βThe team ______ more than 300 runs in 20 overs ___________ rains. However, some players needed to improve their batting skills.β Choose the option with the correct sequence of words to fill the blanks.
a.
score; despite
b.
scoring; instead of
c.
scored; despite
Correct Answer
d.
scoring; in spite of
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Q2mcq
If a positive real $x$ satisfies the following equation
log 2 $x$ + log $x$ = 48,
$\sqrt{2}$ then the value of $x$ is _________________
a.
2 16
Correct Answer
b.
4 16
c.
2 14
d.
4 14
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Q3mcq
The next figure (indicated by β?β) in the sequence is
a.
Correct Answer
b.
c.
d.
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Q4mcq
βAll the mangoes in the basket are good.β If the above statement is false, then which one of the following statements is necessarily true?
a.
All the mangoes in the basket are not good.
b.
No mango in the basket is good.
c.
In the basket, some of the mangoes are good and some are not good.
d.
There exists at least one mango in the basket that is not good.
Correct Answer
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Q5mcq
Consider the following statements about four numbers: (S1) The average of the four numbers is 25 (S2) Each number is at most 40 (S3) Each number is at least 20 Choose the option that is necessarily correct.
a.
(S1) and (S2) together imply (S3)
b.
(S2) and (S3) together imply (S1)
c.
(S1) and (S3) together imply (S2)
Correct Answer
d.
(S1) implies (S3)
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Q6mcq
βPeople are crowding around ___ pit into which ___ elephant has fallen. I have never seen an elephant looking more bewildered ___ miserable. Here it is in a most undignified position, thrust into a pit and made to look up ___ a vast, curiosity-stricken crowd.β Choose the option with the correct sequence of words to fill the blanks.
a.
an; a; at; and
b.
a; an; and; at
Correct Answer
c.
and; a; an; at
d.
at; a; an; and
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Q7mcq
The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The following observations were made: (i) The quantity of S sold was twice that of T. (ii) The quantity of R sold was thrice that of T. (iii) The quantity of Q sold was four times that of T. Product P Q R S T Unit selling price (Rs.) 100 50 40 60 60 What is the quantity of product P sold on that day?
a.
40
b.
50
Correct Answer
c.
60
d.
70
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Q8mcq
Consider a string P of length $l$ that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length $x$ they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of $x/l$ is __________
a.
$Ο$
b.
$Ο-1$ $2Ο$ $Ο$
c.
$2(Ο-1)$
Correct Answer
d.
$Ο$ $Ο-1$
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Q9mcq
The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels. They are seated in rows and columns as shown in the figure with exactly one person sitting in each box. It is known that (i) Meritoriusβ daughter and his brother are seated in the same column. (ii) His son is seated diagonally across the sibling of the worst orator. (iii) The best and worst orators are seated in the same row. Who is the best orator?
a.
Meritorius
b.
Meritoriusβ brother
Correct Answer
c.
Meritoriusβ son
d.
Meritoriusβ daughter
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Q10mcq
Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?
a.
P
b.
Q
Correct Answer
c.
R
d.
S
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A fifth-degree polynomial in $x$ is defined for $x$ > 0. All coefficients of the polynomial are positive. The first derivative of the polynomial is obtained numerically at a point by using the first-order forward as well as the first-order backward difference methods. Identical step lengths are used for both the methods. Following statements are made. (I) Forward difference method underestimates the true derivative. (II) Backward difference method overestimates the true derivative. Which one of the following options is CORRECT?
a.
Both statements (I) and (II) are FALSE.
b.
Both statements (I) and (II) are TRUE.
c.
Statement (I) is TRUE and statement (II) is FALSE.
d.
Statement (I) is FALSE and statement (II) is TRUE.
