A square matrix B is skew-symmetric if

•  (A) B^T = -B
•  (B) B^T = B
•  (C) B^-1 = B
•  (D) B^-1 = B^T

For a scalar function f(x,y,z) = x² +3y² +2z², the gradient at the point P(1,2,-1) is

•  (A) $2\overrightarrow{i}+6\overrightarrow{j}+4\overrightarrow{k}$
•  (B) $2\overrightarrow{i}+12\overrightarrow{j}-4\overrightarrow{k}$
•  (C) $2\overrightarrow{i}+12\overrightarrow{j}+4\overrightarrow{k}$
•  (D) $\sqrt{56}$

The analytic function $f\left(z\right)=\frac{z-1}{z^2+1}$ has singularities at

•  (A) 1 and -1
•  (B) 1 and i
•  (C) 1 and -i
•  (D) i and -i

The analytic function $f\left(z\right)=\frac{z-1}{z^2+1}$ has singularities at

•  (A) 1 and -1
•  (B) 1 and i
•  (C) 1 and -i
•  (D) i and -i

A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed is

•  (A) 14 MPa
•  (B) 1.4 MPa
•  (C) 0.14 MPa
•  (D) 0.014 MPa

The modulus of rupture of concrete in terms of its characteristic cube compressive strength (f_ck) in MPa according to IS 456:2000 is

•  (A) 5000$f_{ck}$
•  (B) 0.7$f_{ck}$
•  (C) 5000$\sqrt{f_{ck}}$
•  (D) 0.7$\sqrt{f_{ck}}$

In the theory of plastic bending of beams, the ratio of plastic moment to yield moment is called

•  (A) shape factor
•  (B) plastic section modulus
•  (C) modulus of resilience
•  (D) rigidity modulus

For limit state of collapse, the partial safety factors recommended by IS 456:2000 for estimating the design strength of concrete and reinforcing steel are respectively

•  (A) 1.15 and 1.5
•  (B) 1.0 and 1.0
•  (C) 1.5 and 1.15
•  (D) 1.5 and 1.0

The point within the cross sectional plane of a beam through which the resultant of the external loading on the beam has to pass through to ensure pure bending without twisting of the cross-section of the beam is called

•  (A) moment centre
•  (B) centroid
•  (C) shear centre
•  (D) elastic centre

The square root of the ratio of moment of inertia of the cross section to its cross sectional area is called

•  (A) Second moment of area
•  (B) Slenderness ratio
•  (C) Section modulus
•  (D) Radius of gyration

Deposit with flocculated structure is formed when

•  (A) Clay particles settle on sea bed
•  (B) Clay particles settle on fresh water lake bed
•  (C) Sand particles settle on river bed
•  (D) Sand particles settle on sea bed

Dilatancy correction is required when a strata is

•  (A) Cohesive and saturated and also has N Value of SPT > 15
•  (B) Saturated silt/fine sand and N value of SPT < 10 after the overburden correction
•  (C) Saturated silt/fine sand and N value of SPT >15 after the overburden correction
•  (D) Coarse sand under dry condition and N value of SPT < 10 after the overburden correction

A precast concrete pile is driven with a 50 kN hammer falling through a height of 1.0 m with an efficiency of 0.6. The set value observed is 4 mm per blow and the combined temporary compression of the pile, cushion and the ground is 6 mm. As per Modified Hiley Formula, the ultimate resistance of the pile is

•  (A) 3000 kN
•  (B) 4285.7 kN
•  (C) 8333 kN
•  (D) 11905 kN

Direct step method of computation for gradually varied flow is

•  (A) Applicable to non-prismatic channels
•  (B) Applicable to prismatic channels
•  (C) Applicable to both prismatic and non-prismatic channels
•  (D) Not applicable to both prismatic and non-prismatic channels

The relationship among specific yield (S_y), specific retention (S_r) and porosity (η) of an aquifer is

•  (A) S_y = S_r + η
•  (B) S_y = S_r − η
•  (C) S_y = η − S_r
•  (D) S_y = S_r + 2η

The depth of flow in an alluvial channel is 1.5 m. If critical velocity ratio is 1.1 and Manning’s n is 0.018, the critical velocity of the channel as per Kennedy’s method is

•  (A) 0.713 m/s
•  (B) 0.784 m/s
•  (C) 0.879 m/s
•  (D) 1.108 m/s

The reference pressure used in the determination of sound pressure level is

•  (A) 20 μPa
•  (B) 20 db
•  (C) 10 μPa
•  (D) 10 db

Particulate matter (fly ash) carried in effluent gases from the furnaces burning fossil fuels are better removed by

•  (A) Cotton bag house filter
•  (B) Electrostatic precipitator (ESP)
•  (C) Cyclone
•  (D) Wet scrubber

The value of lateral friction or side friction used in the design of horizontal curve as per India Roads Congress guidelines is

•  (A) 0.40
•  (B) 0.35
•  (C) 0.24
•  (D) 0.15

During a CBR test, the load sustained by a remolded soil specimen at 5.0mm penetration is 50kg. The CBR value of the soil will be

•  (A) 10.0%
•  (B) 5.0%
•  (C) 3.6%
•  (D) 2.4%