Consider the following statements $(P)$ and $(Q)$ :

$(P):$ Fly ash and ground granulated blast furnace slag can be used as mineral admixtures in concrete.

(Q): As per IS 456:2000, the minimum moist curing period becomes higher when a mineral admixture is added to concrete.

Identify the CORRECT option from choices given below.

The figure shows a network diagram for a construction project. The activities $\mathrm{A}, \mathrm{B}, \mathrm{C}$, D, E, and F are represented by arrows and their durations are in the figure.

The total float available for the activity E in day(s) is equal to _________ (round off to the nearest integer).

For the matrix $[\mathrm{A}]$ given below, the transpose is $\qquad$ .

$$ [A]=\left[\begin{array}{lll} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{array}\right] $$

Integration of $\ln (x)$ with $x$ i.e.

$$ \int \ln (x) d x= $$__________

Consider a velocity vector, $\vec{V}$ in ( $\mathrm{x}, \mathrm{y}, \mathrm{z}$ ) coordinates given below. Pick one or more CORRECT statement(s) from the choices given below:

$$ \vec{V}=u \vec{x}+v \vec{y} $$

The "order" of the following ordinary differential equation is $\qquad$ .

$$ \frac{d^3 y}{d x^3}+\left(\frac{d^2 y}{d x^2}\right)^6+\left(\frac{d y}{d x}\right)^4+y=0 $$

Consider the function given below and pick one or more CORRECT statement(s) from the following choices.

$$ f(x)=x^3-\frac{15}{2} x^2+18 x+20 $$

Pick the CORRECT eigen value(s) of the matrix $[\mathrm{A}]$ from the following choices.

$$ [A]=\left[\begin{array}{ll} 6 & 8 \\ 4 & 2 \end{array}\right] $$

Consider a discrete random variable $X$ whose probabilities are given below. The standard deviation of the random variable is _________ (round off to one decimal place).

$$ \begin{array}{|c|c|c|c|c|} \hline x_1 & 1 & 2 & 3 & 4 \\ \hline P\left(X=x_i\right) & 0.3 & 0.1 & 0.3 & 0.3 \\ \hline \end{array} $$

The bacteria mainly responsible for crown corrosion in a sewer is $\qquad$

Free residual chlorine concentration in water was measured to be $2 \mathrm{mg} / \mathrm{l}$ (as $\mathrm{Cl}_2$ ). The pH of water is 8.5. By using the chemical equation given below, the HOCl concentration (in $\mu$ moles $/ \mathrm{l}$ ) in water is $\qquad$ (round off to one decimal place).

$$ \mathrm{HOCl} \rightleftharpoons \mathrm{H}^{+}+\mathrm{OCl}^{-}, \mathrm{pK}=7.50 $$

Atomic weight: Cl(35.5)

A compound has a general formula $\mathrm{C}_{\mathrm{a}} \mathrm{H}_{\mathrm{b}} \mathrm{O}_{\mathrm{c}} \mathrm{N}_{\mathrm{d}}$ and molecular weight 187. A $935 \mathrm{mg} / \mathrm{l}$ solution of the compound is prepared in distilled deionized water. The Total Organic Carbon (TOC) is measured as $360 \mathrm{mg} / \mathrm{l}$ (as C). The Chemical Oxygen Demand (COD) and the Total Kjeldahl Nitrogen (TKN) are determined as $600 \mathrm{mg} / \mathrm{l}$ (as $\mathrm{O}_2$ ) and $140 \mathrm{mg} /$ I (as N), respectively (as per the chemical equation given below). Which of the following ptions is/are CORRECT?

$$ \mathrm{C}_{\mathrm{a}} \mathrm{H}_{\mathrm{b}} \mathrm{O}_{\mathrm{c}} \mathrm{~N}_{\mathrm{d}}+\frac{(4 \mathrm{a}+\mathrm{b}-2 \mathrm{c}-3 \mathrm{~d})}{4} \mathrm{O}_2 \rightarrow \mathrm{aCO}_2+\frac{\mathrm{b}-3 \mathrm{~d}}{2} \mathrm{H}_2 \mathrm{O}+\mathrm{dNH}_3 $$

