In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.
Statements: All bags are cakes. All lamps are cakes.
Since the middle term 'cakes' is not distributed even once in the premises, no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. So, either I or II follows.
Man does not live by __________ alone.
Man does not live by bread alone.
Extreme focus on syllabus and studying for tests has become such a dominant concern of Indian students that they close their minds to anything ___________ to the requirements of the exam.
Extraneous – irrelevant or unrelated to the subject being dealt with
Select the pair that best expresses a relationship similar to that expressed in the pair:
LIGHT : BLIND
Light cannot be seen by blind.
On the similar logic, Speech cannot be spoken by dumb. Sound cannot be heard by deaf.
If = log(a+b), then:
In an exam, the average was found to be 50 marks. After deducting computational errors the marks of the 100 candidates had to be changed from 90 to 60 each and average came down to 45 marks. Total No of candidates who took the exam were.
Let number of candidates be n
50 × n – 100 × 30 = 45 × n
n = 600
A solid 4cm cube of wood is coated with red paint on all the six sides. Then the cube is cut into smaller 1cm cubes. How many of these 1cm cubes have no colour on any side?
Number of cubes with 3 faces red = 8
Number of cubes with 2 faces red = 24
Number of cubes with 1 face red = 24
Number of cubes with no face red = 64-(24+24+8) = 8
In deriving the equation for the hydraulic jump in a rectangular channel in terms of the conjugate depths and the initial Froude number.
Continuity equation and momentum equation are used for the hydraulic jump in terms of the conjugate depth and Froude number.
Energy equation is further used to determine the loss of energy in the jump.
This paragraph states that warm weather affects the consumer’s inclination to spend the age of father is 4 times more than the age of his son Amit. After 8 years, he would be 3 times older than Amit. After further 8 years, how many times will he be older than Amit?
Let Amit’s age be n years
Age of his father = (4n+n) = 5n years
After 8 years:
Amit’s age = n+8
Father’s age =
3(n+8) = 5n+8
3n+24 = 5n+8
16 = 2n
n = 8 years
After further 8 years:
Amit’s age = 24 years
Father’s age = 5n+16 = 56 years
So father is 2.33 times older than Amit
Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?
Let pipe A, B, C fills the tank in a, b, c minutes respectively.
Pipe A is kept open for t minutes
Pipe B is kept open for 10 minutes
Pipe C is kept open for t-10-2 minutes
t/a=10/b=(t-12)/c since each pipe has equal share of tank
Both pipes fill the tank in time t.
Solving 1st two equations we get 30/b =1 b= 30 minutes
Solving last 2 equations we get 10+t = b t =20 minutes
Therefore, time taken by C to fill it will be 24 minutes from equation 2.
The plastic modulus of a section is 4.8 x 10-4 m3. The shape factor is 1.2. The plastic moment capacity of the section is 120 kN.m. The yield stress of the material is:
Moment Capacity of the Section = Plastic Modulus of Section x Yield Stress of Material
120 x 106 Nmm = 4.8 x 10-4+9 mm3 x Yield stress of Material
Yield stress of Material = 250 N/mm2
MPN index is a measure of one of the following:
MPN- Most Probable Number used to measure Coliform Bacterial
Wrinkler’s Method is used to measure dissolved oxygen and further, which is used to determine BOD5
Hardness is measured in mg/L as CaCO3 via various methods like lime treatment, boiling.
Consider the following statements:
1) Strength of concrete cube is inversely proportional to water-cement ratio.
2) A rich concrete mix gives higher strength than a lean concrete mix since it has more cement content.
3) Shrinkage cracks on concrete surface are due to excess water in mix.
Which of the following statements is correct?
Lower the water cement ratio higher the concrete strength.
A rich concrete due to greater cement content will possess higher strength in comparison to lean cement.
Higher the water content in mix higher will be the shrinkage in concrete.
