# Civil Engineering - GATE 2010 Paper Solution

The $\underset{x\to 0}{\mathrm{lim}}\frac{\mathrm{sin}\left[{}_{3}{}^{2}x\right]}{x}$ is

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

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

Two people weighing W each are sitting on a plank of length L floating on water at $L}{4}$ from either end. Neglecting the weight of the plank, the bending moment at the centre of the plank is

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

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

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

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

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 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

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 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

Quick sand condition occurs when

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

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

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

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

 Group-I Group-II P. Evapotranspiration 1. Penman method Q. Infiltration 2. Snyder’s method R. Synthetic unit hydrograph 3. Muskingum method S. Channel Routing 4.Horton’s method