The temperature T in a room varies as a function of the outside temperature T0 and the number of persons in the room p, according to the relation T = K (θq p+ T0) , where θ is K are constants. What would be the value of θ given the following data?
“The driver applied the __________ as soon as she approached the hotel where she wanted to take a __________.”
The words that best fill the blanks in the above sentence are
• Brake is a device which is used for stopping or moving a vehicle.
• Break refers to a pause in work or during an activity.
Tower A is 90 m tall and tower B is 140 m tall. They are 100 m apart. A horizontal skywalk connects the floors at 70 m in both the towers. If a taut rope connects the top of tower A to the bottom of tower B, at what distance (in meters) from tower A will the rope intersect the skywalk?
“It is no surprise that every society has had codes of behaviour; however; the nature of these codes is often ________.” The word that best fills the blank in the above sentence is
Unpredictable – Contrary word required
Hema’s age is 5 years more than twice Hari’s age. Suresh’s age is 13 years less than 10 times Hari’s age. If Suresh is 3 times as old as Hema. How old is Hema?
Using options (a) and (c) cannot be answer.
As Hema’s age is twice of a natural number +5.
(b) and (d) remain.
Let us take Hema’s age as option (d) which is 19.
Hari’s age = 7, and Suresh age = 57 Verifies all condition “answer (d)”
Hema 2 Hari + 5
Suresh 10 Hari -13 = 3 Hema
Hari = 7
Suresh = 57
Consider a sequence of number a1,a2,a3 ..., an where for each integer n > 0. What is the sum of the first 50 terms?
Sum of series will
All like terms will cancel out and we will be left with
A fruit seller sold a basket of fruits at 12.5% loss. Had he sold it for Rs. 108 more, he would have made a 10% gain. What is the loss in Rupees incurred by the fruit seller?
12.5% x 10% = 108
Each of the letters arranged as below represents a unique from 1 to 9. The letters are positioned in the figure such that (A x B x C),(B x G x E) and (D x Ex F ) are equal. Which integer among the following choices cannot be represented by the letters A, B, C, D, E, F or G?
A x B x C = B x G x E = D x E x F = 72
8 x 9 x 1 = 9 x 2 x 4 x 3 x 4 x 6 = 72
Any of A, B, C, D, E, F , G cannot be 5.
The price of a wire made of a superalloy material is proportional to the square of its length. The price of 10 m length of the wire is Rs. 1600. What would be the total price (in Rs.) of two wires of lengths 4 m and 6 m?
Now total cost = 52k 52 x 16 = 832
What of the following function(s) in an accurate description of the graph for the range(s) indicated?
Put value and verify
A solid circular beam with radius of 0.25 m and length of 2 m is subjected to a twisting moment of 20 kNm about the z-axis at the free end, which is the only load acting as shown in the figure. the stress component txy at Point ‘M’ in the cross-section of the beam at a distance of 1 m from the fixed end is
The only non-zero stresses are
if θ is 90o then θ = y
But in rest of the planes shear stresses are zero, hence,
In a fillet weld, the direct shear stress and bending tensile stress are 50 MPa and 150 MPa, respectively. As per IS 800 : 2007, the equivalent stress (in MPa, up to two decimal places) will be ____________.
Direct bending tensile stress,
fa = 150 MPa
Direct shear stress, q = 50 MPa
According to IS 800 : 2007, clause 10.5.10.1.1
The equivalent stress
Note : The above check for combination of stress need not be done for fillet welds where the sum of normal and shear stresses does not exceed fwd [Clause 10.5.10.1.2. (b)].
Thus, the weld is designed for an equivalent stress of 173.21 MPa.
The percent reduction in the bearing capacity of a strip footing resting on sand under flooding condition (water level at the base of the footing) when compared to the situation where the water level is at a depth much greater than the width of footing, is approximately
For strip footing on sand (c = 0)
In flooding condition water level rises to base of footing hence IIIrd term unit weight of soil will change and IInd term unit weight will be unaffected.
Hence third term reduced and second term will be same thereby percentage reduction will not be 50%.
According to option approach answer should be 25%.
Note : If water table rises to ground level then both γ will reduce to γ hence percentage reduction would be approximately 50%.