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Periodic function $f(x)$ is given below. $f(x)$ = { }; $f(x$ + $2Ο)$ = $f(x)$
-1, when $-Ο <x$ <0
1, when $0<x<Ο$ The CORRECT option representing the Fourier series expansion of $f(x)$ is:
A rectangular singly reinforced concrete beam has a width of 300 mm and an effective depth of 550 mm. The grades of steel and concrete are Fe500 and M25, respectively. The area of steel in tension is 1963 mm 2. The depth of neutral axis is 302 mm. The ratio of the limiting depth of the neutral axis $(x u,max$) to the effective depth (d) of the beam is 0.456. The most probable mode of failure of the beam is
a.
compression failure
b.
bond failure
c.
shear failure
d.
ductile failure
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As per IS:800-2007, design of a cantilever steel beam section for its moment capacity requires fulfilment of an upper bound, expressed as:
$M d \le 1.5Z e y$
$f$
$Ξ³ m0$ The reason for such upper bound is to
a.
control deflection
b.
restrain lateral-torsional buckling
c.
avoid plastic deformation under working load
d.
avoid yielding at ultimate load
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The horizontal beam shown in the figure has fixed supports at F and L. Internal hinges are provided at locations G and J. The beam supports vertically downward concentrated loads as well as uniformly distributed loads, as shown in the figure.
(Figure not to scale) The upward vertical reaction (in kN) at the support L is
a.
23
b.
33
c.
43
d.
58
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The Culturable Command Area (CCA) for a canal is 10000 hectares. The base period for a crop in the CCA is 140 days. Watering depth for the crop is 40 cm. The outlet discharge (in m 3 /s) lies between
a.
3 and 4
b.
13 and 14
c.
23 and 24
d.
33 and 34
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Following statements are made with respect to the mass curve of rainfall: (I) Slope at a point on the curve can be positive. (II) Slope at a point on the curve can be zero. Which one of the following options is CORRECT?
a.
Both statements (I) and (II) are TRUE.
b.
Both statements (I) and (II) are FALSE.
c.
Statement (I) is TRUE and statement (II) is FALSE.
d.
Statement (I) is FALSE and statement (II) is TRUE.
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Information related to foundation design is provided in table below.
Column 1 Column 2 (I) Converse-Labarre formula (P) Pile capacity from dynamic formula (II) Hiley formula (Q) Pile group efficiency (III) Newmarkβs influence chart (R) Bearing capacity factor of saturated
clay (IV) Skemptonβs equation (S) Increase in vertical stress below footing Option giving the CORRECT match between Column 1 and Column 2 is:
An incident occurred on one side of a median on a four-lane dual carriageway road section. This incident disrupted the traffic movement in one direction. Traffic police diverted the traffic from disrupted side to the other side through an opening in a median. The desired sight distance on the four-lane dual carriageway was kept as 360 m under normal conditions. The Stopping Sight Distance (SSD, in m), which should be available on the operating road section after the incident, is
a.
360
b.
240
c.
180
d.
720
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Column I presents common air pollutants, and column II presents treatment technologies commonly employed to control air pollutants.
Air pollutant Treatment technology 1 Dust (size 5-25 Β΅m) P Cyclone separator 2 Carbon monoxide (CO) Q Wet lime-water scrubber 3 Sulfur dioxide (SO 2) R Electrostatic precipitator 4 Fly ash (size Λ 2.5 Β΅m) S Catalytic converter The option that CORRECTLY matches the air pollutant with its treatment technology is:
a.
1 $-$ P; 2 $-$ S; 3 $-$ Q; 4 $-$ R
b.
1 $-$ P; 2 $-$ R; 3 $-$ S; 4 $-$ Q
c.
1 $-$ R; 2 $-$ Q; 3 $-$ P; 4 $-$ S
d.
1 $-$ R; 2 $-$ Q; 3 $-$ S; 4 $-$ P
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One-third of the solid matter in a sludge containing 90 % water is composed of fixed mineral solids with specific gravity 2.5, and two-third is composed of volatile solids with specific gravity 1.0. Specific gravity of all solids lies between
a.
1.2 and 1.3
b.
1.5 and 1.6
c.
1.7 and 1.8
d.
2.0 and 2.1
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2 -3.5 6 The eigenvalues of $[A]$ = [ 3.5 5 2 ] are 8 1 8.5 $$ = $-1.547, $ = 12.330, and $$ = 4.711. 1 2 3 The absolute value of the determinant of matrix $A$ is ______ (rounded off to two decimal places).
