The $\underset{x\to 0}{\lim }\frac{\sin \left[{}_3{}^{2}x\right]}{x}$ is

•  (A) $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$
•  (B) 1
•  (C) $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
•  (D) ∞

Two coins are simultaneously tossed. The probability of two heads simultaneously appearing is

•  (A) $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$8$}\right.$
•  (B) $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$
•  (C) $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$
•  (D) $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

The order and degree of the differential equation

$\frac{d^{3}y}{d{x}^3}+4\sqrt{{\left(\frac{dy}{dx}\right)}^3+y^2}=0$ are respectively

•  (A) 3 and 2
•  (B) 2 and 3
•  (C) 3 and 3
•  (D) 3 and 1

Two people weighing W each are sitting on a plank of length L floating on water at $\raisebox{1ex}{$L$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ from either end. Neglecting the weight of the plank, the bending moment at the centre of the plank is

•  (A) $\frac{WL}{8}$
•  (B) $\frac{WL}{16}$
•  (C) $\frac{WL}{32}$
•  (D) zero

For the truss shown in the figure, the force in the member QR is

•  (A) Zero
•  (B) $\raisebox{1ex}{$P$}\!\left/ \!\raisebox{-1ex}{$\sqrt{2}$}\right.$
•  (C) P
•  (D) $\sqrt{2}P$

The major and minor principal stresses at a point are 3 MPa and -3 MPa respectively. The maximum shear stress at the point is

•  (A) Zero
•  (B) 3 MPa
•  (C) 6 MPa
•  (D) 9 MPa

The number of independent elastic constants for a linear elastic isotropic and homogeneous material is

•  (A) 4
•  (B) 3
•  (C) 2
•  (D) 1

The effective length of a column of length L fixed against rotation and translation at one end and free at the other end is

•  (A) 0.5 L
•  (B) 0.7 L
•  (C) 1.414 L
•  (D) 2L

As per India standard code of practice for prestressed concrete (IS:1343-1980) the minimum grades of concrete to be used for post-tensioned and pre-tensioned structural elements are respectively

•  (A) M20 for both
•  (B) M40 and M30
•  (C) M15 and M20
•  (D) M30 and M40

A solid circular shaft of diameter d and length L is fixed at one end and free at the other end. A torque T is applied at the free end. The shear modulus of the material is G. The angle of twist at three free ends is

•  (A) $\frac{16TL}{{\mathrm{\pi d}}^4\mathrm{G}}$
•  (B) $\frac{32TL}{{\mathrm{\pi d}}^4\mathrm{G}}$
•  (C) $\frac{64TL}{{\mathrm{\pi d}}^4\mathrm{G}}$
•  (D) $\frac{128TL}{{\mathrm{\pi d}}^4\mathrm{G}}$;

In a compaction test, G, w, S and e represent the specific gravity, water content, degree of saturation and void ratio of the soil sample, respectively. If ${\gamma }_w$ represents the unit weight of water and ${\gamma }_d$ represents the dry unit weight of the soil, the equation for zero air voids line is

•  (A) ${\gamma }_d=\frac{G{\gamma }_w}{1+Se}$
•  (B) ${\gamma }_d=\frac{G{\gamma }_w}{1+Gw}$
•  (C) ${\gamma }_d=\frac{Gw}{e+{\gamma }_{w}S}$
•  (D) ${\gamma }_d=\frac{Gw}{1+Se}$

A fine grained soil has liquid limit of 60 and plastic limit of 20. As per the plasticity chart, according to IS classification, the soil is represented by the letter symbols

•  (A) CL
•  (B) CI
•  (C) CH
•  (D) CL-ML

Quick sand condition occurs when

•  (A) The void ratio of the soil becomes 1.0
•  (B) The upward seepage pressure in soil becomes zero
•  (C) The upward seepage pressure in soil becomes equal to the saturated unit weight of the soil
•  (D) The upward seepage pressure in soil becomes equal to the submerged unit weight of the soil

The e-log p curve shown in the figure is representative of

•  (A) Normally consolidated clay
•  (B) Over consolidated clay
•  (C) Under consolidated clay
•  (D) Normally consolidated clayey sand

If ${\sigma }_{h,}{\sigma }_{v,}\stackrel{"}{{\sigma }_h} and \stackrel{"}{{\sigma }_{v,}}$ represent the total horizontal stress, total vertical stress, effective horizontal stress and effective vertical stress on a soil element, respectively, the coefficient of earth pressure at rest is given by

•  (A) $\frac{{\sigma }_h}{{\sigma }_v}$
•  (B) $\frac{{\displaystyle \stackrel{"}{{\sigma }_h}}}{{\displaystyle \stackrel{"}{{\sigma }_v}}}$
•  (C) $\frac{{\sigma }_v}{{\sigma }_h}$
•  (D) $\frac{{\displaystyle \stackrel{"}{{\sigma }_v}}}{{\displaystyle \stackrel{"}{{\sigma }_h}}}$

A mild-sloped channel is followed by a steep-sloped channel. The profiles of gradually varied flow in the channel are

•  (A) M_3, S₂
•  (B) M₃,S₃
•  (C) M₂,S₁
•  (D) M₂,S₂

The flow in a rectangular channel is subcritical.if the width of the channel is reduced at a certain section, the water surface under no-choke condition will

•  (A) drop at a downstream section
•  (B) rise at a downstream section
•  (C) rise at an downstream section
•  (D) not undergo any change

The correct match of Group-I with Group-II is

•  (A) P-1, Q-3, R-4, S-2
•  (B) P-1, Q-4, R-2, S-3
•  (C) P-3, Q-4, R-1, S-2
•  (D) P-4, Q-2, R-1, S-3

Group-I gives a list of devices and Group-II the list of uses

•  (A) P-1, Q-2, R-4, S-3
•  (B) P-2, Q-1, R-3, S-4
•  (C) P-2, Q-1, R-4, S-3
•  (D) P-4, Q-1, R-3, S-2

A coastal city produces municipal solid waste (MSW) with high moisture content, high organic materials, low calorific value and low inorganic materials. The most effective and sustainable option for MSW management in that city is

•  (A) Composting
•  (B) Dumping in sea
•  (C) Incineration
•  (D) Landfill