Concrete of characteristic strength 30 MPa is required. If 40 specimens of concrete cubes are to be tested, the minimum number of specimens having at least 30 MPa strength should be

Consider the statements P and Q.

P: Client’s Preliminary Estimate is used for budgeting costs toward the end of planning and design phase.

Q: Client’s Detailed Estimate is used for controlling costs during the execution of the project.

Which one of the following options is CORRECT?

Which one of the following statements related to bitumen is FALSE?

The smallest positive root of the equation $$x^5 - 5 x^4 - 10 x^3 + 50 x^2 + 9 x - 45 = 0$$ lies in the range

The second-order differential equation in an unknown function $$u : u(x, y)$$ is defined as $$\frac{\partial^2 u}{\partial x^2}= 2$$

Assuming $$g : g(x)$$, $$f : f(y)$$, and $$h : h(y)$$, the general solution of the above differential equation is

The probability that a student passes only in Mathematics is $\frac{1}{3}$. The probability that the student passes only in English is $\frac{4}{9}$. The probability that the student passes in both of these subjects is $\frac{1}{6}$. The probability that the student will pass in at least one of these two subjects is

For the following partial differential equation,

$x \frac{\partial^2 f}{\partial x^2} + y \frac{\partial^2 f}{\partial y^2} = \frac{x^2 + y^2}{2}$

which of the following option(s) is/are CORRECT?

Consider the data of $f(x)$ given in the table.

The value of $f(1.5)$ estimated using second-order Newton’s interpolation formula is ________________ (rounded off to 2 decimal places).

What are the eigenvalues of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2 \end{bmatrix}$ ?

A vector field $\vec{p}$ and a scalar field $r$ are given by:

$\vec{p} = (2x^2 - 3xy + z^2) \hat{i} + (2y^2 - 3yz + x^2) \hat{j} + (2z^2 - 3xz + x^2) \hat{k}$

$r = 6x^2 + 4y^2 - z^2 - 9xyz - 2xy + 3xz - yz$

Consider the statements P and Q:

P: Curl of the gradient of the scalar field $r$ is a null vector.

Q: Divergence of curl of the vector field $\vec{p}$ is zero.

Which one of the following options is CORRECT?

The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the probability that it will be exceeded at least once in 50 years is ______________ % (rounded off to the nearest integer).

A 2 m × 2 m tank of 3 m height has inflow, outflow and stirring mechanisms. Initially, the tank was half-filled with fresh water. At $ t = 0 $, an inflow of a salt solution of concentration 5 g/ $ m^3 $ at the rate of 2 litre/s and an outflow of the well stirred mixture at the rate of 1 litre/s are initiated. This process can be modelled using the following differential equation:

$$ \frac{dm}{dt} + \frac{m}{6000 + t} = 0.01 $$

where $ m $ is the mass (grams) of the salt at time $ t $ (seconds). The mass of the salt (in grams) in the tank at 75% of its capacity is ______________ (rounded off to 2 decimal places).

The beam shown in the figure is subjected to a uniformly distributed downward load of intensity $q$ between supports A and B.

Considering the upward reactions as positive, the support reactions are

The following table gives various components of Municipal Solid Waste (MSW) and a list of treatment/separation techniques.

The CORRECT match is

The primary air pollutant(s) is/are

For assessing the compliance with the emissions standards of incineration plants, a correction needs to be applied to the measured concentrations of air pollutants. The emission standard (based on 11% Oxygen) for HCl is 50 mg/Nm³ and the measured concentrations of HCl and Oxygen in flue gas are 42 mg/Nm³ and 13%, respectively.

Assuming 21% Oxygen in air, the CORRECT statement is:

Activated carbon is used to remove a pollutant from wastewater in a mixed batch reactor, which follows first-order reaction kinetics.

At a reaction rate of 0.38 /day, the time (in days) required to remove the pollutant by 95% is _______________ (rounded off to 1 decimal place).