Atomic weight : $\mathrm{C}(12), \mathrm{H}(1), \mathrm{O}(16), \mathrm{N}(14)$

The analyses results of a water sample are given below. The non-carbonate hardness of the water (in $\mathrm{mg} / \mathrm{L}$ ) as $\mathrm{CaCO}_3$ is __________ (in integer).

$$ \begin{aligned} & \mathrm{Ca}^{2+}=150 \mathrm{mg} / \mathrm{L} \text { as } \mathrm{CaCO}_3 \\ & \mathrm{Mg}^{2+}=40 \mathrm{mg} / \mathrm{L} \text { as } \mathrm{CaCO}_3 \\ & \mathrm{Fe}^{2+}=10 \mathrm{mg} / \mathrm{L} \text { as } \mathrm{CaCO}_3 \\ & \mathrm{Na}^{+}=50 \mathrm{mg} / \mathrm{L} \text { as } \mathrm{CaCO}_3 \\ & \mathrm{~K}^{+}=10 \mathrm{mg} / \mathrm{L} \text { as } \mathrm{CaCO}_3 \\ & \mathrm{CO}_3{ }^{2-}=120 \mathrm{mg} / \mathrm{L} \text { as } \mathrm{CaCO}_3 \\ & \mathrm{HCO}_3{ }^{-}=30 \mathrm{mg} / \mathrm{L} \text { as } \mathrm{CaCO}_3 \end{aligned} $$

$\mathrm{Cl}^{-}=50 \mathrm{mg} / \mathrm{L}$ as $\mathrm{CaCO}_3$; Other anions were not analysed.

A community generates 1 million litres/day (MLD) of wastewater. This wastewater is treated using activated sludge process (ASP). The working volume of the aeration tank of the ASP is $250 \mathrm{~m}^3$, and the biomass concentration in the tank is $3000 \mathrm{mg} / \mathrm{L}$. Analyses results showed that a biomass concentration of $10 \mathrm{mg} / \mathrm{L}$ is present in the treated effluent from the secondary sedimentation tank of the ASP. Sludge wastage from the system is at a rate of $5000 \mathrm{~L} /$ day with a biomass concentration of $10000 \mathrm{mg} / \mathrm{L}$. The system is in steady state condition.

The biological sludge residence time (BSRT) of the system (in days) is _________ (round off to one decimal place).

A settling chamber is used for the removal of discrete particulate matter from air with following conditions. Horizontal velocity of air $=0.2 \mathrm{~m} / \mathrm{s}$; Temperature of air stream $=77^{\circ} \mathrm{C}$; Specific gravity of particle to be removed $=2.65$; Chamber length $=12 \mathrm{~m}$; Chamber height = 2 m ;

Viscosity of air at $77^{\circ} \mathrm{C}=2.1 \times 10^{-5} \mathrm{~kg} / \mathrm{m} . \mathrm{s}$;

Acceleration due to gravity $(\mathrm{g})=9.81 \mathrm{~m} / \mathrm{s}^2$; Density of air at $77^{\circ} \mathrm{C}=1.0 \mathrm{~kg} / \mathrm{m}^3$;

Assume the density of water as $1000 \mathrm{~kg} / \mathrm{m}^3$ and Laminar condition exists in the chamber.

The minimum size of particle that will be removed with 100\% efficiency in the settling chamber (in $\mu \mathrm{m}$ ) is ___________ (round off to one decimal place).

A hydraulic jump occurs in an open channel when the slope of the channel changes from__________ .

Consider steady flow of water in the series pipe system shown below, with specified discharge. The diameters of Pipes A and B are 2 m and 1 m , respectively. The lengths of pipes A and B are 100 m and 200 m , respectively. Assume the Darcy-Weisbach friction coefficient, $f$ as 0.01 for both the pipes.

The ratio of head loss in Pipe-B to the head loss in Pipe-A is ___________ (round off to the nearest integer).

Consider flow in a long and very wide rectangular open channel. Width of the channel can be considered as infinity compared to the depth of flow. Uniform flow depth is 1.0 m . The bed slope of the channel is 0.0001 . The Manning roughness coefficient value is 0.02 . Acceleration due to gravity, g can be taken as $9.81 \mathrm{~m} / \mathrm{s}^2$.

