**Quiz: Civil EngineeringExam: GATETopic: Miscellaneous**

**Each question carries 1 markNegative marking: 1/3 markTime: 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)