Standard 5-day BOD of a waste water sample is nearly x% of the ultimate BOD, where x is:
BOD5 = BODu [ 1-10-k x 5] and the usual value of deoxygenation constant is 0.1
Substituting, the value of k BOD5 = BODu [0.6837]
Therefore, value of x will be 68.37%
The dimensions for the flexural rigidity of a beam element in mass (M), length (L) and time (T) is given by:
In a beam, the flexural rigidity (EI) varies along the length as a function of x as shown in equation:
Where E is the young's modulus (in Pasual, Pa), I is the second moment of area (in m4). Y is the traverse displacement of the beam x and M(x) is the bending moment at x. The SI unit of flexural rigidity is thus Pa. m4 or Nm4
∴ Dimension is ML3T–2
The superelevation needed for a vehicle travelling at a speed of 60 kmph on a curve of radius 128 m on a surface with a coefficient of friction of 0.15 is:
A Correct the options by inserting a zero after the decimal in each option.
e- superelevation; f- coefficient of friction = 0.15; v= speed of vehicle in m/s = 60 kmph = 60x0.278 m/s = 16.68 m/s; R = radius of curvature = 128m
ⅇ+f=v2/gR ⅇ+0.15=〖16.68〗2/(9.81 x 128) e= 0.0716
Which of the following raingauge gives a plot of the accumulated rainfall against the elapsed time?
Weighing bucket type
If the time period between centroid of the rainfall diagram and peak of the hydrograph is 5 hour, using Snyder’s equation the value of the base width of unit hydrograph in hours is?
A river 5 m deep consists of a sand bed with saturated unit weight of 20 kN/m3 . vw = 9.81 kN/m3. The effective vertical stress at 5 m from the top of sand bed is:
Effective Vertical Stress = Total Vertical Stress – Pore Water Pressure
= γ_(sat ) z - γ_(w ) z = 20x 5 – 9.81 x 5 = 50.95 kN/m2
A hydraulic model of a spillway is constructed with a scale 1:16. If the prototype discharge is 2048 cumecs, then the corresponding discharge for which the model should be tested is:
Q = A×V
Spillway model obeys Froude’s Law
A droplet of water at 200C (σ = 0.0728 N/m) has internal pressure 1 kPa greater than that outside it, its diameter is nearly:
For a droplet;
A reinforced concrete structure has to be constructed along a sea coast. The minimum grade of concrete to be used as per IS : 456-2000
Minimum Grade of Concrete on Sea Cost:
Plain Cement Concrete – M20
Reinforced Cement Concrete – M30
The order and degree of the differential equation given, is
Order = 2
Degree = 3
The probability distribution taken to represent the completion time in PERT analysis is:
The distribution curve for the time taken in to complete each activity of a project resembles a beta-distribution curve and the distribution curve for the time taken to complete entire project ( consisting of several activities) in general resembles a normal distribution curve.
Consider the following statements
1) Cambium layer is between sapwood and heartwood
2) Heartwood is otherwise termed as deadwood
3) Timber used for construction is obtained from heartwood
Which of the following is/are correct statements?
Cambium layer is between inner bark and sapwood. Heartwood is dead wood which does not take part in the growth of tree and is used for construction.
The true bearing of a tower T as observed from station A was 3560 and the magnetic bearing of the same was 40.The back bearing of the line AB when measured with prismatic compass was found to be 2960.Then the true fore bearing of line AB will be _____ degrees.
The degree of static indeterminacy of the rigid frame having 2 internal hinges is as shown in the figure below
Number of restraints required = 6
Number of cuts required = 3
= 3×3-6 = 3
If the deformations of the truss-members are as shown in parentheses, the rotation of the member bd is:
The problem of lateral buckling can arise only in those steel beams which have:
Lateral buckling occurs when an applied load causes lateral displacement of a member which generally occurs when moment of inertia about the bending axis smaller than the other.