The critical depth (in m ) corresponding to the flow rate resulting from the above conditions is ________ (round off to one decimal place).

The drag force, $F_D$ on a sphere due to a fluid flowing past the sphere is a function of viscosity, $\mu$, the mass density, $\rho$, the velocity of flow, $V$ and the diameter of the sphere, $D$.

Pick the relevant (one or more) non-dimensional parameter(s) pertaining to the above process from the following list.

The shaft of a 6 m wide gate in the figure will fail at a moment of $3924 \mathrm{kN} . \mathrm{m}$ about the hinge $P$. The maximum value of water depth $h$ (in $m$ ) that the gate can hold is

___________ (round off to the nearest integer).

Note:

Density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$

Acceleration due to gravity $=9.81 \mathrm{~m} / \mathrm{s}^2$

The point where the road alignment changes from a tangent to a curve is known as___________

$\qquad$

A surveyor measured the distance between two points on the plan drawn to a scale of $1 \mathrm{~cm}=40 \mathrm{~m}$ and the result was 468 m . Later, it was discovered that the scale used was $1 \mathrm{~cm}=20 \mathrm{~m}$.

The true distance between the points (in m ) is __________ (round off to the nearest integer).

If the Fore Bearing of the lines AB and BC are $60^{\circ}$ and $122^{\circ}$, respectively, then the interior angle $\angle A B C$ (in degrees) is ________ (round off to the nearest integer).

The most suitable test for measuring the permeability of clayey soils in the laboratory is ___________

From a flow-net diagram drawn under a concrete dam, following information are obtained:

(i) The head difference between upstream and downstream side of the dam is 9 m .

(ii) The total number of equipotential drops between upstream and downstream side of the dam is 10 .

(iii) The length of the field nearest to the toe of the dam in the downstream side is 1 m .

If the soil below the dam is having a saturated unit weight of $21 \mathrm{kN} / \mathrm{m}^3$ and unit weight of water is $9.81 \mathrm{kN} / \mathrm{m}^3$, then the factor of safety against the quick condition will be __________ (round off to two decimal places).

A 6 m thick clay stratum has drainage at both its top and bottom surface due to the presence of sand strata. The time to complete $50 \%$ consolidation is 2 years. The coefficient of volume change $\left(m_v\right)$ is $1.51 \times 10.3 \mathrm{~m}^2 / \mathrm{kN}$ and unit weight of water is $9.81 \mathrm{kN} / \mathrm{m}^3$.

The coefficient of permeability (in m/year) is__________ (round off to three decimal places).

For a partially saturated soil deposit at a construction site, water content $(w)$ is $15 \%$, degree of saturation ( S ) is $67 \%$, void ratio ( e ) is 0.6 and specific gravity of solids in the soil $\left(G_s\right)$ is 2.67 . Consider unit weight of water as $9.81 \mathrm{kN} / \mathrm{m}^3$.

To fully saturate $5 \mathrm{~m}^3$ of this soil, the required weight of water (in kN ) will be __________ (round off to the nearest integer).

In the context of shear strength of soil, which of the following statements is/are CORRECT?

The bank of a canal has the profile shown in the figure. The material is a homogeneous clay with a bulk unit weight of $20 \mathrm{kN} / \mathrm{m}^3$, undrained cohesion of 30 kPa and it is fully saturated ( $\phi_u=0$ ). For the trial slip circle shown, the area ABCDEA is $150 \mathrm{~m}^2$ and the centroid is at P. A tension crack (DE) of 2.5 m deep was also observed. Assume unit weight of water is $9.81 \mathrm{kN} / \mathrm{m}^3$ and consider 1 m run of the bank for the analysis.

Considering the canal is empty and tension crack is completely filled with water, the factor of safety against slope failure of the bank is __________ (round off to two decimal places).

A designer used plate load test to obtain the value of the bearing capacity factor $\mathrm{N}_\gamma$. A circular plate of 1 m diameter was placed on the surface of a dry sand layer extending very deep beneath the ground. The unit weight of the sand is $16.66 \mathrm{kN} / \mathrm{m}^3$. The plate is loaded to failure at a pressure of 1500 kPa .

