# Civil Engineering - GATE 2013 Paper Solution

There is no value of x that can simultaneously satisfy both the given equations.Therefore, find the ‘least squares error’ solution to the two equations, i.e., find the value of x that minimizes the sum of squares of the errors in the two equations. __________
2x=3
4x=1

What is the minimum number of multiplications involved in computing the matrix product PQR? Matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and 1 column. __________

A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each oftwo successive years is:

Maximum possible value of Compacting Factor for fresh (green) concrete is:

As per IS 800:2007, the cross-section in which the extreme fiber can reach the yield stress, but cannot develop the plastic moment of resistance due to failure by local buckling is classified as

The creep strains are

As per IS 456:2000 for M20 grade concrete and plain barsin tension the design bond stress 1.2 .Further, IS 456:2000 permits this design bond stress value to be increased by 60 % for HSD bars. The stress in the HSD reinforcing steel barsin tension,${\sigma }_{s}=360M{P}_{a}$. Find the required development length,Ld for HSD barsin terms of the bar diameter,$\Phi$ . __________

The ‘plane section remains plane’ assumption in bending theory implies:

Two steel columns P (length L and yield strength fy=250 MPa) and Q (length 2L and yield strength fy=500 MPa) have the same cross-sections and end-conditions. The ratio of buckling load of column P to that of column Q is:

The pin-jointed 2-D truss is loaded with a horizontal force of 15 KN at joint S and another 15 KN vertical force at joint U, as shown.Find the force in member RS (in KN) and report your answer taking tension as positive and compression as negative. __________

A symmetric I-section (with width of each flange 50 mm,thickness of each flange = 10 mm,depth of web = 100 mm, and thickness of web =10 mm) of steel is subjected to a shear force of 100 kN. Find the magnitude of the shear stress(in N/mm2 the web at its junction with the top flange. __________

In its natural condition, a soil sample has a mass of 1.980 Kg and a volume of 0.001 m3. After being completely dried in an oven, the mass of the sample is 1.800 Kg.Specific gravity G is 2.7. Unit weight of water is 10 KN/m3. The degree of saturation of the soil is:

The ratio Nf/Nd is known as shape factor, where Nf is the number of flow lines and Nd is the number of equipotential drops. Flow net is always drawn with a constant b/a ratio, where b and a are distances between two consecutive flow lines and equipotential lines, respectively. Assuming that b/a ratio remains the same, the shape factor of aflow net will change if the

Following statementsare made on compacted soils, wherein DS stands forthe soils compacted on dry side of optimum moisture content and WS stands for thesoils compacted on wet side of optimum moisture content. Identify the incorrect statement.

Four columns of a building are to be located within a plot size of 10 m x 10 m. The expected load on each column is 4000 kN. Allowable bearing capacity of the soil deposit is 100 kN/m2. The type of foundation best suited is

For subcritical flow in an open channel, the control section for gradually varied flow profiles is

Group-I contains dimensionless parameters and Group- II contains the ratios.

 Group-I Group -II P. Mach Number 1. Ratio of inertial force and gravitational force Q. Reynolds Number 2. Ratio of fluid velocity and velocity of sound R. Weber Number 3. Ratio of inertial force and viscous force S. Froude Number 4. Ratio of inertial force and surface tension force

The correct match of dimensionless parameters in Group- I with ratios in Group-II is:

For a two dimensional flow field, the stream function $\Psi$ is given as $\Psi =\frac{3}{2}\left({y}^{2}-{x}^{2}\right)$.The magnitude of discharge occurring between the stream lines passing through points (0,3) and (3,4) is: