The product of matrices ${\left(PQ\right)}^{-1} P$ is

•  (A) $P^{-1}$;
•  (B) $Q^{-1}$;
•  (C) $P^{-1 }{Q}^{-1} P$;
•  (D) $PQ P^{-1}$;

The general solution of $\frac{d^{2}y}{d{x}^2}+y=0$ is

•  (A) $y=P \cos x+Q \sin x$
•  (B) $y=P \cos x$
•  (C) $y=P \sin x$
•  (D) $y=P {\sin }^2 x$

A mild steel specimen is under uni-axial tensile stress. Young’s modules and yield stress for mild steel are 2 × 10⁵ MPa and 250 Mpa respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen without permanent set is

•  (A) 156 Nmm/mm³
•  (B) 15.6 Nmm/mm³
•  (C) 1.56 Nmm/mm³
•  (D) 0.156 Nmm/mm³

A reinforced concrete structure has to be constructed along a sea coast. The minimum grade of concrete to be used as per IS: 456-2000 is

•  (A) M 15
•  (B) M 20
•  (C) M 25
•  (D) M 30

In the design of a reinforced concrete beam the requirement for bond is not getting satisfied. The economical option to satisfy the requirement for bond is by

•  (A) bundling of bars
•  (B) providing smaller diameter bars more in number
•  (C) providing larger diameter bars less in number
•  (D) providing same diameter bars more in number

The shape of the cross-section, which has a largest shape factor, is

•  (A) rectangular
•  (B) I-section
•  (C) diamond
•  (D) solid circular

Group symbols assigned to silty sand and clayey sand are respectively

•  (A) SS and CS
•  (B) SM and CS
•  (C) SM and SC
•  (D) MS and CS

When a retaining wall moves away from the back-fill, the pressure exerted on the wall is termed as

•  (A) Passive earth pressure
•  (B) Swelling pressure
•  (C) Pore pressure
•  (D) Active earth pressure

Compaction by vibratory roller is the best method of compaction in case of

•  (A) moist silty sand
•  (B) well graded dry sand
•  (C) clay of medium compressibility
•  (D) silt of high compressibility

A person standing on the bank of a canal drops a stone on the water surface. He notices that the disturbance on the water surface in not traveling up-stream. This is because the flow in the canal is

•  (A) sub-critical
•  (B) super-critical
•  (C) steady
•  (D) uniform

A flood wave with a known inflow hydrograph is routed through a large reservoir. The outflow hydrograph will have

•  (A) attenuated peak with reduced time-base
•  (B) attenuated peak with increased time-base
•  (C) increased peak with increased time-base
•  (D) increased peak with reduced time-base

A stable channel is to be designed for a discharge of Q m³/s with silt factor f as per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by

•  (A) (Qf ² / 140)^1/6
•  (B) (Qf / 140)^1/3
•  (C) (Q ²f² / 140)^1/6
•  (D) 0.48 (Q / f )^1/3

The base width of an elementary profile of gravity dam of height H is b. The specific gravity of the material of the dam is G and uplift pressure coefficient is K. the correct relationship for no tension at the heel is given by

•  (A) $\frac{b}{H}=\frac{1}{\sqrt{\mathrm{G}-\mathrm{K}}}$
•  (B) $\frac{b}{H}=\sqrt{\mathrm{G}-\mathrm{K}}$
•  (C) $\frac{b}{H}=\frac{1}{\mathrm{G}-\mathrm{K}}$
•  (D) $\frac{b}{H}=\frac{1}{\mathrm{K}\sqrt{\mathrm{G}-\mathrm{K}}}$

Two primary air pollutants are

•  (A) sulphur oxide and ozone
•  (B) nitrogen oxide and peroxyacetylnitrate
•  (C) sulphur oxide and hydrocarbon
•  (D) ozone and peroxyacetynitrate

Two biodegradable components of municipal solid waste are

•  (A) plastics and wood
•  (B) cardboard and glass
•  (C) leather and tin cans
•  (D) food wastes and garden trimmings

The specific gravity of paving bitumen as per IS:73 – 1992 lies between

•  (A) 1.10 and 1.06
•  (B) 1.06 and 1.02
•  (C) 1.02 and 0.97
•  (D) 0.97 and 0.92

A combined value of flakiness and elongation index is to be determined for a sample of aggregates. The sequence in which the two tests are conducted is

•  (A) elongation index test followed by flakiness index test on the whole sample
•  (B) flakiness index test followed by elongation index test on the whole sample
•  (C) flakiness index test followed by elongation index test on the non-flaky aggregates
•  (D) elongation index test followed by flakiness index test on non-elongated aggregates

The capacities of “One-way 1.5m wide sidewalk (persons per hour)” and “One-way 2-lane urban road (PCU per hour, with no frontage access, no standing vehicles and very little cross traffic)” are respectively

•  (A) 1200 and 2400
•  (B) 1800 and 2000
•  (C) 1200 and 1500
•  (D) 2000 and 1200

The shape of the STOP sign according to IRC: 67-2001 is

•  (A) circular
•  (B) triangular
•  (C) octagonal
•  (D) rectangular

The type of surveying in which the curvature of the earth is taken into account is called

•  (A) Geodetic surveying
•  (B) Plane surveying
•  (C) Preliminary surveying
•  (D) Topographical surveying