Which of the following equations is correct for the Pozzolanic reaction?

The project activities are given in the following table along with the duration and dependency.

Which one of the following combinations is correct?

Consider the following expression:

z = sin(y + it) + cos(y $$-$$ it)

where z, y, and t are variables, and $$i = \sqrt { - 1} $$ is a complex number. The partial differential equation derived from the above expression is

For the equation

$${{{d^3}y} \over {d{x^3}}} + x{\left( {{{dy} \over {dx}}} \right)^{3/2}} + {x^2}y = 0$$

the correct description is

The matrix M is defined as

$$M = \left[ {\matrix{ 1 & 3 \cr 4 & 2 \cr } } \right]$$

and has eigenvalues 5 and $$-$$2. The matrix Q is formed as

Q = M³ $$-$$ 4M² $$-$$ 2M

Consider the following recursive iteration scheme for different values of variable P with the initial guess x₁ = 1:

$${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {P \over {{x_n}}}} \right)$$, n = 1, 2, 3, 4, 5

For P = 2, x₅ is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x₅ is obtained to be 1.732, rounded-off to three decimal places. If P = 10, the numerical value of x₅ is __________. (round off to three decimal places)

The Fourier cosine series of a function is given by :

$$f(x) = \sum\limits_{n = 0}^\infty {{f_n}\cos nx} $$

For f(x) = cos⁴x, the numerical value of (f₄ + f₅) is _________. (round off to three decimal places)

The Cartesian coordinates of a point P in a right-handed coordinate system are (1, 1, 1). The transformed coordinates of P due to a 45$$^\circ$$ clockwise rotation of the coordinate system about the positive x-axis are

Let max {a, b} denote the maximum of two real numbers a and b. Which of the following statements is/are TRUE about the function f(x) = max{3 $$-$$ x, x $$-$$ 1}?

Consider the differential equation

$${{dy} \over {dx}} = 4(x + 2) - y$$

For the initial condition y = 3 at x = 1, the value of y at x = 1.4 obtained using Euler's method with a step-size of 0.2 is ________. (round off to one decimal place)

A set of observations of independent variable (x) and the corresponding dependent variable (y) is given below.

Based on the data, the coefficient a of the linear regression model

y = a + bx

is estimated as 6.1. The coefficient b is _________. (round off to one decimal place)

A horizontal force of P kN is applied to a homogeneous body of weight 25 kN, as shown in the figure. The coefficient of friction between the body and the floor is 0.3. Which of the following statements is/are correct?

The total hardness in raw water is 500 milligram per liter as CaCO₃. The total hardness of this raw water, expressed in milligram equivalent per liter, is (Consider the atomic weights of Ca, C, and O as 40 g/mol, 12 g/mol, and 16 g/mol, respectively.)

For wastewater coming from a wood pulping industry, Chemical Oxygen Demand (COD) and 5-day Biochemical Oxygen Demand (BOD₅) were determined. For this wastewater, which of the following statement(s) is/are correct?

Which of the following processes can be used for conversion of salt water into fresh water?

Henry's law constant for transferring O₂ from air into water, at room temperature, is 1.3 $${{mmol} \over {liter - atm}}$$. Given that the partial pressure of O₂ in the atmosphere is 0.21 atm, the concentration of dissolved oxygen (mg/liter) in water in equilibrium with the atmosphere at room temperature is

(Consider the molecular weight of O₂ as 32 g/mol)

In a water sample, the concentrations of Ca²⁺, Mg²⁺ and HCO$$_3^ - $$ are 100 mg/L, 36 mg/L and 122 mg/L, respectively. The atomic masses of various elements are : Ca = 40, Mg = 24, H = 1, C = 12, O = 16. The total hardness and the temporary hardness in the water sample (in mg/L as CaCO₃) will be

A wastewater sample contains two nitrogen species, namely ammonia and nitrate. Consider the atomic weight of N, H, and O as 14 g/mol, 1 g/mol, and 16 g/mol, respectively. In this wastewater, the concentration of ammonia is 34 mg NH₃/liter and that of nitrate is 6.2 mg NO$$_3^ - $$/liter. The total nitrogen concentration in this wastewater is _________ milligram nitrogen per liter.

(round off to one decimal place)

A 2% sewage sample (in distilled water) was incubated for 3 days at 27$$^\circ$$C temperature. After incubation, a dissolved oxygen depletion of 10 mg/L was recorded. The biochemical oxygen demand (BOD) rate constant at 27$$^\circ$$C was found to be 0.23 day^$$-$$1 (at base e). The ultimate BOD (in mg/L) of the sewage will be ________. (round off to the nearest integer)

A water treatment plant has a sedimentation basin of depth 3 m, width 5 m, and length 40 m. The water inflow rate is 500 m³/h. The removal fraction of particles having a settling velocity of 1.0 m/h is ________. (round off to one decimal place) (Consider the particle density as 2650 kg/m³ and liquid density as 991 kg/m³)

With respect to fluid flow, match the following in Column X with Column Y:

Which one of the following combinations is correct?

