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There are two lines made by joining points A, B,C. B lies between the line joining A and C. Is the distance between the A and C passes through the B more then 7 Km.
I. The distance between A and B is 6 Km
II. Distance between B to C is 7 Km long,
From Statement I
We know the distance between Points B and C but we do not know about the distance between A and B
Statement II
This statement tells us about the distance between A and B and by using Both statement we can calculate the distance between A and C that is longer than the 7 Km.
Direction: In the given question, a word/phrase is given followed by three statements; I, II and III. Choose the pair of sentences which can be combined using the given word/ phrase when used at the beginning of the new sentence.
And
I: When Lionel Messi, Ronaldo and Neymar kick and dribble the football, they don’t remain confined to Argentina, Portugal or Brazil, respectively.
II: Let the entire world realise that through sports, especially football, we all can cement our bonds, wash away our bitterness and prejudices.
III: Live with a greater sense of closeness and joy with each other.
‘And’ is used as a conjunction here which is used to introduce an additional comment or interjection.
Here sentences II and III are displaying same sense that is realizing the benefit of football in our lives whereas sentence I is providing entirely different aspect of football as a sport.
Hence option (B) will be the most appropriate choice.
New sentence: Let the entire world realise that through sports, especially football, we all can cement our bonds, wash away our bitterness and prejudices, and live with a greater sense of closeness and joy with each other.
Which of the following is the MOST SIMILAR in meaning to Accreditation?
Accreditation = an acknowledgement of a person's responsibility for or achievement of something.
Certification = an official document attesting to a status or level of achievement.
Meticulous = showing great attention to detail; very careful and precise.
Lurid = very vividly shocking.
Suppressive = tending or acting to suppress.
Agreement = harmony or accordance in opinion or feeling.
In how many ways can you place 2 white bishops on an empty chess board?
One white bishop can be placed on any of the 32 white boxes and the other white bishop can be placed on any of the 32 black boxes.
Ways of doing that = ^{32}C_{1} * ^{32}C_{1}
= 32 * 32 = 1024
Direction: In the question below are given statements followed by some conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statement:
No physics is maths.
Some chemistry is maths.
All sciences are chemistry.
Conclusion:
I. No science is physics.
II. Some physics are science.
III. Some physics are chemistry
The least possible Venn diagram for the given statements is as follows.
Conclusions:
I. No science is physics → False (It is possible but not definite).
II. Some physics are science → False (It is possible but not definite)
III. Some physics are chemistry → False (It is possible but not definite)
Conclusion I and II form complementary pair.
Hence, either conclusion I or II follows.
Direction: Read the information carefully and give the answer of the following questions
(This pie chart shows the percentage of students appear in six different exams in 2016)
(This bar graph shows the percentage of failed students which appear in these six different exams in 2016)
If in 2016, total number of failed students in exam F was 4080, then how many passed students appears in the exam B?
14280 ( Let total number of students be = 100z.
Total number of students appears in exam F = 16% of 100z = 16z;
Total number of failed students in exam F = 30% of 16z = 4.8z = 4080;
=> z = 850;
Total number of passed students appears in the exam B = (100 – 30)% of 24% of 100z = 16.8z = 16.8 × 850 = 14280 ;)
Direction: Two sentences with two blanks in each, followed by five alternatives with two words in each, are given. Choose that option as the answer which can fill both the blanks of both the sentences.
i. A sinking feeling of panic ________ over them and a temporary paralyzing fear engulfed them ________.
ii. Being a cleanliness freak, she ________ the floor and went down to the market only after the house was _________ clean.
‘Sweep’ is to clean (an area) by brushing away dirt or litter. It fits the first blank of the second sentence, as the subject is cleaning the floor. Further, ‘sweep over’ means to overcome or overwhelm, thus fits in the first blank of the first sentence. The second blank of both the sentences can be filled by "completely", thus conveying an appropriate sense. Thus, option D is the correct answer.
Direction: Five statements are given below, labelled 1, 2, 3, 4 and 5 which are supposed to be in a logical order. A statement labelled P is given thereafter. P can replace one of the five statements such that the four statements along with P would make a coherent paragraph. You have to identify which statement should P replace and then the find out the correct sequence from the options. If the five options are in logical order and form a coherent paragraph/passage, choose the fifth option “12345”.