The deformation in concrete due to sustained loading is
Creep is inelastic deformation with time due to sustained loading.
The speed-density relationship for a road section is shown in the figure.
The shape of the flow-density relationship is
A steel column of ISHB 350 @ 72.4 kg/m is subjected to a factored axial compressive load of 2000 kN. The load is transferred to a concrete pedestal of grade M20 through a square base plate. Consider bearing of concrete as 0.45 fck , where fck is the characteristic strength of concrete. Using limit state method and neglecting the self weight of base plate and steel column, the length of a side of the base plate to be provided is
Area required for base plate
So, side of base plate
= 471.4 mm
= 47.14 mm
Since, provided area must be more than required so answer should be 48 cm.
For routing of flood in a given channel using the Muskingum method, two of the routing coefficients are estimated as
C0 =−0.25 and C1 = 0.55. The value of the third coefficient C2 would be _________.
In Muskingum flood routing method
C0 + C1 + C2 = 1
A column of height h with a rectangular cross-section of size a x 2a has a buckling load of P. If the cross-section is changed to 0.5a x 3a and its height changed to 1.5 h, the buckling load of the redesigned column will be
For new column,
Bernoulli’s equation is applicable for
The frequency distribution of the compressive strength of 20 concrete cube specimen is given in the table.
If μ is the mean strength of the specimens and σ is the standard deviation, the number of specimens (out of 20) with compressive strength less than m μ − 3σ is _________.
Now, μ − 3σ = 26.575 - 3 x 3.7 = 15.48
Thus, no specimen is having compressive strength less than μ − 3σ
The width of a square footing and the diameter of a circular footing are equal. If both the footings are placed on the surface of sandy soil, the ratio of the ultimate bearing capacity of circular footing to that of square footing will be
Footing placed on surface
∴ Df = 0
For square footing,
For circular footing,
For sandy soil, C = 0
In a shrinkage limit test, the volume and mass of a dry soil pat are found to be 50 cm3 and 88 g. respectively. The specific gravity of the soil solids is 2.71 and the density of water is 1 g/cc. The shrinkage limit (in % up to two decimal places) is___________.
Dry soil mass = 88 gm
Volume of dry soil = 50 cc
Dry density of soil mass,
∴ Shrinkage limit,
A core cutter of 130 mm height has inner and outer diameters of 100 mm and 106 mm respectively. The area ratio of the core cutter (in %, up to two decimal places) is ______________.
Two rectangular under-reinforced concrete beam sections X and Y are similar in all aspects except that the longitudinal compression reinforcement in section Y is 10% more. Which one of the following is the correct statement?
Due to presence of more compression steel in section Y, NA of section of Y is above than as of X. It means Y is more under-reinforced than X so ductility of Y is more. Since compression steel of Y is more so flexure resistance of X is less than as of Y.
At the point x = 0, the function f ( x ) = x3 has
f(x) = x3 at x= 0
At x = 0, the function y =x3 has neither minima nor maxima.
A well-designed signalized intersection is one in which the
A flow field is given by Value of the zcomponent of the angular velocity (in radians per unit time, up to two decimal places) at the point (0, -1, 1) is ________.
A bitumen sample has been graded as VG30 as per IS : 73-2013. The ‘30’ in the grade means that
The Le Chatelier apparatus is used to determine
Le Chatelier Apparatus is used to determine the soundness of cement as per IS code 4031 (part 3); this cement testing procedure is called Le Chatelier test for determining the unsoundness properties of cement due t presence of “free lime”.
A city generates 40 ´ 106 kg of municipal solid waste (MSW) per year, out of which only 10% is recovered/recycled and the rest goes to landfill. The landfill has a single lift of 3 m height and is compacted to a density of 550 kg/m3. If 80% of the landfill is assumed to be MSW, the landfill area (in m2, up to one decimal place) required would be __________.