The available moisture holding capacity of soil is 15cm per meter depth of soil. If a crop with a root zone of 0.8m and consumptive use of 6 mm/day is to be grown, the frequency of irrigation for restricting the moisture depletion to 60% of available moisture is?
Available moisture holding capacity = 15×0.8 = 12cm
Readily available moisture content = 0.4×12 = 4.8cm
Frequency of irrigation = 48/6 = 8 days
6 boys and 6 girls sit in a row at random. Find the probability that-
1) The six girls sit together
2) The boys and girls sit alternately.
\Total ways of making sit 12 persons 12!
Considering set of 6 girls as a single group. Within the group girls can be arranged in 6! Ways. Now only among 7 persons—> 6 boys + 1 girl group arrangement needs to be done. Thus, number of ways for the same = 7!.
Therefore, probability = Favourable outcomes/ total number of outcomes = (7!) (6!) / (12!) = 1/1322
We can only make sit boys and girls in alternate manner in two possible ways, boys at even and girls at even. But, among boys group and girls group itself, rearrangement can be done in 6! Ways each.
Therefore, probability =(2)(6!)(6!)/ 12! = 1/462
Match List-I (contract types) with List-II (Characteristics):
a. Labour contract
b.Item rate contract
c. Piecework contract
d.Lump sum contract
1.Petty works and regular maintenance work
2.Adopted for buildings, roads, bridges and electrical works
3.Payment made by detailed measurement of different time
4.Not practiced in government
Labour Contract- Workers who are hired for a specific task and a finite period.
Item Rate Contract- Contractor gets paid on ‘per item basis’-Payment by detailed measurement of different time.
Piecework Contract- Paying contractor pay rate for each unit/ work they produce/accomplish-Petty works and regular maintenance work
Lump sum Contract-A single lump sum price for all works is agreed before works begin. Adopted for buildings, roads, bridges and electrical works.
Plate bearing test with 20 cm diameter plate on soil subgrade yielded a pressure of 1.25 x 105 N/m2 at 0.5 cm deflection. What is the elastic modulus of subgrade?
For Rigid Plate
Δ=(1⋅18pa)/Es 0.005 =(1⋅18 x 1.25 x 105 x 0.1 )/Es Es = 29.5 x 105 N/m2
Δ – Settlement = 0.5 cm = 0.005 m
P – pressure = 1.25 x 105 N/m2
radius of plate = (20/2) cm =10 cm = 0.1m
Es – modulus of subgrade
A ductile metal bar is subjected to pure shear test and its yield strength was found to be 230 N/mm2 the maximum permissible shear stress on that metal will be:
fy = 230 kN/m2
Shear strength = 230/2 = 115 N/mm2
When ductile metal bar is subjected to pure shear test, maximum permissible shear stress is 115N/mm2
Which of the following is characteristic of colliform organism?
Select the correct answer using the codes given below:
Colliform organism is bacillus and gives gram negative test. It is lactose fermenter.
A light rope fixed at one end of a wooden clamp on the ground passes over a tree branch and hangs on the other side. It makes an angle with the ground. A man weighing (60 kg) wants to climb up the rope. The wooden clamp can come out of the ground if an upward force greater than 360N is applied to it. Find the maximum acceleration in the upward direction with which the man can climb safely. Neglect friction at the tree branch. Take g = 10
Let T be the tension in the rope.
The upward force on the clamp is, T sin= T/2
The maximum tension that will not detach the clamp from the ground is:
T = 720 N
T – 600 = 60a
where a is the acceleration of man in upward direction.
