²) of the survey is

A water treatment plant is required to process 28800 m³/d of raw water (density = 1000 kg/m³, kinematic viscosity = 10^-6m²/s). The rapid mixing tank imparts a velocity gradient of 900 s^-1 to blend 35 mg/I of alum with the flow for a detention time of 2 minutes. The power input (W) required for rapid mixing is

A roundabout is provided with an average entry width of 8.4 m, width of weaving section as 14 m, and length of the weaving section between channelising islands as 35 m. the crossing traffic and total traffic on the weaving section are 1000 and 2000 PCU per hour respectively. The nearest rounded capacity of the roundabout (in PCU per hour) is

The 5-day BOD of a wastewater sample is obtained as 190mg/I (with k = 0.01h^-1). The ultimate oxygen demand (mg/I) of the sample will be

A linear relationship is observed between speed and density on a certain section of a highway. The free flow speed is observed to be 80 km per hour and the jam density is estimated as 100 vehicles per km length. Based on the above relationship, the maximum flow expected on this section and the speed at the maximum flow will respectively be

The focal length of the object glass of a tacheometer is 200 mm, the distance between the vertical axis of the tacheometer and the optical centre of the object glass is 100 mm and the spacing between the upper and lower line of the diaphragm axis is 4 mm with the line of collimation perfectly horizontal, the staff intercepts are 1 m (top), 2 m (middle), and 3 m (bottom). The horizontal distance (m) between the staff and the instrument station is

A rectangular channel 6.0 m wide carries a discharge of 16.0 m³/s under uniform condition with normal depth of 1.60 m. Manning’s n is 0.015.

The channel width is to be contracted. The minimum width to which the channel can be contracted without affecting the upstream flow condition is

Group I lists estimation methods of some of the water and wastewater quality parameters. Group II lists the indicators used in the estimation methods. Match the estimation method (Group I) with the corresponding indicator (Group II).

Beam GHI is supported by the pontoons as shown in the figure below. The horizontal cross sectional area of each pontoon is 8 m², the flexural rigidity of the beam is 10000 kN-m² and the unit weight of water is 10 kN-m³.

When the middle pontoon is removed, the deflection at H will be

Match Group I (Terminology) with Group II (Definition / Brief Description) for wastewater treatment systems.

The ground conditions at a site are shown in the figure below.

The total stress, pore water pressure and effective stress (kN/m²) at the point P are, respectively

A column is supported on a footing as shown in the figure below. The water table is at a depth of 10 m below the base of the footing.

The net ultimate bearing capacity (kN/m²) of the footing based on Terzaghi’s bearing capacity equation is

Beam GHI is supported by these pontoons as shown in the figure below. The horizontal cross-sectional area of each pontoon is 8 m², the flexural rigidity of the beam is 10000 kN-m² and the unit weight of water is 10 kN-m³.

When the middle pontoon is brought back to its position as shown in the figure above, the reaction at H will be

A rectangular channel 6.0 m wide carries a discharge of 16.0 m³/s under uniform condition with normal depth of 1.60 m. Manning’s n is 0.015.

The longitudinal slope of the channel is

A column is supported on a footing as shown in the figure below. The water table is at a depth of 10 m below the base of the footing.

The safe load (kN) that the footing can carry with a factor of safety 3 is

An automobile with projected area 2.6 m² is running on a road with speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 kg/m³ and 1.5x10^-5 m² /s, respectively. The drag coefficient is 0.30.

The drag force on the automobile is

A horizontal circular curve with a centre line radius of 200 m is provided on a 2-lane, 2-way SH section. The width of the 2-lane road is 7.0 m. Design speed for this section is 80 km per hour. The brake reaction time is 2.4s, and the coefficients of friction in longitudinal and lateral directions are 0.355 and 0.15, respectively.

The safe stopping sight distance on the section is

A rectangular channel 6.0 m wide carries a discharge of 16.0 m³/s under uniform condition with normal depth of 1.60 m. Manning’s n is 0.015.