Considering Terzaghi's bearing capacity theory, the bearing capacity factor $\mathrm{N}_\gamma$ is________ (round off to the nearest integer).

A $4 \times 4$ group pile, with each pile 20 m long and 500 mm in diameter, is installed in a square pattern in a clayey soil, as shown in the figure. The average unconfined compressive strength of the soil is $100 \mathrm{kN} / \mathrm{m}^2$, and the adhesion factor is 0.8 . Neglect the bearing at the tip of the piles. For a group efficiency factor of 1.0 , the centre to centre spacing (s) of the piles (in m ) would be ________ (round off to two decimal places).

In the context of the effect of drainage density on the run-off generation and the hydrograph at the catchment outlet, all other factors remaining the same, pick one or more CORRECT statement(s) from the choices given below.

A 60 cm diameter well completely penetrates a confined aquifer of permeability $5 \times 10^{-4} \mathrm{~m} / \mathrm{s}$. The length of the strainer (spanning the entire thickness of the aquifer) is 10 m . The drawdown at the well under steady state pumping is 1.0 m . Assume that the radius of influence for this pumping is 300 m .

The discharge from the well (in litres per minute) is ________ (round off to the nearest integer).

The peak of flood hydrograph due to a 3 -hour duration storm in a catchment is $180 \mathrm{~m}^3 / \mathrm{s}$. The total rainfall depth is 6.6 cm . It can be assumed that the average infiltration loss is $0.2 \mathrm{~cm} / \mathrm{h}$. There are no other losses. The base flow is constant at a value of $30 \mathrm{~m}^3 / \mathrm{s}$.

The peak value of the 3-hour unit hydrograph for this catchment (in $\mathrm{m}^3 / \mathrm{s}$ ) is ________ (round off to the nearest integer).

In the context of construction materials, which of the following statements is/are CORRECT?

The design shear strength of a reinforced concrete rectangular beam with a width of 250 mm and an effective depth of 500 mm , is 0.3 MPa . The torsional moment capacity of the section (in kN.m) under pure torsion, as per IS 456:2000, is _________ (round off to one decimal place).

Consider a reinforced concrete beam section of 350 mm width and 600 mm depth. The beam is reinforced with the tension steel of $800 \mathrm{~mm}^2$ area at an effective cover of 40 mm . Consider M20 concrete and Fe415 steel. Let the stress block considered for concrete in IS 456:2000 be replaced by an equivalent rectangular stress block, with no change in (a) the area of the stress block, (b) the design strength of concrete (at the strain of 0.0035), and (c) the location of neutral axis at flexural collapse. The ultimate moment of resistance of the beam (in kN.m) is __________ (round off to the nearest integer).

A reinforced concrete beam has a support section with width of 300 mm and effective depth of 500 mm . The support section is reinforced with 3 bars of 20 mm diameter at the tension side. Two-legged vertical stirrups of 10 mm diameter and Fe415 steel at a spacing of 100 mm are provided as shear reinforcement. Assume that there is no possibility of diagonal compression failure at the section.

As per IS 456:2000, the maximum shear resisted by the vertical stirrups (in kN), as per limit state design, is__________ (round off to one decimal place).

A circular tube of thickness 10 mm and diameter 250 mm is welded to a flat plate using 5 mm fillet weld along the circumference. Assume Fe410 steel and shop welding.

As per IS 800:2007, the torque that can be resisted by the weld (in kN.m) is __________ (round off to one decimal place).

The figure shows a propped cantilever with uniform flexural rigidity EI (in N.m²) and subjected to a moment $M$ (in N.m). Consider forces and displacements in the upward direction as positive.

Find the upward reaction at the propped support B (in N) when this support settles by $(-\Delta)$, given in metres.

Let the state of stress at a point in a body be the difference of two plane states of stress shown in the figure. Consider all the possible planes perpendicular to the $x-y$ plane and passing through that point. The magnitude of the maximum compressive stress on any such plane is $k \sigma_0$, where $k$ is equal to _________ (round off to one decimal place).