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A fully saturated sandy soil deposit has water content 20 % and specific gravity 2.65. The critical hydraulic gradient for seepage through the soil to create the quicksand condition is _____________ (rounded off to two decimal places).
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A downgrade of 1 in 100 meets an upgrade of 1 in 125 on a road. If the rate of change of grade is 0.10 % per 30 m, the length (in m) of the vertical curve between the two grades is ______ (rounded off to the nearest integer).
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A tourist visiting a city holds a map prepared at a scale of 1:25000. The tourist measures the distance between place A and place B in the city as 12.0 cm on the map. Assuming both the places are connected by a straight road, the distance (in km) the tourist needs to walk from A to B is __________ (rounded off to the nearest integer).
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A simply supported, linearly elastic, homogeneous, prismatic beam of length L and flexural rigidity EI is shown in the figure.
$x$
B A
$ΞΈ B (x)$
L The expression for the Influence Line Diagram (ILD) of the rotation $ΞΈ B (x)$ at the support B is
a.
1 $(x$ 2 - $L$ 2) $6EI$
b.
1 $(x$ 3 - $L$ 2 $x)$ $6EIL$
c.
1 $(x$ 2 - $Lx)$ $3EI$
d.
1 $(x$ 3 - $L$ 2 $x)$ $3EIL$
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The plane truss shown in the figure is hinge-supported at E and F. The truss is subjected to vertical downward force at R and horizontal force at G.
(Figure not to scale) The force (in kN) along with its nature in member JF is
a.
$10\sqrt{2}$ compression
b.
$10\sqrt{2}$ tension
c.
$25\sqrt{2}$ compression
d.
$25\sqrt{2}$ tension
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Consider the following statements with respect to rigid pavements: Statement-1: Bottom-up cracking (BUC) in rigid pavements is caused at the edge
of the slab due to combined effect of single or tandem rear axle load
and positive temperature differential. Statement-2: Top-down fatigue cracking (TDC) in rigid pavements is caused due to
repeated cycles of axle loads and negative temperature differential. The CORRECT option is:
a.
Both statements are TRUE.
b.
Statement-1 is TRUE, but Statement-2 is FALSE.
c.
Statement-1 is FALSE, but Statement-2 is TRUE.
d.
Both statements are FALSE.
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For the traverse given below, the benchmark is at ground point L. The Reduced Level (RL) of L is 150.000 m. The direction of the traverse is from L to N. The readings on levelling staff using the same levelling instrument kept at Stations S1 and S2 during the traversing are shown in the figure.
Column 1 Column 2
(P) 3.300 m
(I)
Sum
of Back
Sights
(Q)
2.500
m
(II)
Sum
of Fore
Sights
(R)
150.300
m
(III)
RL
of Point
N
(S)
3.000
m
(T) 150.500 m Matching the information given under Column 1 and Column 2, which one of the following options is CORRECT?
a.
(I) $-$ (P); (II) $-$ (S); (III) $-$ (R)
b.
(I) $-$ (P); (II) $-$ (Q); (III) $-$ (R)
c.
(I) $-$ (S); (II) $-$ (P); (III) $-$ (T)
d.
(I) $-$ (S); (II) $-$ (Q); (III) $-$ (T)
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The 2.4 ml of raw sewage is diluted to 240 ml. The Dissolved Oxygen (DO) of the diluted sample at the beginning of Biochemical Oxygen Demand (BOD) test was 8 mg/l and it was 6 mg/l after 5-day incubation at 20 $$ C. The BOD 5 (in mg/l) of the raw sewage is
a.
200
b.
100
c.
250
d.
150
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Types of flood routing and methods are given in the table below.
Column
1
Type
of Flood
Routing
(P) Hydrologic
routing
(Q) Hydraulic routing (ii) Modified Pulβs method (R) Reservoir routing (iii) Method of Characteristics (S) Channel routing Option(s) giving the CORRECT match(es) between Column 1 and Column 2 is/are:
a.