1) The future of Germany’s coalition government is hanging in the balance after the country’s interior minister reportedly announced his intention to resign over a migration showdown with Angela Merkel.
2) Horst Seehofer, who is also leader of the Christian Social Union, on Sunday night offered to step down from his ministerial role and party leadership in a closeddoor meeting in which he and fellow CSU leaders had debated the merits of the migration deal Merkel hammered out with fellow European Union leaders in Brussels.
3) But with CSU hardliners believed to have tried to talk the combative interior minister into staying, a press conference was postponed until Monday, with Seehofer seeking to go back to Merkel in search of a final compromise.
4) At a 2am media conference, Seehofer said he had agreed to meet again with Merkel’s party before he made his decision final.
5) “We’ll have more talks today with the CDU in Berlin with the hope that we can come to an agreement,” Seehofer said.
Direction: In the given question, a statement with a single blank is given. Choose the most effective word from the given options to complete the sentence meaningfully.
The fog was so thick during the morning, that it seemed like walking _________ a cloud.
Here the sense conveyed is that the fog being too thick, appeared like clouds. You would walk "through" a fog or a tunnel, thus, option D is the best fit answer in the given context. 'Along' means to walk side by side and does not fit in the given context.
4 identical solid spheres are melted and reformed into a solid hemisphere. Then, the ratio of the curved surface area of the hemisphere to half of the surface area of a single sphere is 
Let radius of sphere be ‘r’ and radius of hemisphere be ‘R’.
Then, ATQ, Volume of Spheres = Volume of Hemisphere
4 x (4/3)πr^{3} = (2/3)πR^{3}
Or, R / r = (8)^{1/3} = 2 …(1)
C.S.A of hemisphere = 2πR^{2}
And, Surface area of sphere = 4πr^{2}
ATQ, 2πR^{2} :( ½) of 4πr^{2}
= 2πR^{2} :2πr^{2} = R^{2} :r^{2} {using (1)}
= 4 :1
A study of people who reduced the calories they consumed has found the strongest evidence yet that such restrictions slow down metabolism, raising hopes that a low calories lifestyle or treatments stimulating biological effects of restricted eating, could prolong health in old age. The report provides the most robust evidence to date that everything we have learnt in other animals can be applied to humans.
Which of the following argument will prove that the above conclusion is flawed?
The given passage gives the benefits of reducing calories to attain a healthier lifestyle and out of the given options, option B seems to give a contradictory fact stating that the lack of required calories may cause problems to the body. Hence, option B is correct.
The order and degree of the differential equation, are respectively.
After removing radical sign
The order is 4 since highest differential is d^{2}y/dx^{2 }and the degree is 2 since power of highest differential 2.
The divergence of the vector field x^{2}i + 2y^{3}j + z^{4}k at x =1 , y= 2, z = 3 is
Given
Let , then the smallest positive integer I , such that is ______________
so any integer less than 12 is not possible for this condition.
Since this function has form, limit can be found by application of L’Hospitals Rule
In levelling, if the sum of back sight and fore sight is 1.365 and 0.875 m and reduced level of B.M. is 100 m. then reduced level of end point will be
According to arithmetic check;
∑B.S  ∑F.S = first R.L – last R.L
So, last R.L = first R.L + ∑F.S  ∑B.S
= 100 + 0.875 – 1.365
= 99.51 m
The maximum height of a low gravity dam of elementary profile made up of concrete of relative density 2.4 and safe allowable stress on foundation is 3.6MPa (Ignoring uplift force).
Maximum height of dam is given by
H= F/(ϒ_{w} × (Sc – C+1))
Here F=3.6MPa
ϒ_{w} = 9.81KN/m^3
S_{c} =2.4
C=0
On solving H=107.93m hence correct option is A
The level of water in the reservoir is 1.25 m. If there is a rainfall of 38 cm occurring in a month, during this period evaporation as measured by the class A pan is 32 cm. What is the level of water in m at the end of the month.
Evaporation in lake = Pan coefficient × Pan evaporation
= 0.7 × 32 = 22.4 cm
Initial level + Rainfall – Evaporation = Final level
Final level = 1.25 + 0.38 – 0.224 = 1.406 m
The permeability coefficient of sand with void ratio of 0.65 is 3.048 cm/min. Estimate the permeability coefficient at a void ratio of 0.8 using casagrande empirical relationship.
