[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?

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

The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x² – N = 0. If i denotes the iteration index, the correct iterative scheme will be

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

For the fillet weld of size ‘s’ shown in the adjoining figure, the effective throat thickness is

A 16 mm thick plate measuring 650 mm ^_x 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

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 the 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?

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

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 the bottom of the beam) the state of stress is best represented by which of the following pairs?

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

The results for 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 FM_P, FM_Q and FM_R, it can be stated that

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

Two geometrically identical isolated footings, X (linear elastic) and Y (rigid), are loaded identically (shown alongside). The soil reactions will

A watershed got transformed from rural to urban over a period of time. The effect of urbanisation on storm runoff hydrograph from the watershed is to

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

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

The flow in a horizontal, frictionless rectangular open channel is supercritical. 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

Anaerobically treated effluent has MPN of total coliform as 10⁶/100 mL. After chlorination, the MPN value declines to 10²/100 mL. The percent removal (%R) and log removal (log R) of total coliform MPN is

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

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

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

Curvature correction to a staff reading in a differential levelling survey is

The probability that k number of vehicles arrive (i.e. cross a predefined line) in time t is given as^{$(\lambda t)^k e^{- \lambda t} / K!$}, where ^$\lambda$ is the average vehicle arrival rate. What is the probability that the time headway is greater than or equal to time t₁?

What is the value of the definite integral ^{$\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}}dx$}?

For an analytic function f(x + iy) = u(x, y) + i v(x, y), u is given by u = 3x² – 3y². The expression for v, considering K to be a constant is

What should be the value of ^$\lambda$ such that the function defined below is continuous at^{$x = \pi / 2$}?

The solution of the differential equation ^{$\frac{dy}{dx} + \frac{y}{x} = x$}, with the condition that y = 1 at x = 1, is

The value of W that results in the collapse of the beam shown in the adjoining figure and having a plastic moment capacity of M_p is

A singly 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 within stiff, saturated silty clay (undrained shear strength is 50 kPa, adhesion factor is 0.3 and the applicable bearing capacity factor is 9.0 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, what would be the estimated ultimate tensile capacity (rounded off to the nearest integer value of kN) of the pile?

If ^$\bar{a}$and ^$\bar{b}$ are two arbitrary vectors with magnitudes a and b respectively, ^{$|\bar{a} \times \bar{b}|^2$}will be equal to

In an aquifer extending over 150 hectares, the water table was 21 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 retention is 0.15, what is the change in ground water storage of the aquifer?

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 spillway discharges flood flow at a rate of 9 m³/s per metre 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?

If the jam density is given as k_j and the free flow speed is given as u_f, the maximum flow for a linear traffic speed-density model is given by which of the following options?

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

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 g. 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 1.4 m³/min. The dry weight of the filter paper after 24 hour sampling was 10.283 g. Assuming a linear decline in the air flow rate during sampling, what is the 24 hour average TSP concentration in the ambient air?

If v is the initial speed of a vehicle, g is the gravitational acceleration, G is the upward longitudinal slope of the road and f_r is the coefficient of rolling friction during braking, the braking distance (measured horizontally) for the vehicle to stop is

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

Identical surcharges 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 large 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?

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 OCF ions in the water? Assume that the chlorine gas added to the water is completely converted to HOCI and OCI^–. Atomic Weight of Cl is 35.5. Given: OCl^– + H^{+$\underline{\underrightarrow{K}}$}HOCl, K = 10^7.5

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?

Consider two RCC beams P and Q, each having the section 400 mm ^_x 750 mm (effective depth, d = 750 mm) made with concrete having a ^{$\tau_{c max}$}= 2.1 N/mm². For the reinforcement provided and the grade of concrete used, it may be assumed that the ^$\tau_c$= 0.75 N/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 sand layer found at sea floor under 20 m water depth is characterised 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 9.81 kN/m³.

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 sand layer found at sea floor under 20 m water depth is characterised 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 9.81 kN/m³.

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

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 statements will be TRUE?

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

What is the catchment area represented by the unit hydrograph?

Consider a bar of diameter ‘D’ embedded in a large concrete block as shown in the adjoining figure, with a pull out force P being applied. Let ^$\sigma_b$ and ^{$\sigma_{st}$} be the bond strength (between the bar and concrete) and the tensile strength of the bar respectively. If the block is held in position and it is assumed that the material of the block does not fail, which of the following options represents the maximum value of P?

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

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

A storm of 6.6 cm occurs uniformly over the catchment in 3 hours. If 0-index is equal to 2 mm/h and base flow is 5 m³/s, what is the peak flow due to the storm?

The sludge from the aeration tank of the activated sludge process (ASP) has solids content (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/m³.

What is the density of the sludge removed from the aeration tank?

Which of the following options is the closest in meaning to the word below? Inexplicable

Choose the word from the options given below that is most nearly opposite in meaning to the given word. Amalgamate

If Log (P) (1/2)Log (Q) = (1/3)Log (R), then which of the following options is TRUE?

The sludge from the aeration tank of the activated sludge process (ASP) has solids content (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/m³.

What is the solids content (by weight) of the thickened sludge?

Directions: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of ‘k’) at points ‘1’ and ‘2’, and an inclined load acts at ‘2’, as shown.

Which of the following options represents the deflections ^$\delta_1$ and ^$\delta_2$ at points ‘1’ and ‘2’?

Choose the most appropriate word from the options given below to complete the following sentence. If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or ____________.

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.

Directions: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of ‘k’) at points ‘1’ and ‘2’, and an inclined load acts at ‘2’, as shown.

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’?

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 minimise the total cost (V + F)?

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 container originally contains 10 litres of pure spirit. From this container, 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?

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?

The observations from a closed loop traverse around an obstacle are as follows

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

A transporter receives the same number 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 4^th 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 10^th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5^th day?

For a sample of dry, cohesionless soil with friction angle ^_$\phi$, the failure plane will be inclined to the major principal plane by an angle equal to