(P) β (i); (Q) β (iii); (R) β (ii)
b.
(Q) β (i); (R) β (iii); (S) β (ii)
c.
(P) β (i); (R) β (ii); (S) β (i)
d.
(P) β (ii); (Q) β (iii); (R) β (ii)
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Consider differential equation + $xy$ = $x$ with the condition as y = 0 at x = 0.
$dx$ The value of y at x = 1.0 is ______ (rounded off to two decimal places). The age (in years) of a population is normally distributed with a mean of 36 and standard deviation of 12. The height (in cm) of the same population is also normally distributed with a mean of 160 and standard deviation of 10. If the probability of age greater than 50 years is equal to the probability of height greater than h, the value of h (in cm) is ______ (rounded off to two decimal places).
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A 250 mm wide $\times$ 600 mm deep rectangular concrete beam is prestressed by means of 4 high-tensile tendons, each of 14 mm diameter. The centre of the tendons is 200 mm from the soffit of the beam. The effective stress in each tendon is 700 N/mm 2. The maximum bending moment (in kN-m), that can be applied to the section without causing tension at the soffit of the beam due to prestressing only, is ______ (rounded off to one decimal place). Use $$ = 3.14
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A rigid-jointed portal frame, shown in the figure, consists of beam and columns of equal length L. The frame has a fixed support at one end and a roller support at the other end. The frame is subjected to a uniformly distributed load w and a lateral load P as shown in the figure. The plastic moment capacity of the beam and column sections is $M p$. Consider a combined beam-column mechanism for plastic collapse. By applying the virtual work equation corresponding to the combined plastic collapse mechanism, $M p$ is expressed as
$M$ = $C PL$ + $C wL$ 2
$p$ 1 2 where C 1 and C 2 are constants.
w per w/m unit length
P P
L
L L The value of (C 1 /C 2) is ______ (in integer).
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Linearly elastic, homogeneous, uniform bars BCD and FG shown in the figure have fixed supports at B and G, respectively. For both the bars, axial rigidity is 20000 kN. A gap of 2 mm exists between D and F prior to application of any load (i.e. P = 0). Small deformation and infinitesimal strain assumptions are valid for the given bars.
(Figure not to scale) The magnitude of the horizontal reaction (in kN) at B after application of the axial force P of 20 kN at C is ______ (rounded off to the nearest integer).
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A simply-supported rectangular reinforced concrete beam has a width 250 mm and an overall depth 600 mm. The effective span of the beam is 6.23 m. The beam carries a live load of 5 kN/m and super imposed dead load of 5 kN/m, in addition to its own weight. The unit weight of reinforced concrete is 25 kN/m 3. Consider the load factor of 1.5 for all stated loads. The design bending moment (in kN-m) for the limit state of collapse is ______ (rounded off to two decimal places).
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Width (in m) of a rectangular channel required to carry a discharge of 96 m 3 /s at a critical depth of 9.8 m is _____ (rounded off to two decimal places). Use acceleration due to gravity = 9.8 m/s 2
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The cross section of a 0.5 m wide vertical gate holding water and oil is shown in the figure. The unit weights of water and oil are 10 kN/m 3 and 7.5 kN/m 3, respectively.
(Figure not to scale) The horizontal hydrostatic force (in kN) acting on the vertical gate is _________ (rounded off to two decimal places).
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A centrifugal pump is delivering water from an underground tank to an overhead reservoir against a static head of 35 m through a 2 km long, 250 mm diameter pipe. The head-discharge characteristic of the pump is given by
$H$ = 140 - $9000Q$ 2 where $H$ is the head (in m) generated by the pump and $Q$ is the discharge (in m 3 /s) of the pump. Neglecting all minor losses, the head (in m) generated by the pump is ______ (rounded off to the nearest integer). Use: Darcy-Weisbach friction factor f = 0.04 Acceleration due to gravity = 9.81 m/s 2 $$ = 3.14
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The flow depth for a discharge of 10 m 3 /s in a wide rectangular channel is 2.0 m. Assume that the flow is uniform. If the discharge is doubled, the flow depth (in m) in this channel is _________ (rounded off to two decimal places).