From the Casagrande relationship,
Note:
A, Casagrande has also given an empirical relation for k for the fine or medium clean sands with bulky grain as
K = 1.4e^{2}k_{0.85}Where k_{0.85} is the coefficient of permeability at a void ratio of 0.85
A 12 m^{3} moist soil sample with volume of soil solid as 9m^{3} is examined and the laboratory results reveal that the porosity of the soil sample is 25 %. The relative porosity of the sample is _____.
Which one of the following is correctly showing the level of manometer column.
AV=constant
By applying Bernoulli's theorem, we know that if velocity increases then the pressure will decrease.
Lets take option 1
at the throat, the area will be less so velocity will increase and pressure will decrease. so the fluid will rise in the tube. Hence this option is right.
option 2
this can not be true as at the throat side fluid is falling which indicate a decrease in velocity and increase in pressure. That is wrong
Same concept follows for option 3 and 4. only option 4 depicts the continuity concept. So only case 1and 4 are right.
A singly reinforced rectangular beam has a width of 200 mm and an effective depth of 350 mm. The limiting value of the moment of resistance of the beam is _________ kNm.
[Take M20 grade concrete and Fe415 grade steel and adopt the stress block for concrete as given in IS 456: 2000]
For Feb 15,
The slack of events 3 and 5 is from the project network given below?
The earliest expected time and latest allowable time of event ‘3’ is 2 and 4 respectively. Thus slack = 42 =2.
Similarly, the earliest expected time and latest allowable time of event ‘5’ is 6 and 6 respectively. Thus slack = 66=0.
Figure shows the network for a particular project which consists of four activities.
Normal duration time and crash time for each activity are given below
The velocity of fluid 2.234 m/s having a viscosity 0.023 Pa.s with density 2.345 is measured at a distance of 95 mm from the boundary. Find the shear stress at the boundary?
From the boundary conditions:
We see that the gradient will be:
dV/dy = 2.234 m/s /0.095 m
= 23.5/s
Now we will see for shear stress by:
Ʈ = µ dV/dy = 0.023 Pa.s x 23.5 s = 0.540 Pa
Which acid is used to distinguish the steel and the wrought iron on the field?
Nitric acid (HNO_{3}) is used to distinguish. If a drop of nitric acid is placed on steel, it will produce a dark grey stain because of higher carbon content whereas in wrought iron, the stain will not be appreciable due to very low carbon content.
The topmost layer is loose, clean sand, 1.5 meter thick. Its vertical permeability can be estimated using Hazen’s formula with C = 1.5 and D10 = 0.016mm. Its horizontal permeability is known to be 350% of the Kv. Below the sand stratum is a layer of marl, 3.5 meters thick, with a kv = Kh = 10^{4} m/s. what is the Equivalent Horizontal permeability for the upper 5 m in cm/sec?
Given that the vertical permeability in sand layer can be estimated using Allen Hazen’s formula
Kv = C (D10)^{2}
C = 1.5 and D10 = 0.016mm
Kv = 0.0384 x 10^{3} cm/sec
Horizontal permeability for sandy layer is 350% of Kv
i.e. K_{h} = 3.5 (0.0384 x10^{3} ) = 0.134 x10^{3} cm/sec
Kh(equ) =(K1H1+K2H2)/(H1+H2)
Here K_{1} = 0.134 x103 cm/sec; H1 = 1.5m
K_{2} = 10^{4} cm/sec; H2 = 3.5m
On substituting, we get Kh(equ) = 1.102 x 10^{4} cm/sec
CayleyHamilton Theorem states that a square matrix satisfies its own characteristic equation. Consider a matrix A satisfies the relation
Characteristic equation is given by, ,  A  λ  = 0
As CayleyHamilton Theorem states, a square matrix satisfies this equation, then,
A^{2} + 3A + 2I = 0
Multiplying A^{–1} to both sides, we get
⇒ ? + 3? + 2? ^{−1} = 0
The hardness of a ground water sample was found to be 420 mg/L as CaCO_{3} A softener containing ion exchange resins was installed to reduce the total hardness to 75 mg/L as CaCO_{3} before supplying to 4 households. Each household gets treated water at a rate of 540 L/day. If the efficiency of the softener is 100%, the bypass flow rate (expressed in L/day) is _____________.
Since each household gets water = 540 L/day
So, total treated water = 540×4=2160 L/day
Let bypass flow rate is QL/day
So,
Consider the matrix:
J6= [0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 ]
Which is obtained by reversing the order of the columns of the identity matrix I6.
