1. science
2. physics
3. optics

Civil Engineering – Exercise 1
1.
There is no value of x that can simultaneously satisfy both the given
equations. Therefore, find the ‘least squares error’ solution to the two
equations, i.e., find the value of x that minimizes the sum of squares
of the errors in the two equations ______________
2x = 3
2.
4x = 1
What is the minimum number of multiplications involved in
computing the matrix product PQR? Matrix P has 4 rows and 2
columns, matrix Q has 2 rows and 4 columns, and matrix R has 4
rows and 1 column. __________
3.
A 1-h rainfall of 10 cm magnitude at a station has a return period of
50 years. The probability that a 1-h rainfall of magnitude 10 cm or
more will occur in each of two successive years is:
a. 0.04
4.
b. 0.2
c. 0.02
d. 0.0004
Maximum possible value of Compacting Factor for fresh (green)
concrete is:
a. 0.5
5.
b. 1.0
c. 1.5
d. 2.0
As per IS 800:2007, the cross-section in which the extreme fiber can
reach the yield stress, but cannot develop the plastic moment of
resistance due to failure by local buckling is classified as
a. plastic section
c. semi-compact section
b. compact section
d. slender section
6.
The creep strains are
a. caused due to dead loads only
b. caused due to live loads only
c. caused due to cyclic loads only
d. independent of loads
7.
As per IS 456:2000 for M20 grade concrete and plain barsin tension
the design bond stress πbd = 1.2 MPq. Further, IS 456:2000 permits
this design bond stress value to be increased by 60% for HSD bars.
The stress in the HS D reinforcing steel basin tension σS = 360MPa.
Find the required development length, Ld, for HSD basin terms of the
bar diameter, φ. __________
8.
The ‘plane section remains plane’ assumption in bending theory
implies:
a. strain profile is linear
b. stress profile is linear
c. both strain and stress profiles are linear
d. shear deformations are neglected
9.
Two steel columns P (length L and yield strength fy = 250 MPa) and Q
(length 2L and yield strength fy = 500 MPa) have the same crosssections and end-conditions. The ratio of buckling load of column P
to that of column Q is:
a. 0.5
b. 1.0
c. 2.0
d. 4.0
10.
T pin-jo
The
ointed 2-D
D truss is loaded
l
wiith a horizzontal forcce of 15 kN
N at
jo
oint S and
d another 15 kN verrtical forcce at jointt U, as sho
own. Find
d the
fo
orce in member RS
S (in kN) and
a reporrt your an
nswer takiing tension as
p
positive
an
nd compreession as negative.
n
_______
____
11.
A symmetrric I-sectiion (with width of each
e
flang
ge = 50 mm,
m thickn
ness
o each fla
of
ange = 10
0 mm, dep
pth of weeb = 100 mm, and
d thicknesss of
w = 10 mm)
web
m of steeel is subjected to a sheer forrce of 100
0 kN. Find
d the
m
magnitude
e of the sh
hear stresss (in N/m
mm2) in the
t web at
a its juncction
w the to
with
op flange. _______
____
12.
In
n its natu
ural condiition, a so
oil samplee has a mass
m
of 1.9
980 kg an
nd a
v
volume
off 0.001 m3. After being com
mpletely dried in an oven, the
m
mass
of th
he sample is 1.800 kg. Speciific gravityy G is 2.7
7. Unit weeight
o water is 10 kN/m
of
m3. The deg
gree of satturation of
o the soil is:
a 0.65
a.
b. 0.7
70
c. 0.54
4
d. 0.61
13.
The ratio Nf/Nd is known as shape factor, where Nf is the number of
flow lines and Nd is the number of equipotential drops. Flow net is
always drawn with a constant b/a ratio, where b and a are distances
between two consecutive flow lines and equipotential lines,
respectively. Assuming that b/a ratio remains the same, the shape
factor of a flow net will change if the
a. upstream and downstream heads are interchanged
b. soil in the flow space is changed
c. dimensions of the flow space are changed
d. head difference causing the flow is changed
14.
Following statements are made on compacted soils, wherein DS
stands for the soils compacted on dry side of optimum moisture
content and WS stands for the soils compacted on wet side of
optimum moisture content. Identify the incorrect statement.
a. Soil structure is flocculated on DS and dispersed on WS.
b. Construction pore water pressure is low on DS and high on WS.
c. On drying, shrinkage is high on DS and low on WS.
d. On access to water, swelling is high on DS and low on WS.