A steel beam supported by three parallel pin-jointed steel rods is shown in the figure. The moment of inertia of the beam is $8 \times 10^7 \mathrm{~mm}^4$. Take modulus of elasticity of steel as 210 GPa . The beam is subjected to uniformly distributed load of $6.25 \mathrm{kN} / \mathrm{m}$, including its self-weight.

The axial force (in kN ) in the centre rod CD is___________ (round off to one decimal place).

Consider the pin-jointed truss shown in the figure. Influence line is drawn for the axial force in the member G-I, when a unit load travels on the bottom chord of the truss. Identify the CORRECT influence line from the following options:

Note: Positive value corresponds to tension and negative value corresponds to compression in the member.

In the pin-jointed truss shown in the figure, the members that carry zero force are identified. Which of the following options is/are zero-force members?

After applying the correction for elevation and temperature, the runway length is 700 m . The corrected runway length (in m ) for an effective gradient of $1 \%$ is __________ (round off to the nearest integer).

$$ \text { Match the following in Column I with Column II. } $$

The free flow speed of a highway is 100 km/h and its capacity is 4000 vehicle/h. Assume speed density relation is linear.

For a traffic volume of 2000 vehicle/h, choose all the possible speeds (in km/h) from the options given below (round off to two decimal places).

On a two-lane highway, a horizontal curve of radius 300 m is provided. The design speed is $80 \mathrm{~km} / \mathrm{h}$.

If the longest wheelbase of vehicle expected on this highway is 7 m , then the extra widening required (in m ) is ________ (round off to two decimal places).

Even though I had planned to go skiing with my friends, I had to __________ at the last moment because of an injury.

Select the most appropriate option to complete the above sentence.

The President, along with the Council of Ministers, _________to visit India next week. Select the most appropriate option to complete the above sentence.

An electricity utility company charges ₹ 7 per kWh (kilo watt-hour). If a 40-watt desk light is left on for 10 hours each night for 180 days, what would be the cost of energy consumption? If the desk light is on for 2 more hours each night for the 180 days, what would be the percentage-increase in the cost of energy consumption?

In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively?

A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:

(i) The sum of Yellow balls and twice the number of Violet balls is 50.

(ii) The sum of Violet and Green balls is 50.

(iii) The sum of Yellow and Red balls is 50.

(iv) The sum of Violet and twice the number of Red balls is 50 .

Which one of the following Pie charts correctly represents the balls in the bag?

"His life was divided between the books, his friends, and long walks. A solitary man, he worked at all hours without much method, and probably courted his fatal illness in this way. To his own name there is not much to show; but such was his liberality that he was continually helping others, and fruits of his erudition are widely scattered, and have gone to increase many a comparative stranger's reputation."

(From E.V. Lucas's "A Funeral")

Based only on the information provided in the above passage, which one of the following statements is true?

For the clock shown in the figure, if

$$ \begin{aligned} & O^*=O Q S Z P R T, \text { and } \\ & X^*=X Z P W Y O Q, \end{aligned} $$

then which one among the given options is most appropriate for $\mathrm{P}^*$ ?

Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:

$$ \begin{aligned} & P < Q \\ & S > P > T \\ & R < T \end{aligned} $$

If integers 1 through 5 are used to construct such a number, the value of $P$ is:

A business person buys potatoes of two different varieties $P$ and $Q$, mixes them in a certain ratio and sells them at ₹192 per kg.

The cost of the variety P is $Rs\,800$ for 5 kg .

The cost of the variety Q is $Rs\, 800$ for 4 kg .

If the person gets $8 \%$ profit, what is the $\mathrm{P}: Q$ ratio (by weight)?

Three villages $P, Q$, and $R$ are located in such a way that the distance $P Q=13 \mathrm{~km}$, $Q R=14 \mathrm{~km}$, and $R P=15 \mathrm{~km}$, as shown in the figure. A straight road joins $Q$ and $R$. It is proposed to connect $P$ to this road $Q R$ by constructing another road. What is the minimum possible length (in km ) of this connecting road?

Note: The figure shown is representative.