Let P=I_{6}+αJ_{6}, where α is a nonnegative real number. The value of α for which det(P) = 0 is ___________.
Consider, (I) Let
∵ α is non negative
∵ the value of (1  α^{2}) = 0 given in the question
∴ α = 1
A beam of uniform strength is to be produced for a special purpose of application. But the section of the beam needs to be varied, and this could be achieved by;
Beam of uniform strength is one in which the maximum bending stress is same in every section along the longitudinal axis.
Uniform strength can be achieved by :
Keeping the width constant throughout the length and varying the depth. This is the most widely used method.
Keeping the depth constant throughout the length and varying the width
Or by varying both width and depth suitably.
A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.
[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]
Height of building above instrument,
from (I) and (ii)
A distributed line load of 100 kN per meter run may occupy any position on the girder shown in the figure below. The ratio of the magnitude of the maximum positive bending moment to negative bending moment that can occur at the section marked at C (not hinge) is ___________.
Influence line diagram
Position of load for maximum negative BM at C
Maximum positive BM at C,
Maximum negative BM at C,
Curing period is minimum for concrete using _______.
Curing period is minimum for concrete using Ordinary Portland cement
Rapid hardening cement requires more curing due to more heat of hydration in shorter time which may leads to shrinkage.
A student began experiment for determination of 5–day, 20 °C BOD on Monday. Since the 5th day fell on Saturday, the final DO readings were taken on next Monday. On calculation, BOD (i.e. 7 days, 20 °C) was found to be 150 mg/L. What would be the 5–day, 20 °C BOD (in mg/L)? Assume value of BOD rate constant (k) at standard temperature of 20 °C as 0.23 / day (base e). ________
The F/M ratio is controlled in the activated sludge process by adjusting the
F/M ratio is defined as
F/M = Daily BOD load supplied to the aerator system / Total microbial mass in the system
The effluent ROD to the plant cannot be changed by the operator. Hence it can be taken as constant. The mass of microorganisms can be regulated by the operator by adjusting the amount of sludge wasting. Greater sludge wasting will lower' in the F/M ratio.
An isolated L beam, as shown below, is fixed at both ends and has a span of 20 m. The effective width of the flange is ____ mm.
For isolated LBeam,
Effective width of flange,
l_{0}= 0.7 x 20 (for fixed ends) = 14 m
∴ Effective width of flange
For the single V unsealed butt welded joint shown in the figure, the permissible load will be _________ kN.
[Assume safe stress in weld to be 143 N/mm^{2}]
Since the joint is as unsealed Vbutt joint, the effective thickness of the throat of weld
Permissible load = Length of weld x Effective throat thickness x Permissible tensile stress in the weld
= 130 x 5 x 143 = 92950 N = 92.95 kN
In two samples of water A and B, A has pH value of 6.5 and B has pH value of 8.5 respectively. Sample B is ___times more acidic than sample A.
PH =  log_{10} [H^{+}]
 log^{10} [H+] = pH
[H^{+}]_{A} = 10^{6.5}
and pH of sample B = 14 – pOH
= 14 – 8.5 = 5.5
The leaching requirement of a soil is 10%. If the consumptive use requirement of the crop is 90 mm, then the depth of water required to be applied to the field is
Leaching requirement in % is given by
Where, D_{i} = Total irrigation water depth to be applied
Cu=Consumptive use
Which of the following statements are CORRECT about affecting the bactericidal efficiency of chlorine?
1) When the time of contact increases, bactericidal efficiency increases.
2) pH range 57 is the most effective, beyond this range, bactericidal efficiency decreases.
3) Bactericidal efficiency decreases with increase in turbidity.
Factors affecting Bactericidal efficiency of Chlorine
1. Turbidity: The effect of turbidity in water is to make it difficult to obtain free residual chlorine. Also, the penetration of chlorine and therefore the destruction of bacteria in particles of suspended matter of a turbid water may be very uncertain.
2. pH of water: Increasing pH reduces effectiveness of chlorine. The effective sterilising compound, hypochlorous acid, is formed in greater quantities at low pH than(5 to 7) at high pH values.
3. Time of Contact: Bactericidal efficiency of chlorine increases with increases in time of contact in general also the bactericidal activity of chlorine is not spontaneous.
