# Civil Engineering - GATE 2007 Paper Solution

The minimum and the maximum eigen velue of the matrix $\left[\begin{array}{ccc}1& 1& 3\\ 1& 5& 1\\ 3& 1& 1\end{array}\right]$ are -2 and 6, respectively. What is the other eigen value?

The degree of the differential equation $\frac{{\mathit{d}}^{2}x}{\mathit{d}{t}^{2}}+2{x}^{3}=0$ is

The solution for the differential equation $\frac{\mathit{d}y}{\mathit{d}x}={x}^{2}y$ with the condition that y = 1 at x = 0 is

An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is

A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be

The stiffness coefficient kij indicates

For an isotropic material, the relationship between the Young’s modulus (E), shear modulus (G) and Poisson’s ratio ($\mu$) is given by

A clay soil sample is tested in a triaxial apparatus in consolidated-drained conditions at a cell pressure of 100 kN/m2. What will be the pore water pressure at a deviator stress of 40 kN/m2?

The number of blows observed in a Standard Penetration Test (SPT) for different penetration depths are given as follows

 Penetration of sampler Number of blows 0-150 mm 6 150-300 mm 8 300-450 mm 10

The observed N value is

The vertical stress at some depth below the corner of a 2m×3m rectangular footing due to a certain load intensity is 100 kN/m2. What will be the vertical stress in kN/m2 below the centre of a 4m×6m rectangular footing at the same depth and same load intensity?

There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate?

The consumptive use of water for a crop during a particular stage of growth is 2.0 mm/day. The maximum depth of available water in the root zone is 60 mm. Irrigation is required when the amount of available water is 50% of the maximum available water in the root zone. Frequency of irrigation should be

As per the Lacey’s method for design of a alluvail channels, identify the TRUE statement from the following:

At two points 1 and 2 in a pipeline the velocities and V and 2V, respectively. Both the points are at the same elevation. The fluid density is $\mathrm{\rho }$. The flow can be assumed to be in compressible, inviscid, steady and irrotational. The difference in pressures P1 and P2 at poiunts 1 and 2 is

The presence of hardness in excess of permissible limit causes

The dispersion of pollutants in atmosphere is maximum when

The alkalinity and hardness of a water sample are 250 mg/L and 350 mg/L as CaCO3, respectively. The water has