Total weight generated by city = 40 x106 kg/year Weight of MSW going into landfill
= 0.9 x 40 x 106 kg/year
= 36 x 106 kg/year
Compacted density = 550 kg/m3
Compacted volume of MSW
Total landfill volume = Volume of MSW + Volume of cover
Given, Volume of MSW = 0.8 x Total landfill volume ∴ Volume of cover = 0.2 x Total landfill volume
∴ Total landfill volume
m3 /year = 81818.18175 m3 /year
Height of landfill = 3 m
∴ Area of landfill
= 27272.7 m /year
There are 20,000 vehicles operating in a city with an average annual travel of 12,000 km per vehicle. The NOx emission rate is 2.0 g/km per vehicle. The total annual release of NOx will be
Total no. of kms. travelled by all the vehicles
= 20000 x 12000 km
= 24 x 107 km
Total NOx emission 2 g/km x 24 x107 km
= 48 x107 g
= 48 x 104 kg
For the given orthogonal matrix Q,
The inverse is
A 10 m wide rectangular channel carries a discharge of 20 m3/s under critical condition. Using g = 9.81 m/s2, the specific energy (in m, up to two decimal places) is _______________
A 1:50 model of a spillway is to be tested in the laboratory. The discharge in the prototype spillway is 1000 m3 /s. The corresponding discharge (in m3/s up to two decimal places) to be maintained in the model, neglecting variation in acceleration due to gravity, is __________.
Froude law is valid
Which one of the following matrices is singular?
Option (a): | A | = 6 − 5 = 1
Option (b): | A |= 9 − 4 = 5
Option (c): | A | = 12 − 12 = 0
Option (d): | A |= 8 − 18 = −10
Hence matrix (c) is singular.
A waste activated sludge (WAS) is to be blended with green waste (GW). The carbon (C) and nitrogen (N) contents, per kg of WAS and GW on dry basis are given in the table.
The ratio of WAS to GW required (up to two decimal places) to achieved a blended C:N ratio of 20:1 on dry basis is ________.
Let 20 kg xof C and 1 kg of N is required
Let x kg of WAS is taken
∴ Carbon in x kg = 0.054 x kg
Nitrogen in x kg = 0.010 x kg
Let y kg of GW is taken
∴ Carbon in x kg = 0.360 y kg
Nitrogen in x kg = 0.006 x kg
0.054x + 0.36y= 20 kg
0.01x + 0.0 06 y = 1 kg
Variation of water depth (y) in a gradually varied open channel flow is given by the first order differential equation
Given initial conditions: y (x = 0)= 0.8 m.
The depth (in m, up to three decimal places) of flow at a downstream section at x = 1 from one calculation step of Single Step Euler Method is ___________.
A rapid sand filter comprising a number of filter beds is required to produce 99 MLD of potable water. Consider water loss during backwashing as 5%, rate of filtration as 6.0 m/h and length to width ratio of filter bed as 1.35. The width of each filter bed is to be kept equal to 5.2 m. One additional filter bed is to be provided to take care of break-down repair and maintenance. The total number of filter required will be
Total water to be filtered = 99 x 1.05 MLD
= 103.95 MLD
(Addition of 5% to be used for backwashing)
where B = 5.2 m
∴ L= 7.02 m
∴ Surface area of each filter = 36.504 m2
Total surface area required
Total no. of working units required
1 unit is to added as standby, thus total no. of units required = 21
Consider the deformable pin-jointed truss with loading, geometry and section properties as shown in figure.
Given that E = 2 x 1011 N/m2,A = 10 mm2, L = 1m and P = 1 kN. the horizontal displacement of Joint C (in mm, up to one decimal place) is ___________.
Force is each member due to applied loading.
Force in each member due to unit load.
∴ Total deflection
Rainfall depth over a watershed is monitored through six number of well distributed rain gauges. Gauged data are given below:
Thiessen mean value;
The infiltration rate f in a basin under ponding condition is given by f = 30+ 10e-2t , where, f is in mm/h and t is time in hour. Total depth of infiltration (in mm, up to one decimal place) during the last 20 minutes of a storm of 30 minutes duration is _________
Infiltration rate f (t ) = 30+ 10 e−2t
Total infiltration depth in time 10 min. to 30 min. i.e., 0.166 hour to 0.5 hour
A rigid smooth retaining wall of height 7 m with vertical backface retains saturated clay as backfill. The saturated unit weight and undrained cohesion of the backfill are 17.2 kN/m3 and 20 kPa, respectively. The difference in the active lateral forces on the wall (in kN per meter length of wall, up to decimal places), before and after the occurrence of tension cracks is _________
For clay ø = 0
Earth pressure when tension cracks are not developed.