The pavement designer has obtained the value of design traffic as 200 million standard Axles for a newly developing highway. The design life adopted is 15 years. Annual traffic growth rate of 8% is taken into account. Commercial vehicles count before pavement construction was 5000 vehicles/day. The vehicle damage factor used in the calculation was:
Rate of population increase = 1100 people/year
Number of people who would consume 65000 m3/day is equal to = 32500 people
Number of years when plant reach design capacity = = 4.091 years
The present population of a community is 28000 with an average water demand of 150 Lpcd. The existing water
treatment plant has a design capacity of 6000 m3/d. It is expected that population will increase to 48,000 in the next 20 years. What is the number of years from now when the plant will reach its design capacity assuming an arithmetic rate of population growth?
A square plate 5m × 5m hangs in water from one of its corners and its centroid lies at 8m from the free water surface. Find the total pressure force on the top half of the plate. (γw = 10 kN/m3)
Pressure force = Pressure at CG × Area of plate
h is the height of CG from top of water surface.
A sample of clay was coated with paraffin wax and its mass, including the mass of wax was found to be 650 gm, the sample was immersed in water and the volume of the water displaced was found to be 325 Ml. The mass of the sample without wax was 640 gm and water content of the specimen was 20%. Specific gravity of wax is 0.9 and specific gravity of soil solids is 2.7. The void ratio and density of the sample is:
Mass of wax is 650-640 = 10 gm
e = 0.588
For a highway with design speed of 100 kmph, the safe overtaking sight distance is (assume accelerations as 0.53 m/sec2)
V = 100kmph, Vb = V - 16 = 100 - 16 = 84kmph
Take, t = reaction time = 2secs
A = 0.53 m/s2 = 0.53 * 36 = 1.92 kN/s2
Now d1 = 0.28 * Vb * t = 0.28 * 84 * 2 = 47.04m
d2 = 0.28Vb * T; T = ; s = 0.2Vb + 6 = 0.28 * 84 + 6 = 22.8m
then T = 13.11secs
d2 = 0.28 * Vb * T = 0.28*84*13.11 = 354.13m
d3 = 0.28V * T = 0.28 * 100 * 13.11 = 367.08m
d1 +d2 + d3 = 768.25m = 750m
The insitu moisture content of a soil is 18% and its bulk unit weight is 19.65 kN/m3 .The specific gravity of the soil solids is 2.7. The soil is to be excavated and transported to a construction site and then compacted to a minimum dry unit weight of 16.65 kN/m3 at a moisture content of 20%. How many truck loads are needed to transport the excavated soil if each truck can carry 25 tons? Total volume of the compacted fill is 10,000 m3 (γw = 10 kN/m3)
Horizontal stiffness coefficient, K11 of bar ab is given by:
In the given figure below, the slope at point P will be:
A father notes that when his teenage daughter uses the phone she takes no less than 6 minutes for a call but sometimes as much as an hour. 20 minutes calls are more frequent than calls of any other duration.If the daughter’s calls were to be represented as an activity in PERT project, the expected duration of each phone call is:
Calculate the quantity of cement (in kg) required to produce 1 of concrete for mix proportion of 1:2:4 (by volume). Water cement ratio = 0.48
Percentage of entrapped air is 2%
Let the volume of cement, fine aggregates and coarse aggregates be x, 2x and 4x
Weight of cement added = 1450 × 0.2092 = 303.4 kg
The beams in the two storey frame shown in the figure below have a cross – section such that the flexural rigidity may be considered infinite. Which among the following is the stiffness matrix for the structure in respect of the global coordinates 1 and 2?
A uniformly distributed load of 6 kN/m, 6m long crosses a girder 24m long. What is the maximum bending moment at a section 8m from the right end in a simply supported girders?
The staff reading taken on a staff held at 200m from the instrument. The division of bubble tube is 2.5mm. Following observations were made.
The radius of curvature of bubble will be ________m
Vertical reaction developed at B in frame below due to applied load of 100 kN (with is
The maximum permissible deflection for a gantry girder, spanning over 6 m, on which an EOT (electric overhead travelling) crane of capacity 200 kN is operating, is
Maximum vertical deflection of Gantry girder for EOT of capacity less than 500KN is ( L/750), where L in mm
For EOT having capacity more then 500KN deflection is (L/1000) and for manually operated crane Deflection is (L/500)
A rectangular link AB made of steel is used to support a load W through a road CD as shown in the figure. If the link AB is 30mm wide, determine its thickness for a factor of safety 2.5. The ultimate strength of steel may be assumed to be 450 MPa.