A rectangular channel with Gradually Varied Flow (GVF) has a changing bed slope. If the change is from a steeper slope to a steep slope, the resulting GVF profile is

Two reservoirs are connected by two parallel pipes of equal length and of diameters 20 cm and 10 cm, as shown in the figure (not drawn to scale). When the difference in the water levels of the reservoirs is 5 m, the ratio of discharge in the larger diameter pipe to the discharge in the smaller diameter pipe is ___________. (round off to two decimal places)

Consider only loss due to friction and neglect all other losses. Assume the friction factor to be the same for both the pipes)

Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m³/s. Take g = 9.8 m/s². The bed width (in m) at contraction, which just causes the critical flow, is _________ without changing the upstream water level. (round off to two decimal places)

An aerial photograph is taken from a flight at a height of 3.5 km above mean sea level, using a camera of focal length 152 mm. If the average ground elevation is 460 m above mean sea level, then the scale of the photograph is

A line between stations P and Q laid on a slope of 1 in 5 was measured as 350 m using a 50 m tape. The tape is known to be short by 0.1 m.

The corrected horizontal length (in m) of the line PQ will be

The bearing of a survey line is N31$$^\circ$$17'. Its azimuth observed from north is __________ deg. (round off to two decimal places)

Four different soils are classified as CH, ML, SP, and SW, as per the Unified Soil Classification System. Which one of the following options correctly represents their arrangement in the decreasing order of hydraulic conductivity?

Let $$\sigma$$'_v and $$\sigma$$'_h denote the effective vertical stress and effective horizontal stress, respectively. Which one of the following conditions must be satisfied for a soil element to reach the failure state under Rankine's passive earth pressure condition?

Let $$\psi $$ represent soil suction head and K represent hydraulic conductivity of the soil. If the soil moisture content $$\theta$$ increases, which one of the following statements is TRUE?

An uncompacted heap of soil has a volume of 10000 m³ and void ratio of 1. If the soil is compacted to a volume of 7500 m³, then the corresponding void ratio of the compacted soil is __________. (round off to one decimal place)

A concentrated vertical load of 3000 kN is applied on a horizontal ground surface. Points P and Q are at depths 1 m and 2 m below the ground, respectively, along the line of application of the load. Considering the ground to be a linearly elastic, isotropic, semi-infinite medium, the ratio of the increase in vertical stress at P to the increase in vertical stress at Q is ___________. (in integer)

At a site, Static Cone Penetration Test was carried out. The measured point (tip) resistance q_c was 1000 kPa at a certain depth. The friction ratio (f_r) was estimated as 1% at the same depth.

The value of sleeve (side) friction (in kPa) at that depth was __________. (in integer)

The correct match between the physical states of the soils given in Group-I and the governing conditions given in Group-II is

As per Rankine's theory of earth pressure, the inclination of failure planes is $$\left( {45 + {\phi \over 2}} \right)^\circ $$ with respect to the direction of the minor principal stress.

The above statement is correct for which one of the following options?

A square concrete pile of 10 m length is driven into a deep layer of uniform homogenous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is 100 kPa. If the ultimate compressive load capacity of the driven pile is 632 kN, the required width of the pile is __________ mm. (in integer)

Bearing capacity factor N_c = 9; adhesion factor $$\alpha$$ = 0.7)

A raft foundation of 30 m $$\times$$ 25 m is proposed to be constructed at a depth of 8 m in a sand layer. A 25 m thick saturated clay layer exists 2 m below the base of the raft foundation. Below the clay layer, a dense sand layer exists at the site. A 25 mm thick undisturbed sample was collected from the mid-depth of the clay layer and tested in a laboratory oedometer under double drainage condition. It was found that the soil sample had undergone 50% consolidation settlement in 10 minutes. The time (in days) required for 25% consolidation settlement of the raft foundation will be ___________. (round off to the nearest integer)

A two-hour duration storm event with uniform excess rainfall of 3 cm occurred on a watershed. The ordinates of streamflow hydrograph resulting from this event are given in the table.

Considering a constant baseflow of 10 m³/s, the peak flow ordinate (in m³/s) of one-hour unit hydrograph for the watershed is ____________. (in integer)

During a particular stage of the growth of a crop, the consumptive use of water is 2.8 mm/day. The amount of water available in the soil is 50% of the maximum depth of available water in the root zone. Consider the maximum root zone depth of the crop as 80 mm and the irrigation efficiency as 70%. The interval between irrigation (in days) will be ___________. (round off to the nearest integer)

In the context of cross-damage structures, the correct statement(s) regarding the relative positions of a natural drain (stream/river) and an irrigation canal, is/are

In the context of elastic theory of reinforced concrete, the modular ratio is defined as the ratio of

A reinforced concrete beam with rectangular cross section (width = 300 mm, effective depth = 580 mm) is made of M30 grade concrete. It has 1% longitudinal tension reinforcement of Fe415 grade steel. The design shear strength for this beam is 0.66 N/mm². The beam has to resist a factored shear force of 440 kN. The spacing of two-legged, 10 mm diameter vertical stirrups of Fe415 grade steel is _________ mm. (round off to the nearest integer)