Earth pressure when tension cracks are developed
Difference 188.136 - 141.4098
= 46.7262 kN/m2
An aircraft approaches the threshold of a runway strip at a speed of 200 km/h. The pilot decelerates the aircraft at a rate of 1.697 m/s2 and takes 18 s to exit the runway strip. If the deceleration after exiting the runway is 1 m/s2, then the distance (in m, up to one decimal place) of the gate position from the location of exit on the runway is ____________
Speed of aircraft, μ = 200 km/hr
Deceleration of aircraft on the runway Aircraft takes 18 sec to exit the runway strip.
Speed of the aircraft at the exit of the runway
uf = ui+ at
= 55.56 - 1.697 x18 = 25.014 m/s
After runway aircraft decelerate with Total distance travelled by the aircraft from the location of exit on the runway
U2 = u2 + 2aS
0 = 25.0142 - 2 x1 x S
S = 312.8 m
A 0.5 m x 0.5 m square concrete pile is to be driven in a homogeneous clayed soil having undrained shear strength
cu = 50 kPa and unit weight, γ = 18.0 kN/m3 . The design capacity of the pile is 500 kN. The adhesion factor α is given 0.75. The length of the pile required for the above design load with a factor of safety of 2.0 is
An RCC beam of rectangular cross-section has factored shear of 200 kN at its critical section. Its width b is 250 mm and effective depth d is 350 mm. Assume design shear strength tc of concrete as 0.62 N/mm2 and maximum allowable shear stress tc max in concrete as 2.8 N/mm2 . If two legged 10 mm diameter vertical stirrups of Fe250 grade steel are used, then the required spacing (in cm, up to one decimal place) as per unit state method will be _____________
Nominal shear stress
2.286 N/mm2 < Tc max (OK)
SF taken by stirrups = (tv - tc ) bd
= 2.286 − 0.62) x 250 x 350 = 145.75 kN
A priority intersection has a single-lane one-way traffic road crossing an undivided two-lane two-way traffic road. The traffic stream speed on the single-lane road is 20 kmph and the speed on the two-lane road is 50 kmph. The perception-reaction time is 2.5 s, coefficient of longitudinal friction is 0.38 and acceleration due to gravity is 9.81 m/s2. A clear sight triangle has to be ensured at this intersection. The minimum lengths of the sides of the sight triangle along the two-lane road and the single-lane road, respectively will be
An RCC short column (with lateral ties) of rectangular cross-section of in 250 mm ´ 300 mm reinforced with four members of 16 mm diameter longitudinal bars. The grades of steel and concrete are Fe415 and M20, respectively. Neglect eccentricity effect. Considering limit state of collapse in compression (IS 456 : 2000), the axial load carrying capacity of the column (in kN, up to one decimal place) is _____________
Since eccentricity effect is being neglected so column can be considered as concentrically loaded.
Ultimate axial load carrying capacity of column.
Pu = 0.45 f ck Ag + (0.75 fy - 0.45 f ck) Asc
= 0.45 x 20 x 250 x 300 + ( 0.75 x 415 x 20 )
= 91.1 kN
The ultimate BOD (L0 ) a wastewater sample is estimated as 87% of COD. The COD of this wastewater is 300 mg/L. Considering first order BOD reaction rate constant k (use natural log) = 2.3 per day and temperature coefficient θ = 1.047, the BOD value (in mg/L, up to one decimal place) after three days of incubation at 27oC for the wastewater will be ________
= 0.87 COD = 0.87 x 300 = 261mg/l
A cylinder of radius 250 mm and weight, W = 10 kN is rolled up an obstacle of height 50 mm by applying a horizontal force P at its centre as shown in the figure.
All interfaces are assumed frictionless. The minimum value of P is
Given: r = 250 mm,W= 10 kN
Note: 1. When the cylinder will be about to move out of the cylinder, it will loose its contact at point A, only contact will be at point B.
2. Considering equation of cylinder of that instant under P, W and RB (contact force at B).
At a construction site, a contractor plans to make an excavation as shown in the figure.