A water treatment plant treats 25 MLD water with a natural alkalinity of 4.0 mg/L (as CaCO₃). It is estimated that, during the coagulation of this water, 450 kg/day of calcium bicarbonate (Ca(HCO₃)₂) is required based on the alum dosage.

Consider the atomic weights as: Ca-40, H-1, C-12, O-16.

The quantity of pure quick lime, CaO (in kg) required for this process per day is _______ (rounded off to 2 decimal places).

The number of degrees of freedom for a natural open channel flow with a mobile bed is

A 30 cm diameter well fully penetrates an unconfined aquifer of saturated thickness 20 m with hydraulic conductivity of 10 m/day. Under the steady pumping rate for a long time, the drawdowns in two observation wells located at 10 m and 100 m from the pumping well are 5 m and 1 m, respectively. The corresponding pumping rate (in m³/day) from the well is _____________ (rounded off to 2 decimal places).

A flow velocity field $\vec{V} : \vec{V}(x, y)$ for a fluid is represented by

$\vec{V} = 3 \hat{i} + (5x) \hat{j}$

In the context of the fluid and the flow, which one of the following statements is CORRECT?

A standard round bottom triangular canal section as shown in the figure has a bed slope of 1 in 200. Consider the Chezy’s coefficient as 150 m^1/2/s.


The normal depth of flow, y (in meters) for carrying a discharge of 20 m³/s is ___________ (rounded off to 2 decimal places).

A 5 m × 5 m closed tank of 10 m height contains water and oil, and is connected to an overhead water reservoir as shown in the figure. Use $\gamma_w$ = 10 kN/m³ and Specific gravity of oil = 0.8.

The total force (in kN) due to pressure on the side PQR of the tank is _______________ (rounded off to the nearest integer).

During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the ratio of the Earth-Sun and Earth-Moon distances is closest to

If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by

A surveyor observes a zenith angle of 93° 00′ 00″ during a theodolite survey. The corresponding vertical angle is

Among the following statements relating the fundamental lines of a transit theodolite, which one is CORRECT?

A map is prepared with a scale of 1:1000 and a contour interval of 1 m. If the distance between two adjacent contours on the map is 10 mm, the slope of the ground between the adjacent contours is

A 2 m wide strip footing is founded at a depth of 1.5 m below the ground level in a homogeneous pure clay bed. The clay bed has unit cohesion of 40 kPa. Due to seasonal fluctuations of water table from peak summer to peak monsoon period, the net ultimate bearing capacity of the footing, as per Terzaghi’s theory, will

Consider the statements P and Q.

P: Soil particles formed by mechanical weathering, and close to their origin are generally subrounded.

Q: Activity of the clay physically signifies its swell potential.

Which one of the following options is CORRECT?

An embankment is constructed with soil by maintaining the degree of saturation as 75% during compaction. The specific gravity of soil is 2.68 and the moisture content is 17% during compaction. Consider the unit weight of water as 10 kN/m$^3$. The dry unit weight (in kN/m$^3$) of the compacted soil is _________________ (rounded off to 2 decimal places).

A vertical smooth rigid retaining wall is supporting horizontal ground with dry cohesionless backfill having a friction angle of 30°. The inclinations of failure planes with respect to the major principal plane for Rankine’s active and passive earth pressure conditions, respectively, are

Which of the following statement(s) is/are CORRECT?

The total primary consolidation settlement ($S_c$) of a building constructed on a 10 m thick saturated clay layer is estimated to be 50 mm. After 300 days of the construction of the building, primary consolidation settlement was reported as 10 mm. The additional time (in days) required to achieve 50% of $S_c$ will be ________________ (rounded off to the nearest integer).

An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is 30° with respect to the horizontal ground surface. The unit weights of the saturated soil and water are 20 kN/m³ and 10 kN/m³, respectively.

The minimum angle of shearing resistance of the soil (in degrees) for the critically stable condition of the slope is ________________ (rounded off to the nearest integer).