A weld is used for joining an angle section ISA 100 mm $$\times$$ 100 mm $$\times$$ 10 mm to a gusset plate of thickness 15 mm to transmit a tensile load. The permissible stress in the angle is 150 MPa and the permissible shear stress on the section through the throat of the fillet weld is 108 MPa. The location of the centroid of the angle is represented by C_yy in the figure, where C_yy = 28.4 mm. The area of cross-section of the angle is 1903 mm². Assuming the effective throat thickness of the weld to be 0.7 times the given weld size, the lengths L₁ and L₂ (rounded off to the nearest integer) of the weld required to transmit a load equal to the full strength of the tension member are, respectively

The hoop stress at a point on the surface of a thin cylindrical pressure vessel is computed to be 30.0 MPa. The value of maximum shear stress at this point is

Consider the cross-section of a beam made up of thin uniform elements having thickness t(t << a) shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure.

The coordinates of the shear center of this cross-section are :

Consider a simply supported beam PQ as shown in the figure. A truck having 100 kN on the front axle and 200 kN on the rear axle, moves from left to right. The spacing between the axles is 3 m. The maximum bending moment at point R is _________ kNm. (in integer)

A semi-circular bar of radius R m, in a vertical plane, is fixed at the end G, as shown in the figure. A horizontal load of magnitude PkN is applied at the end H. The magnitude of the axial force, shear force, and bending moment at point Q for $$\theta$$ = 45$$^\circ$$, respectively, are

The plane truss shown in the figure is subjected to an external force P. It is given that P = 70 kN, a = 2 m, and b = 3 m.

The magnitude (absolute value) of force (in kN) in member EF is ________. (round off to the nearest integer)

Consider the linearly elastic plane frame shown in the figure. Members HF, FK and FG are welded together at joint F. Joints K, G and H are fixed supports. A counter-clockwise moment M is applied at joint F. Consider flexural rigidity El = 10⁵ kN-m² for each member and neglect axial deformations.

If the magnitude (absolute value) of the support moment at H is 10 kN-m, the magnitude (absolute value) of the applied moment M (in kN-m) to maintain static equilibrium is ___________. (round off to the nearest integer)

A horizontal curve is to be designed in a region with limited space. Which of the following measure(s) can be used to decrease the radius of curvature?

Consider the four points P, Q, R and S shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by k_P, k_Q, k_R and k_S, respectively. The correct order of these densities is :

A two-phase signalized intersection is designed with a cycle time of 100 s. The amber and red times for each phase are 4 s and 50 s, respectively. If the total lost time per phase due to start-up and clearance is 2 s, the effective green time of each phase is _________ s. (in integer)

At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is __________. (round off to two decimal places)

The vehicle count obtained in every 10 minute interval of a traffic volume survey done in peak one hour is given below.

The peak hour factor (PHF) for 10 minute sub-interval is _____________. (round off to one decimal place)

For the dual-wheel carrying assembly shown in the figure, P is the load on each wheel, a is the radius of the contact area of the wheel, s is the spacing between the wheels, and d is the clear distance between the wheels. Assuming that the ground is an elastic, homogenous, and isotropic half space, the ratio of Equivalent Single Wheel Load (ESWL) at depth z = d/2 to the ESWL at depth z = 2s is __________. (round off to one decimal place)

(Consider the influence angle to be 45$$^\circ$$ for the linear dispersion of stress with depth)

You should __________ when to say __________.

Two straight lines pass through the origin (x₀, y₀) = (0, 0). One of them passes through the point (x₁, y₁) = (1, 3) and the other passes through the point (x₂, y₂) = (1, 2). What is the area enclosed between the straight lines in the interval [0, 1] on the x-axis?

If

p : q = 1 : 2

q : r = 4 : 3

r : s = 4 : 5

and u is 50% more than s, what is the ratio p : u?

Given the statements :

$$\bullet$$ P is the sister of Q.

$$\bullet$$ Q is the husband of R.

$$\bullet$$ R is the mother of S.

$$\bullet$$ T is the husband of P.

Based on the above information, T is _________ of S.

In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is

Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babies who start eating healthy in the first year are more likely to have better overall health as they get older. Which one of the following is the CORRECT logical inference based on the information in the above passage?

P invested Rs.5000 per month for 6 months of a year and Q invested Rs. x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year. If at the end of that investment year, Q receives $${4 \over 9}$$ of the total profit, what is the value of (in Rs.)?

The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.

From the data presented above, which one of the following is CORRECT?

In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.

The only movement allowed for a step involves, "two moves along one direction followed by one move in a perpendicular direction". The permissible directions for movement are shown as dotted arrows in the right.

For example, a person at a given position Y can move only to the positions marked X on the right.

Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is

Consider a cube made by folding a single sheet of paper of appropriate shape. The interior faces of the cube are all blank. However, the exterior faces that are not visible in the above view may not be blank.

Which one of the following represents a possible unfolding of the cube?