For a fully developed laminar flow of water (dynamic viscosity 0.001 Pas) through a pipe of radius 5 cm. the axial pressure gradient is —10 Pa/m. The magnitude or axial velocity (in m/s) at a radial location of 0.2 cm is ___________ m/sec
For incompressible laminar flows through pipes velocity distribution
Converting the matrix into Echelon form,
Now since the matrix is in Echelon
Rank=Number of nozero rows = 2
A rod of length L having uniform crosssectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from E1 to E2 along the length of the rod, the normal stress developed at the sectionSS is
The normal stress across any section depends only on external force (P) & acrosssection area is independent of young's of material
Given that one root of the equation x^{3} –10x^{2} + 31x –30 = 0 is 5, the other two roots are
Given, x^{3}10x^{2}+31x30=
It's one root is 5, hence
(x5) (x^{2}5x+6)=0
⇒(x5) (x^{2}3x2x+6)=0
⇒(x5) (x3)(x2)=0
⇒x=5,3,2
A steel column section ISHB 350 (width of flange is 250mm and thickness of flange 11.6mm) has to carry a factored load of 2400kN. The yield stress and the ultimate tensile stress of steel and welds are 250MPa and 410MPa respectively and partial safety factor governed by yield and ultimate tensile strength respectively are 1.10 and 1.25. The bearing strength of M25 grade concrete in limit state method of design as per IS 456:2000(inN/mm^{2}) is
For ISHB 350 steel column,
b_{f}=250mm and t_{f}=11.6mm.
P=2400kN, f_{y}=250 MPa.
For M25 grade concrete Fck=25N/mm^{2}
Bearing strenght of concrete=0.45f_{ck}=11.25N/mm^{2}
The magnitude of bending moment at fixed end of beam shown in figure above is _________ KNm
Calculation of FEM
FINAL MOMENT AT FIXED END = 72KNm
If the total float of an activity in CPM has a value ‘x’ units and the head event slack has a value ‘y’ units, find out the value of independent float if the tail event slack is 10. ?
Reason: Free float = Total float – Head event slack
Free float =xy
We know that,
Free float = Independent float + Tail event slack
xy = Independent float + 10
Then, Independent float = xy10
The data given below pertain to the design of a flexible pavement are Initial traffic = 1213 cvpd
Traffic growth rate = 8 per cent per annum
Design life = 12 years
Vehicle damage factor = 2.5
Distribution factor = 1.0
The design traffic in terms of million standard axles (msa) to be catered would be
Cumulative number of standard axle load
A = Number of commercial vehicle or initial traffic = 1213 cvpd
r = Traffic growth rate = 8% per annum
n = design life = 2 years
f = vehicle damage factor = 2.5
The velocity potential function in a two dimensional flow field is given by ∅=x^{2}y^{2}. The magnitude of velocity at point (1, 1) is
The flow in a rectangular channel is subcritical. If width of the channel is reduced at a certain section, the water surface under no–choke condition will
In the subcritical region of flow for a given specific energy, as the discharge per unit width q is increased due to reducing width at the section, the depth of flow will decrease.
Therefore water surface drop at a downstream section.
Alternately
From the discharge diagram, it can be seen that, for subcritical flow as q increases, depth decreases.
Therefore at the reduced section, depth decreases.
Match ListI (End condition of the column) with ListII (Lowest critical load) and select the correct answer using the code given below the Lists:
ListI
A) Column with both ends hinged
B) Column with both ends fixed
C) Column with one end fixed and the other end hinged
D) Column with one end fixed and the other end free
ListII
Euler’s Formula is given by Pe
where, E=Young'S Modulus of Elasticity
Imin=Min. Moment of inertia about centroid axis
le=Effective length = Original length × Effective length factor
Consider the following statements:
1) There will be no defects in select grade timbers.
2) The codal values for strength of gradeII timer without defects may be reduced by 37.5%.
3) For timber used as columns, the permissible stress in ungraded timbers is adopted with a multiplying factor of 0.50.
4) In case of wind force and earthquakes, a modification factor of 1.33 is adopted.
Which of the above statements are correct?
Some defects are permitted in all grades of timber and all other defects unlikely to affect any of the mechanical strength properties.
As IS: 1331 –1971 provides for reduction in strength of GradeII timber without defects not by more than 37.5%.
