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# Quiz: Civil Engineering 10 May 2021

Quiz: Civil Engineering
Exam: GATE
Topic: Miscellaneous

Each question carries 1 mark
Negative marking: 1/3 mark
Time: 20 Minutes

Q1. A plan of an area drawn with the original scale of 1 cm = 10 m, the shrunk such that a line, originally 15 cm long on the plan, measures now 14.5 cm. the shrunk scale is given by 1 cm equal to:
(a) 10.34 m
(b) 10.97m
(c) 0.97 m
(d) 9.70 m

Q2. The maximum diameter that a capillary tube can have to ensure that a capillary rise of at least 6 mm is achieved when the tube is dipped into a body of liquid with surface tension = 0.08 N/m and density = 900 kg/m³, is-
(a) 3 mm
(b) 6 mm
(c) 5 mm
(d) 8 mm

Q3. As per IS 456 : 2000, using working stress method, the modular ratio of M25 grade of concrete for permissible compressive strength due to bending in concrete σ_cbc = 8.5 MPa is:
(a) 15.63
(b) 14.939
(c) 12.04
(d) 10.98

Q4. A certain crop is grown in an area of 3000 hectares which is fed by a canal system. The data pertaining to irrigation is as follows:
1. field capacity of soil = 29%
2. optimum moisture = 17%
3. effective depth of root zone = 80 cm
4. relative density of soil = 1.302
if the frequency of irrigation is 10 days and permanent wilting point = 10%, then find the daily consumptive use.
(a) 1.25 cm
(b) 125 cm
(c) 0.125 cm
(d) 12.5 cm

Q5. What will be the unit weight of a fully saturated soil sample having water content of 38% and grain specific gravity of 2.65?
(a) 19.88 kN/m³
(b) 17.88 kN/m³
(c) 16.52 kN/m³
(d) 14.65 kN/m³

Q6. The figure (all dimensions are in mm) below shows an I-section of the beam. The shear stress at point P (very close to the bottom of the flange) is 12 MPa. The stress at point Q in the web (very close to the flange) is

(a) Indeterminable due to incomplete data
(b) 60 MPa
(c) 18 MPa
(d) 12 MPa

Q7. On a standard road braking test, a vehicle travelling at a speed of 10m/s was stopped by applying full brakes and the skid marks were observed for a length of 10m. what is the skid resistance of this pavement surface, assuming gravitational acceleration to be 10 m/s²?
(a) 0.50
(b) 0.60
(c) 0.70
(d) 0.80

Q8. The true and magnetic bearing of a line are 78° 45’ and 75° 30’ respectively. What is the magnetic declination for these pair of readings?
(a) 3° 15’ North
(b) 11° 15’ East
(c) 3° 15’ East
(d) 3° 15’ West

Q9. The degree of static indeterminacy D_S, and the degree of kinematic indeterminacy D_k, for the plane frame shown below, assuming axial deformations to be negligible, are given by

(a) D_S=6 and D_k=6
(b) D_S=6 and D_k=11
(c) D_S=4 and D_k=4
(d) D_S=4 and D_k=6

Q10. A volume of 3.0 × 10^6 m³ of groundwater was pumped out from an unconfined aquifer uniformly from an area of 5 km². the pumping lowered the water table from initial level of 102 m to 99 m. the specific yield of the aquifer is
(a) 0.20
(b) 0.30
(c) 0.40
(d) 0.50

Solutions

S1. Ans.(a)
Sol. Original scale (S) ⇒ 1 cm = 10 m ⇒ 1/1000
Shrinkage factor (S.F) = (Shrunk length)/(Original length )
=14.5/15
▭(S.F.=0.96666)
Revised or shrunk scale (S.S) = Original sale (S) × Shrinkage factor (S.F)
=1/1000×0.96666
=1/1034.5
1 cm=1034.5 cm
▭(1cm=10.345m)

S2. Ans.(b)
Sol. Given,
Capillary rise (h) = 6mm = 6 × 10^(-3)m.
Surface tension (σ) = 0.08 N/m
Density (ρ) = 900 kg/m³
diameter of tube (d) = ?
We know
Capillary rise (h) = 4σcosθ/ρgd
6×10^(-3)=(4×0.08)/(900×9.81×d) (∵θ=0°)
d = 0.006m
▭(d=6mm)

S3. Ans.(d)
Sol. Given, σ_cbc= Permissible stress due to bending = 8.5 MPa
Modular ratio (m) =?
In WSM,
m=280/(3 σ_cbc )
=280/(3×8.5)
▭(m=10.98 )

S4. Ans.(a)
Sol. FC=29%=0.29
OMC = 17% = 0.17
d = 80 cm.
y_d=1.302 gm\/cc
y_w=1 gm\/cc
Consumptive use (c_u )= ?
Depth of water required (d’) = y_d/y_w ×d [FC-OMC]
=1.302/7×80 [0.29-0.17]
▭(d^’=12.49≈12.5 cm.)
C_u=d^’/frequency
=12.5/10
▭(C_u=1.25 cm.)

S5. Ans.(b)
Sol. Given,
w=38%=0.38
G=2.65
γ_sat= ?
S=1 (Fully Saturated Soil)
We know,
Se=wG
1×e=0.38×2.65
▭(e=1.007)
Now,
γ_sat=((G+e) γ_w)/((1+e) )
=((2.65+1.007)×9.81)/((1+1.007) )
▭(γ_sat=17.88 kN\/m^3 )

S6. Ans.(b)
Sol. Given,
τ_1=12 MPa,B_1=100 mm,B_2=20 mm τ_2= ?
We know,
τ α 1/B
τ_1 B_1=τ_2 B_2
12×100=τ_2×20
▭(τ_2=60 MPa)

S7. Ans.(a)
Sol. Given,
Breaking distance = 10m
Speed (v) = 10m/sec
g = 10 m/sec²
f = ?
breaking distance = v^2/2gf
10=(10)^2/(2×10×f)
▭(f=0.5)

S8. Ans.(c)
Sol.

Given,
True bearing of line (T.B.) = 78°45’
Magnetic bearing of line (M.B.) = 75°30’
Magnetic Declination (δ) = ?
δ=(T.B.)-(M.B.)
=78°45^’-75°30^’
▭(δ=3°15^’ East)
→ Declination is positive then it will be in East.

S9. Ans.(d)
Sol. Degree of static indeterminacy (Ds)
▭(D_S=3m+r_e-3 j-r_r )
m = Total no. of member = 5
r_e = Total no. of external reaction = 3+2+2
= 7
j = total no. of joints = 6
r_r = Internal hinged reaction = 0
D_s=(3×5)+7-3×6=0
▭(D_s=4 )
Degree of kinematic indeterminacy (D_k )
▭(D_S=3j+r_e-m-r_r )
m = 5
D_k = (3×6)- 7 – 5 + 0
= 18 -12
▭(D_k=6)

S10. Ans.(a)
Sol. Specific yield (S_Y )=(Volume of water drained out to the aquifer)/(Total volume of aquifer)
=(3×10^6)/(5×10^6×(102-99) )
▭(S_Y=0.20)

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