Drawing Free body diagram
An RCC beam of size 350mm (width) and 600mm (overall depth) is subjected to shear force of 100 kN, bending moment of 200 kNm and twisting moment of 50 kNm. Effective cover to reinforcement is 25 mm. Find the equivalent bending moment which is contributed by torsional moment?
Here we have to calculate the equivalent bending moment contributed by torsional moment.
If the statically indeterminate beam as shown in the figure below, carries a load P at Q and a load nP at S. What is the value of n to make the structure collapse with at least 3 hinges?
For atleast 3 hinges to form PR and RS span should collapse simultaneously.For PR span
The length of runway at sea level, standard atmosphere condition and zero gradient is 1500m. The airport site has an elevation of 1200m and the reference temperature asIt is proposed to construct a runway at an effective gradient of 2%. Find the actual runway length at the site:
On sag (or valley) curves the available sight distance is determined based on:
Driver can see the obstacles or vehicle which moves at either side of curvature & reduce the accident.
A rectangular concrete beam of width 150mm and depth 200m is prestressed by pretensioning to a force of 200 kN at eccentricity of 30mm. The cross sectional area of prestressing steel is 200mm2 . Given Ec = 3 x 104 MPa and Est = 2 x 105 MPa. The percentage loss of stress in the prestressing steel due to elastic deformation of concrete is:
P = 200 kN
E = 30mm
A = 150mm × 200mm
Stress in concrete at the level of steel bar
A portion of an embankment having a uniform up-gradient 1 in 500 is circular with radius 1000 m of the centre line. It subtends 180° at the centre. If the height of the bank is 1 m at the lower end, and side slopes 2:1, the earth work involved.
For 2:1 slope top radius is 500m, and we have bottom radius is 1000m.
Volume of truncated cone is 3.14*h*((R*R) + (r*r) + (R*r))*(1/3).
= 3.14*1**((1000*1000) + (500*500) + (1000*500))*(1/3).
The value of bearing capacity factor for cohesion, Nc, for piles as per Meyerhof, is taken as:
Meyehoff bearing capacity factors for cohesive clays (phi=0) are
Nc = 5.14; Nq = 1; Ny = 0
If ,Find the value of
A trapezoidal channel with side slope of 450 is to be designed to convey a discharge of 9 m3/sec at a velocity of 1.5 m/s such that the amount of concrete lining for the bed and side is minimum. The area of lining required per meter length of channel will be?
A man of mass m is standing on a platform of mass M kept on a smooth ice. If the man starts moving on the platform with a speed v relative to the platform, with what velocity relative to the ice does the platform recoil?
v = w + V
Taking the platform and man to be a system, there is no external horizontal force on the system. The linear momentum of the system is constant.
0 = MV – mw
MV = m (v-V)
A 40 year flood data at a point on a river yielded and a standard deviation of 750 For what discharge would the structure be designed to provide 90% assurance that the structure would not fail in next 60 years.
Assurance = 90%
Risk = 10%
The left canal of tank irrigation carries a discharge of 10 cumecs and a culturable commanded area of 9000 Ha. The intensity of irrigation of Rabi crop is 70 percent and base period is 120 days. The right canal scheme carries a discharge of 24 cumecs and has a culturable commanded area of 1500 Ha. The intensity of Rabi crop is 80 percent and base period is 120 days.
Since left canal has more duty, hence left canal is more efficient than right canal
A straight line AC of length 2000m is required to be set out at right angles to a given line AB. This is done by travelling from A towards C. The observations are as follows:
Compute the necessary length of FC.