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For a clayey soil stratum, the time required for degree of consolidation from 25 % to 50 % is 30 days. The total time (in days) required for 90 % degree of consolidation of the same soil stratum is ______ (rounded off to the nearest integer).
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The ultimate bearing capacity of a 1 m wide strip footing is 532.80 kPa, when it is embedded at 1 m depth in dry cohesionless soil. The soil has a unit weight of 18 kN/m 3. The ultimate bearing capacity is 864 kPa when the depth of embedment becomes 2 m. Neglecting the effect of the depth factor, the bearing capacity factor N q is ______ (rounded off to one decimal place).
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A building is proposed in an area having thick deposit of silty clay. The water table is at the ground surface. The saturated unit weight of soil is 18 kN/m 3 and unit weight of water is 10 kN/m 3. The maximum vertical load (P) on a column of the proposed building is 2000 kN. Consider $Ο z \le$ 0.1 $Ο vβ²$ for computation of the minimum depth of soil exploration. $Ο vβ²$ is the effective vertical overburden stress. $Ο$ is the increase in the vertical stress
$z$ at depth z below load P as per the Boussinesqβs stress theory. Based on above, the minimum depth (in m) of soil exploration required for the foundation design is ________ (rounded off to two decimal places).
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A soil sample has following properties: Natural water content = 30 % Plasticity index = 40 % Liquidity index = 50 % The estimated plastic limit (in %) of the soil is ________ (rounded off to one decimal place).
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For a given traffic stream, the speed-density relationship is given as:
$k j v$ = $v$ ln
$o$ () $k$ where $v$ is the mean speed (in km/h), and $k$ is the density (in veh/km). Considering $v o$ as 45 km/h, and $k j$ as 200 veh/km, the maximum flow (in veh/h) for the given stream is __________ (rounded off to the nearest integer).
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A vertical curve is formed by a descending gradient of 1 in 40 meeting an ascending gradient of 1 in 50. Consider the following: Stopping Sight Distance (SSD) = 90 m Height of headlight of a vehicle above the road surface = 0.75 m Headlight beam angle with respect to the longitudinal axis of the vehicle = 1.2 o Based on the sight distance criteria, the design length (in m) of the vertical curve is __________ (rounded off to the nearest integer).
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The analysis of major cations and anions in a water sample collected from a cityβs water supply is given below. Ions present in minor concentrations are not given.
Anions
$Cl$ -
$SO$ 42-
$HCO$
$CO$
Concentration
1.5
0.5
1.0
0.01
Cations
Na +
Ca
Mg
K
Concentration
2
0.5
0.25
0.02
β $H$ +
= -3
$H$ 2 $SO$ 42- β $2H$ + + $SO$ 42- $pK$ = -3 $H$ 2 $CO$ 3 β $H$ + + $HCO$ 3- $pK$ = 6.3 $HCO$ 3- β $H$ + + $CO$ 32- $pK$ = 10.3 $HOCl$ β $H$ + + $OCl$ - $pK$ = 7.5 $HOCl$ (in %) present in the total free chlorine in the water is _____ (rounded off to the nearest integer).
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Anaerobic bacteria are being utilized for the destruction of biodegradable organic content of wastewater measured in terms of Chemical Oxygen Demand (COD). The yield coefficient (Y) is 0.06 gram Volatile Suspended Solids (VSS) per gram of COD. Bacterial biomass forms the sludge during the process. The proximate chemical formula of anaerobic bacteria is C 6 H 7 NO 2. The COD (in %) converted into bacterial biomass is ______ (rounded off to the nearest integer).
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In an industry, a cyclone collector with 80 % efficiency is installed for air purification, followed by an electrostatic precipitator with 50 % efficiency. The concentration of particles entering the cyclone collector is 10 mg/m 3. The concentration (in mg/m 3) of particles exiting the precipitator is __________ (rounded off to two decimal places).
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