Permissible stress in ungraded timbers is adopted with a multiplying factor of 0.80
Modification factor of 1.33 is adopted in case of wind and earthquake forces
A tractor has a permissible loaded speed of 200 m/minute, which can increase by 25% when the load is removed/deposited. Generally, it is operated at 80% of the permissible speed (loaded unloaded). It works at a location where haul distance is 120 m. Rest allowance per roundtrip is taken as 50 seconds on an average. Fixed time per trip, for loading and unloading and turnaround, etc., is 30 seconds.
What is its effective cycle time157 seconds
Running speed of loaded tractor
= 200 x 0.8 x = 160m/minutes
Running speed of unloaded tractor
= 200 x 1.25 x 0.8
= 200m/minute total time for the trip
A uniform ladder 24 m long weighs 400 N. It is placed against a vertical wall at an angle of 60° with the ground. How far along the ladder can a 1600 N man climb before the ladder is on the verge of slipping? The angle of friction at all contact surfaces is 15°.
A mass of 2 kg is hung by a string of length 1.5m as shown in the figure. The mass revolves in a circular path at 50 revolutions per minute. The tension in the string (in N) is
What is the value of the definite integral
Given
Putting ax=t, we get
Adding equations (i) and (ii), we have
An effective rainfall of 2hour duration produced a flood hydrograph peak of 200m^{3}/s. The flood hydrograph has a base flow of 20m^{3}/s. If the spatial average rainfall in the watershed for the duration of storm is 2cm and the average loss rate is 0.4cm/hour, the peak of 2hour unit hydrograph (in m^{3}/scm, up to one decimal place) is_________(water resource engineering: hydrology)
Peak of DRH =20020=180m^{3}/s
let peak of UH beQ_{p}
So, Q_{p}×1.2=180
⇒Q_{p}=150m^{2}/s
The peak discharge of a 4hr unit hydrograph, triangular in shape, for a basin of 108〖km〗^{2}, is 20 cumecs. The time base (in hrs) of this hydrograph is
Where b is the time base in seconds.
Volume in UH=Volume of runoff with 1 cm depth over the catchment
A joist of 8 m span has to carry a load of 30kN/m. The permissible stress limit is 10N/mm2 and the depth of the joist has to be twice the width. Now, find the dimensions of the joist.
Depth of joist =2×width
= 2 x b
Now, from the bending stress formula,
Permissible stress,
The maximum size of sand particles (with relative density of 2.65) which will settle in water, according to Stoke’s law, is ___________mm.
(Density of water = 998kg/m^{3} , Dynamic viscosity = 1×10^{3} Pa.s).
Stoke’s law is valid up to
Re = 1.0
For maximum size particle that obey stoke’s law,
Also the setting velocity,
Substituting for V_{t}
A catchment is idealized as a 25 km x 25 km square. It has five rain gauges, one at each corner and one at the center, as shown in the figure.
During a month, the precipitation at these gauges is measured as G_{1} = 300 mm, G_{2} = 285 mm, G_{3} = 272mm, G_{4} = 290mm and G_{5} =288mm. The average precipitation (in mm, up to one decimal place) over the catchment during this month by using the Thiessen polygon method is ______
By thiessen polygon method
For a given matrix where the inverse of matrix p is
Consider a nonhomogeneous system of linear equations representing mathematically an overdetermined system. Such a system will be
Determined system In this system, the number of equations is more than number of unknown variables, i.e., (m>n)
So, in determined system it is necessary that the system should be consistent and having unique solution.
Match ListI (Type of shear tests) with ListII (Mohr failure envelops of total stress) and select the correct answer using the codes given below the lists:
ListI
A) Undrained test on normally consolidated saturated clays.
B) Consolidated undrained test on normally consolidated saturated clays.
C) Drained tests on normally consolidated saturated cohesive soil.
D) Unconfined test on clays.
ListII
A) If undrained test is done on a saturated soil, then the total stress envelope will have the same diameter for all tests, i.e., diagram 1.
C) In drained test, higher the confining stress higher will be the consolidation which increases soil’s shearing strength, hence, failure stress will be high and therefore diameter of Mohr failure envelope gets on increasing in size.
D) Unconfined test means confining pressure should be zero, hence, diagram 4 only.
Note: CU and CD tests will have similar diagram for normally consolidated clays.
Applying L' Hospital rule
Applying L' Hospital rule
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