A soil sample was consolidated at a cell pressure of 20 kPa and a back pressure of 10 kPa for 24 hours during a consolidated undrained (CU) triaxial test. The cell pressure was increased to 30 kPa on the next day and it resulted in the development of pore water pressure of 1 kPa. The soil sample failed when the axial stress was gradually increased to 50 kPa. The pore water pressure at failure was recorded as 21 kPa. The value of Skempton's pore pressure parameter B for the soil sample is ________________ (rounded off to 2 decimal places).

The ordinates of a 1-hour unit hydrograph (UH) are given below.

These ordinates are used to derive a 3-hour UH. The peak discharge (in m³/s) for the derived 3-hour UH is ___________ (rounded off to the nearest integer).

A spillway has unit discharge of 7.5 m³/s/m. The flow depth at the downstream horizontal apron is 0.5 m. The tail water depth (in meters) required to form a hydraulic jump is ___________ (rounded off to 2 decimal places).

The following figure shows the arrangement of formwork for casting a cantilever RC beam.

The correct sequence of removing the Shores/Props is:

Consider a balanced doubly-reinforced concrete section. If the material and other sectional properties remain unchanged, for which of the following cases will the section becomes under-reinforced?

An inverted T-shaped concrete beam (B1) in the figure, with centroidal axis X – X, is subjected to an effective prestressing force of 1000 kN acting at the bottom kern point of the beam cross-section. Also, consider an identical concrete beam (B2) with the same grade of concrete but without any prestressing force.

The additional cracking moment (in kN.m) that can be carried by beam B1 in comparison to beam B2 is ________ (rounded off to the nearest integer).

The initial cost of an equipment is Rs. 1,00,000. Its salvage value at the end of accounting life of 5 years is Rs. 10,000. The difference in depreciation (in Rs.) computed using ‘double-declining balance method’ and ‘straight line method’ of depreciation in Year-2 is ___________ (in positive integer).

A slab panel with an effective depth of 250 mm is reinforced with 0.2% main reinforcement using 8 mm diameter steel bars. The uniform center-to-center spacing (in mm) at which the 8 mm diameter bars are placed in the slab panel is __________ (rounded off to the nearest integer).

The elements that DO NOT increase the strength of structural steel are

The three-dimensional state of stress at a point is given by

$$\sigma = \begin{pmatrix} 10 & 0 & 0 \\ 0 & 40 & 0 \\ 0 & 0 & 0 \end{pmatrix} \text{ MPa.}$$

The maximum shear stress at the point is

Find the correct match between the plane stress states and the Mohr’s circles.

A homogeneous shaft PQR with fixed supports at both ends is subjected to a torsional moment T at point Q, as shown in the figure. The polar moments of inertia of the portions PQ and QR of the shaft with circular cross-sections are $J_1$ and $J_2$, respectively. The torsional moment reactions at the supports P and R are $T_P$ and $T_R$, respectively.

If $T_P/T_R = 4$ and $J_1/J_2 = 2$, the ratio of the lengths $L_1/L_2$ is:

The plane frame shown in the figure has fixed support at joint A, hinge support at joint F, and roller support at joint I. In the figure, A to I indicate joints of the frame.

If the axial deformations are neglected, the degree of kinematic indeterminacy is _________ (in integer).

The plane truss shown in the figure has 13 joints and 22 members. The truss is made of a homogeneous, prismatic, linearly elastic material. All members have identical axial rigidity. A to M indicate the joints of the truss. The truss has pin supports at joints A and L and roller support at joint K. The truss is subjected to a 10 kN vertically downward force at joint H and a 10 kN horizontal force in the rightward direction at joint B as shown.

The magnitude of the reaction (in kN) at the pin support L is __________ (rounded off to 1 decimal place).