15.
Four columns of a building are to be located within a plot size of 10 m
x 10 m. The expected load on each column is 4000 kN. Allowable
bearing capacity of the soil deposit is 100 kN/m2. The type of
foundation best suited is
a. isolated footing
b. raft foundation
c. pile foundation
16.
d. combined footing
For subcritical flow in an open channel, the control section for
gradually varied flow profiles is
a. at the downstream end
b. at the upstream end
c. at both upstream and downstream ends
d. at any intermediate section
17.
Group-I contains dimensionless parameters and Group- II contains
the ratios.
Group-I
Group -II
P. Mach Number
1. Ratio of inertial force and gravitational force
Q. Reynolds Number
2. Ratio of fluid velocity and velocity of sound
R. Weber Number
3. Ratio of inertial force and viscous
force
S. Froude Number
4. Ratio of inertial force and surface
tension force
The correct match of dimensionless parameters in Group- I with
ratios in Group-II is:
a. P-3, Q-2, R-4, S-1
b. P-3, Q-4, R-2, S-1
c. P-2, Q-3, R-4, S-1
d. P-1, Q-3, R-2, S-4
18.
For a two dimensional flow field, the stream function ψ is given as
3
ψ = ( y 2 − x 2 ) . The magnitude of discharge occurring between the
2
stream lines passing through points (0, 3) and (3, 4) is:
a. 6
19.
20.
b. 3
c. 1.5
d. 2
An isohyet is a line joining points of
a. equal temperature
b. equal humidity
c. equal rainfall depth
d. equal evaporation
Some of the water quality parameters are measured by titrating a
water sample with a titrant. Group-I gives a list of parameters and
Group-II gives the list of titrants.
Group-I
Group-II
P.Alkalinity
1. N/35.5 AgNO3
Q. Hardness
2. N/40 Na2S2O3
R. Chloride
3. N/50 H2SO4
S. Dissolved oxygen
4. N/50 EDTA
The correct match of water quality parameters in Group-I with
titrants in Group-II is:
a. P-1, Q-2, R-3, S-4
b. P-3, Q-4, R-1, S-2
c. P-2, Q-1, R-4, S-3
d. P-4, Q-3, R-2, S-1
21.
A water treatment plant is designed to treat 1 m3/s of raw water. It
has 14 sand filters. Surface area of each filter is 50 m2. What is the
loading rate (in
m3
) with two filters out of service for routine
day ⋅ m2
backwashing? __________
22.
Select the strength parameter of concrete used in design of plain
jointed cement concrete pavements from the following choices:
a. Tensile strength
c. Flexural strength
23.
b. Compressive strength
d. Shear strength
It was observed that 150 vehicles crossed a particular location of a
highway in duration of 30 minutes. Assuming that vehicle arrival
follows a negative exponential distribution, find out the number of
time headways greater than 5 seconds in the above observation?
__________
24.
For two major roads with divided carriageway crossing at right angle,
a full clover leaf interchange with four indirect ramps is provided.
Following statements are made on turning movements of vehicles to
all directions from both roads. Identify the correct statement:
a. Merging from left is possible, but diverging to left is not possible.
b. Both merging from left and diverging to left are possible.
c. Merging from left is not possible, but diverging to left is possible.
d. Neither merging from left nor diverging to left is possible.
25.
The latitude and departure of a line AB are +78 m and -45.1 m,
respectively. The whole circle bearing of the line AB is:
a. 30°
b. 150°
c. 210°
d. 330°
Q. 26 to Q. 55 carry two marks each.
26.
The state of 2D-stress at a point is given by the following matrix of
stresses:
⎡ σ xx
⎢σ
⎣ xy
σ xy ⎤ ⎡100 30 ⎤
=
MPa
σ yy ⎥⎦ ⎢⎣ 30 20 ⎥⎦
What is the magnitude of maximum shear stress in MPa?
a. 50
27.
b. 75
c. 100
d. 110
Find the magnitude of the error (correct to two decimal places) in the
estimation of following integral using Simpson’s
1
Rule. Take the
3
step length as 1. __________
4
∫ (x
4
+ 10)dx
0
π /6
28.
The solution for
∫ cos
4
3θ sin 3 6θ d θ is :
0
a. 0
b.
1
15
c. 1
d.
8
3
29.
F
Find
the value
v
of λ such tha
at the funcction f (x) is a valiid probab
bility
d
density
fun
nction. __
_______
___
30.
f ( x) = λ( x − 1)(2 − x)
for1 ≤ x ≤ 2
=0
otherw
wise
L
Laplace
eq
quation for water flo
ow in soils is given below.