A hump is to be provided on the channel bed. The maximum height of the hump without affecting the upstream flow condition is

An automobile with projected area 2.6 m² is running on a road with speed of 120 km per hour. The mass density and the kinematic viscosity of air are 1.2 kg/m³ and 1.5x10^-5 m² /s, respectively. The drag coefficient is 0.30.

The metric horse power required to overcome the drag force is

A light house of 120 m height is just visible above the horizon from a ship. The correct distance (m) between the ship and the light house considering combined correction for curvature and refraction, is

A horizontal circular curve with a centre line radius of 200 m is provided on a 2-lane, 2- way SH section. The width of the 2-lane road is 7.0 m. Design speed for this section is 80 km per hour. The brake reaction time is 2.4 s, and the coefficients of friction in longitudinal and lateral directions are 0.355 and 0.15, respectively.

The set-back distance from the centre line of the inner lane is

Design parameters for a signalised intersection are shown in the figure below. The green time calculated for major and minor roads are 34 and 18 s, respectively. The critical land volume on the major road changes to 440 vehicles per hour per lane and the critical lane volume on the minor road remains unchanged. The green time will

A road is provided with a horizontal circular curve having deflection angle 55^o and centre line radius of 250 m. A transition curve is to be provided at each end of the circular curve of such a length that the rate of gain of radial acceleration is 0.3 m/s³ at a curve required at each of the ends is

It is proposed to widen and strengthen an existing 2-lane NH section as a divided highway. The existing traffic in one direction is 2500 commercial vehicles (CV) per day. The construction will take 1 year. The design CBR of soil subgrade is found to be 5 percent. Given: traffic growth rate for CV = 8 percent, vehicle damage factor = 3.5 (standard axles per CV), design life = 10 years and traffic distribution factor = 0.75. The cumulative standard axles (msa) computed are

The length and bearings of a closed traverse PQRSP are given below |||| |---|---|---| | Line| Length (m)| Bearing (WCB)| | PQ| 200| 0^o| | QR| 1000| 45^o| | RS| 907| 180^o| | SP| ?| ?|

The missing length and bearing, respectively of the line SP are

A direct shear test was conducted on a cohesion-less soil (c = 0) specimen under a normal stress of 200 kN/m². The specimen failed at a shear stress of 100 kN/m². The angle of internal friction of the soil (degrees) is

A reinforced concrete beam of rectangular cross section of breadth 230 mm and effective depth 400 mm is subjected to maximum factored shear force of 120kN. The grades of concrete, main steel and stirrup steel are M20, Fe415 and Feb250 respectively. For the area of main steel provided, the design shear strength ^{_{$ \tau_c $}} is per IS: 456-2000 is 0.48 N/mm². The beam is designed for collapse limit state.

The spacing (mm) of 2-legged 8mm stirrups to be provided is

A pre-tensioned concrete member of section 200 mm × 250 mm contains tendons of area 500 mm² at the centre of gravity of the section. The pre-stress in tendons is 1000 N/mm². Assuming modular ratio as 10, the stress (N/mm²) in concrete is

The shape of the cross section which has the largest shape factor is

A reinforced concrete structure has to be constructed along a sea coast. The minimum grade of concrete to be used as per IS: 456-2000 is

A reinforced concrete beam of rectangular cross section of breadth 230 mm and effective depth 400 mm is subjected to maximum factored shear force of 120 kN. The grades of concrete, main steel and stirrup steel are M20, Fe415 and Feb250 respectively. For the area of main steel provided, the design shear strength ^{$ \tau_c $} is per IS: 456-2000 is 0.48 N/mm². The beam is designed for collapse limit state.

In addition, the beam is subjected to a torque whose factored value is 10.90 kNm. the stirrups have to be provided to carry a shear (kN) equal to

The degree of static indeterminacy of the rigid frame having two internal hinges as shown in the figure below, is

If NaOH is added to the solution of CH₃COOH

The ground conditions at a site are shown in the figure below.

The saturated unit weight of the sand (kN/m³) is