A car is travelling at a speed of 60 km/hr on a section of a National Highway having a downward gradient of 2%. The driver of the car suddenly observes a stopped vehicle on the car path at a distance 130 m ahead, and applies brake. If the brake efficiency is 60%, coefficient of friction is 0.7, driver’s reaction time is 2.5 s, and acceleration due to gravity is $9.81 \text{ m/s}^2$, the distance (in meters) required by the driver to bring the car to a safe stop lies in the range

As per the International Civil Aviation Organization (ICAO), the basic runway length is increased by $x$ (%) for every $y$ (m) rise in elevation from the Mean Sea Level (MSL). The values of $x$ and $y$, respectively, are

The free mean speed is 60 km/hr on a given road. The average space headway at jam density on this road is 8 m. For a linear speed-density relationship, the maximum flow (in veh/hr/lane) expected on the road is

The number of trains and their corresponding speeds for a curved Broad Gauge section with 437 m radius, are

• 20 trains travel at a speed of 40 km/hr
• 15 trains travel at a speed of 50 km/hr
• 12 trains travel at a speed of 60 km/hr
• 8 trains travel at a speed of 70 km/hr
• 3 trains travel at a speed of 80 km/hr

If the gauge (center-to-center distance between the rail heads) is taken as 1750 mm, the required equilibrium cant (in mm) will be _______ (rounded off to the nearest integer).

The figure presents the trajectories of six vehicles within a time-space domain. The number in the parentheses represents a unique identification of each vehicle.


The mean speed (in km/hr) of the vehicles in the entire time-space domain is ____________ (rounded off to the nearest integer).

The following data is obtained from an axle load survey at a site:

Average rear axle load = 12000 kg
Number of commercial vehicles = 800 per day

The pavement at this site would be reconstructed over a period of 5 years from the date of the survey. The design life of the reconstructed pavement is 15 years. Use the standard axle load as 8160 kg and the annual average vehicle growth rate is 4.0%. Assume that Equivalent Wheel Load Factor (EWLF) and Vehicle Damage Factor (VDF) are equal.

The cumulative standard axle (in msa) for the pavement design is ____________ (rounded off to 2 decimal places).

A bird is resting on a point P at a height of 8 m above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point Q which is located at a height of 3 m above MSL. The ground surface has a falling gradient of 1 in 2. Ignoring the effects of curvature and refraction, the horizontal distance (in meters) between points P and Q is _______________ (in integer).

If ‘→’ denotes increasing order of intensity, then the meaning of the words [simmer → seethe → smolder] is analogous to [break → raze → _______ ].

Which one of the given options is appropriate to fill the blank?

In a locality, the houses are numbered in the following way:

The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the other side of the road are consecutive even numbers starting from 302. The total number of houses is the same on both sides of the road.

If the difference of the sum of the house-numbers between the two sides of the road is 27, then the number of houses on each side of the road is

For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1$, $\left(\frac{p}{q}\right)^\frac{p}{q}= p^{\left(\frac{p}{q}-1\right)}$. Then,

Which one of the given options is a possible value of x in the following sequence?

3, 7, 15, x, 63, 127, 255

On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?

In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks.

From the ancient Athenian arena to the modern Olympic stadiums, athletics ___(i)___ the potential for a spectacle. The crowd ___(ii)___ with bated breath as the Olympian artist twists his body, stretching the javelin behind him. Twelve strides in, he begins to cross-step. Six cross-steps ___(iii)___ in an abrupt stop on his left foot. As his body ___(iv)___ like a door turning on a hinge, the javelin is launched skyward at a precise angle.

Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people.

How many unique seating arrangements are possible such that each person is sitting next to their twin?

The chart given below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3, and T4, and their Electricity Generation (MWh) in a time of 1000 hours (h).

The Capacity Factor of a power generation technology is:

Capacity Factor $=\frac{\text { Electricity Generation }(\mathrm{MWh})}{\text { Installed Capacity }(\mathrm{MW}) \times 1000(\mathrm{~h})}$

Which one of the given technologies has the highest Capacity Factor?

In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.

Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals).

As per this rule, the maximum number of crosses possible in the empty column is