∂2H ∂2H ∂2H
+ 2 + 2 =0
∂x 2
∂y
∂z
H
Head
H do
oes not va
ary in y an
nd z directtions.
B
Boundary
condition
ns are: at x = 0, H = 5; and
ddH
= −1
d
dx
W
What
is the value off H at x = 1.2? ____
_______
_
31.
A membeers in the rigid-join
All
nted frame shown are
a prismatic and have
h
th
he same flexural stiffness
s
E Find the magn
EI.
nitude off the bend
ding
m
moment
att Q (in kN
Nm) due to
o the given loading. ______
_____
32.
A uniform
m beam (E
EI = consttant)PQ in
n the form
m of a qua
arter-circlle of
ra
adius R is fixed att end P an
nd free att the end Q, wheree a load W is
a
applied
ass shown. The vertical down
nward dissplacemen
nt, δq, at the
⎛ WR
R3 ⎞
lo
oaded poiint Q is giiven by: δq = β ⎜
⎟ . Find the valuee of β (corrrect
EI
I
⎝
⎠
to
o 4-decim
mal places)). ______
_____
33.
A uniform
m beam weeighing 18
800 N is supporteed at E an
nd F by cable
A
ABCD.
Deetermine the tension (in N)
N in segm
ment AB of this cable
(ccorrect to
o 1-decima
al place). Assume the
t cabless ABCD, BE
B and CF to
b weightless.____
be
_______
34.
B
Beam
PQR
RS has internal hin
nges in sp
pans PQ and
a
RS ass shown. The
b
beam
mayy be subjjected to a movin
ng distrib
buted verrtical load
d of
m
maximum
intensityy 4 kN/m of
o any len
ngth anyw
where on th
he beam. The
m
maximum
absolute value of the
t sheer force (in kN)
k that can
c occur due
to
o this load
ding just to
t the righ
ht of supp
port Q sha
all be:
a 30
a.
35.
b. 40
c. 45
4
d. 55
5
A rectangu
ular concrrete beam
m 250 mm
m wide and
d 600 mm
m deep is prep
sttressed byy means of 16 high
h tensile wires, ea
ach of 7 mm
m diameeter,
lo
ocated att200 mm from th
he bottom
m face of the beam
m at a giiven
section. If the effecttive pre-sttress in th
he wires is700 MPa
a, what iss the
m
maximum
sagging bending moment
m
(in kNm)) (correct to 1-deciimal
p
place)
duee to live load
l
that this sectiion of thee beam can withsttand
w
without
ca
ausing ten
nsile stresss at the bo
ottom facee of the beeam? Neg
glect
th
he effect of
o dead load of beam
m._____
______
36.
T soil prrofile belo
The
ow a lake with watter level at
a elevatio
on = 0 m and
la
ake bottom
m at eleva
ation = -10
0 m is sho
own in the figure, where
w
k iss the
p
permeabili
ity coefficcient. A piezomete
p
er (stand pipe) insstalled in the
sand layerr shows a reading
g of +10 m elevattion. Assu
ume that the
p
piezometri
ic head iss uniform in the sa
and layer. The quan
ntity of water
w
(iin m3/s) flowing in
nto the la
ake from the sand layer thrrough thee silt
la
ayer per unit
u area of
o the lakee bed is:
37.
–
a 1.5 × 10–6
a.
b. 20
2 × 10–6
–
c 1.0 × 10–6
c.
d. 0.5
0 × 10–6
T soil prrofile abovve the rocck surface for a 25° infinite sllope is sho
The
own
in
n the figu
ure, wheree su is the undraineed shear strength
s
a ψt is total
and
t
u weigh
unit
ht. The slip
p will occu
ur at a dep
pth of
a 8.83 m
a.
b. 9.79 m
c. 7.83
7
m
d. 6..53 m
38.
T
Two
differrent soil tyypes (Soill 1 and So
oil 2) are used
u
as ba
ackfill beh
hind
a retaining
g wall as shown
s
in the figurre, where ψt is totall unit weiight,
a
and
c' and
d φ' are effective
e
c
cohesion
a
and
effecctive anglee of shea
aring
reesistance.. The resu
ultant actiive earth force
f
per unit leng
gth (in kN
N/m)
a
acting
on the
t wall iss:
a 31.7
a.