The water level in the adjacent river is at an elevation of +20.0 m. Unit weight of water is 10 kN/m3. The factor of safety (up to two decimal places) against sand boiling for the proposed excavation is __________
he solution (up to three decimal places) at x = 1 of the differential equation subject to boundary conditions
from eq. (ii) and (iii),
The void ratio of a soil is 0.55 at an effective normal stress of 140 kPa. The compression index of the soil is 0.25. In order to reduce the void ratio to 0.4, an increase in the magnitude of effective normal stress (in kPa, up to one decimal place) should be _____________
A water sample analysis data is given below:
The carbonate hardness (expressed as mg/L of CaCO3, up to one decimal place) for the water sample is ___________
Carbonate hardness = min. (Total hardness, alkalinity)
The dimensionless of a symmetrical welded I-section are shown in the figure.
The plastic section modulus about the weaker axis (in cm3, up to one decimal place) is ___________
The figure shows a simply supported beam PQ of uniform flexural rigidity EI carrying two moments M and 2M
A conventional drained triaxial compression test was conducted on a normally consolidated clay sample under an effective confining pressure of 200 KPa. The deviator stress at failure was found to be 400 kPa. An identical specimen of the same clay sample is isotropically consolidated to a confining pressure of 200 kPa and subjected to standard undrained triaxial compression test. If the deviator stress at failure is 150 kPa, the pore pressure developed (in kPa, up to one decimal place) is _______________
1st Specimen : Drained condition
Let pore pressure developed is u
From stress relationship
For second specimen,
Given the following data: design life n = 15 years, lane distribution factor D = 0.75, annual rate of growth of commercial vehicles r = 6%, vehicle damage factor F = 4 and initial traffic in the year of completion of construction = 3000 Commercial Vehicles Per Day (CVPD). As power IRC : 37-2012, the design traffic in terms of cumulative number of standard axles (in million standard axles, up to two decimal places) is _________
A plate in equilibrium is subjected to uniform stresses along its edges with magnitude σxx =30 MPa and σyy = 50 MPa as shown in the figure
The Young’s modulus of the material is 2 X 1011 N/m2 and the Poisson's ratio is 0.3.
If σzz is negligibly small and assumed to be zero, then the strain ∈zz is
In a laboratory, a flow experiment is performed over a hydraulic structure. The measured values of discharge and velocity are 0.05 m3 /s and 0.25 m/s, respectively. If the full scale structure (30 times bigger) is subjected to a discharge of 270 m3/s, then the time scale (model to full scale) value (up to two decimal places) is _______________
Froude Law (Fr)m = (fr)p
(gm = gp)
The following details refer to a closed traverse :
The length and direction (whole circle bearing) of closure, respectively are
∑L = 101 + 419 - 437 - 83 = 0
∑D = 173 + 558 - 96 - 634 = 1
Therefore departure of closure is 1 m and WCB is 90o.
A square area (on the surface on the earth) with side 100 m and uniform height, appears as 1 cm2 on a vertical aerial photograph. The topographic map shows that a contour of 650 m passes through the area. If focal length of the camera lens is 150 mm, the height from which the aerial photograph was taken, is
A = 100 x 100 m2
Area on photo, a = 1 cm2
Scale 1 cm = 100 m
f = 150 mm
h = 650 m
The solution at x = 1,t= 1 of the partial differential equation subject to initial conditions of u (0) =3x and is ____________
The value of the integral is
A cantilever beam of length 2 m with a square section of side length 0.1 m is loaded vertically at the free end. The vertical displacement at the free end is 5 mm. The beam is made of steel with Young’s modulus of 2.0 x 1011 N/m2. The maximum bending stress at the fixed end of the cantilver is
A closed tank contains 0.5 m thick layer of mercury (specific gravity = 13.6) at the bottom. A 2.0 m thick layer of water lies above the mercury layer. A 3.0 m thick layer of oil (specific gravity = 0.6) lies above the water layer. The space above the oil layer contains air under pressure. The gauge pressure at the bottom of the tank is 196.2 kN/m2. The density of water is 1000 kg/m3 and the acceleration due to gravity is 9.81 m/s2. The value of pressure in the air space is
Pair is in gauge pressure.