39.
b. 35.2
c. 51.8
5
d. 57
7.0
A 2 km lo
ong pipe of 0.2 m diameter connectts two reservoirs. The
d
difference
between water levvels in thee reservoiirs is 8 m.
m The Da
arcyW
Weisbach
friction fa
actor of th
he pipe is 0.04. Acccounting for frictio
onal,
e
entry
and exit
e lossess, the velo
ocity in the pipe (in
n m/s) is:
a 0.63
a.
40.
b. 0.35
2
c. 2.52
d. 1.25
T norma
The
al depth in a wide rectangullar channeel is increeased by 10%.
1
T percen
The
ntage incrrease in th
he discharrge in the channel is:
a 20.1
a.
41.
b. 15.4
c. 10.5
7.2
d. 17
T transp
The
plantation
n of rice requires
r
10
0 days an
nd total deepth of water
w
reequired during
d
tra
ansplanta
ation is 48
4 cm. Du
uring tra
ansplantattion,
th
here is an
n effective rainfall (u
useful forr irrigation
n) of 8 cm
m. The dutty of
irrrigation water
w
(in hectares//cumec) iss:
a 612
a.
b. 216
d..
c. 300
108
42.
A settling tank in a water trreatment plant is designed
d
for a surrface
o
overflow
rate
r
of 30
m3
. Assum
me specificc gravity of sedim
ment
day ⋅ m2
p
particles
= 2.65, den
nsity of water
w
(ρ) = 1000 kg//m3, dyna
amic visco
osity
o water (μ) = 0.001
of
0
N.s/m2, an
nd Stokess’ law iss valid. The
a
approxima
ate minim
mum size of particcles that would be
b compleetely
reemoved iss:
a 0.01mm
a.
m
43.
b. 0.02 mm
m
c. 0.03
0
mm
d. 0..04 mm
A student began
b
exp
periment for
f determ
mination of
o 5-day, 20°C
2
BOD
D on
M
Monday.
Since
S
the 5th day felll on Saturrday, the final
f
DO readings
r
w
were
ta
aken on next
n
Mon
nday. On calculatio
on, BOD (i.e. 7 da
ay, 20°C) was
fo
ound to be
b 150 mg/L.
m
Wh
hat would
d be the 5-day, 20
0°C BOD
D (in
m
mg/L)?
Assume
A
v
value
of BOD ra
ate consttant (k) at stand
dard
teemperatu
ure of 20°C
C as 0.23//day (basee e). ____
_______
_
44.
E
Elevation
and
a temperature da
ata for a place
p
are tabulated
t
below:
B
Based
on the
t above data, lapsse rate can
n be referred as:
45.
a. Super-adiabatic
b. Neutral
c. Sub-adiabatic
d. Inversion
The percent voids in mineral aggregate (VMA) and percent air voids
(Vv) in a compacted cylindrical bituminous mix specimen are 15 and
4.5 respectively. The percent voids filled with bitumen (VFB) for this
specimen is:
a. 24
46.
b. 30
c. 54
d. 70
Following bearings are observed while traversing with a compass.
Line
Fore Bearing
Back Bearing
AB
126°45’
308°00’
BC
49°15’
227°30’
CD
340°30’
161°15’
DE
258°30’
78°30’
EA
212°30’
31°45’
After applying the correction due to local attraction, the corrected for
bearing of line BC will be:
a. 45°15´
47.
b. 50°15´
c. 49°15´
d. 48°15´
A. the odolite is set up at station A and a 3 m long staff is held
vertically at station B. The depression angle reading at 2.5 m marking
on the staffis 6°10´. The horizontal distance between A and B is 2200
m. Height of instrument at station A is 1.1 m and R.L. of A is 880.88
m Apply the
m.
t curvatture and refraction
n correctio
on, and determine
d
e the
R of B (iin m).___
R.L.
_______
__
Comm
mon Da
ata Ques
stions
Comm
mon Data
a for Que
estions 48
4 and 49
9:
A prop
pped canttilever ma
ade of a prismaticc steel beeam is su
ubjected to
t a
concen
ntrated loa
ad P at miid span ass shown.
48.
Iff load P = 80 kN, find the reaction R(in kN)) (correct to 1-deciimal
place)using elastic analysis.
p
a
_
_______
____
49.
Iff the mag
gnitude of load P is increassed till co
ollapse an
nd the pla
astic
m
moment
ca
arrying ca
apacity of steel beam
m section
n is 90 kNm
m, determ
mine
reeaction R(in kN) (correcct to 1-decimal place) using
u
pla
astic
a
analysis.__
_______
___
mon Data
a for Que
estions 50
5 and 511:
Comm
For a portion
p
off nationall highwayy where a descendiing gradieent of 1 in
n 25
meets with an ascending
a
g gradientt of 1 in 20, a vallley curvee needs to
o be
designed for a vehicle travelling at 90 kmph based on the following
conditions.
(i)
headlight sight distance equal to the stopping sight distance (SSD) of
a level terrain considering length of valley curve > SSD.
(ii)
comfort condition with allowable rate of change of centrifugal
acceleration = 0.5 m/sec3.
Assume total reaction time = 2.5 seconds; coefficient of longitudinal
friction of the pavement = 0.35; height of head light of the vehicle = 0.75 m;
and beam angle = 1°.
50.
What is the length of valley curve (in m) based on the head light sight
distance condition? __________
51.
What is the length of valley curve (in m)based on the comfort
condition? _________
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53:
A multistory building with a basement is to be constructed. The top 4 m
consists of loose silt, below which dense sand layer is present up to a great
depth. Ground water table is at the surface. The foundation consists of the
basement slab of 6 m width which will rest on the top of dense sand as
shown in the figure. For dense sand, saturated unit weight = 20 kN/m3, and
bearing capacity factors Nq = 40 and Nγ = 45. For loose silt, saturated unit
weight = 18 kN/m3, Nq = 15 and Nγ = 20. Effective cohesion c' is zero for
both so
oils. Unitt weight of
o water is 10 kN
N/m3. Neg
glect shap
pe factor and
depth factor.
f
Averag
ge elastic modulus E and Poisson’s
P
ratio μ of
o dense sand
s
is 60
6 ×
103kN//m2 and 0.3
0 respecttively.
52.
U
Using
facto
or of safety = 3, the net safee bearing capacity (in
( kN/m2) of
th
he founda
ation is:
a 610
a.
0
b. 320
c 983
c.
93
d. 69
53.
T found
The
dation slab
b is subjected to veertical dow
wnward stresses
s
eq
qual
to
o net saffe bearing
g capacityy derived
d in the above
a
queestion. Using
in
nfluence factor If = 2.0, and negllecting em
mbedmen
nt depth and
riigidity corrrections,, the immediate setttlement of
o the den
nse sand la
ayer
w be:
will
a 58 mm
a.
b. 111 mm
c. 126 mm
d. 17
79 mm
ment for Linked Answer
A
Question
ns 54 an
nd 55:
Statem
At a station, Storm I of 5 hour duration with intensity 2 cm/h resulted in a
runoff of 4 cm and Storm II of 8 hour duration resulted in a runoff of 8.4
cm. Assume that the φ-index is the same for both the storms.
54.
The φ-index (in cm/h) is:
a. 1.2
55.
b. 1.0
c. 1.6
d. 1.4
The intensity of storm II (in cm/h) is:
a. 2.00
b. 1.75
c. 1.50
d. 2.25
Key for Excerise1
Q.NO
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
KEY
0.5
16
D
B
C
A
46 to 47
A
D
0
780 to 72
C
C
C
C
A
C
B
C
B
143 to 145
C
Marks to
all
B
D
A
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
0.52 to
0.55
B
6
3.8
25
0.785 to
0.786
1310 to
1313
C
85.5
D
A
A
A
D
B
B
127 to 132
A
D
D
641.9 to
642.3
25
60
308 to 311
51.
52.
53.
106 to 107
Marks to
all
Marks to
all
54.
55.
A
D
Exercise 2
1.
⎛ x + sin x ⎞
lim ⎜
⎟ is equal to
x →∞
x
⎝
⎠
(A) – ∞
2.
(B) 0
(C) 1
(D) ∞
⎡3 2 1⎤
⎡1⎤
⎢
⎥
Given the matrices J = ⎢ 2 4 2⎥ and K = ⎢⎢ 2 ⎥⎥ , the product KT JK is
⎣⎢1 2 6 ⎥⎦
⎣⎢ −1⎦⎥
___________
3.
The probability density function of evaporation E on any day during a
year in a watershed is given by
⎧1
⎪ o ≤ E ≤ 5mm / day
f (E) = ⎨5
otherwise
⎪⎩0
The probability that E lies in between 2 and 4 mm/day in a day in the
watershed is (in decimal) _____________
4.
The sum of Eigen values of the matrix, [M] is