GATE CE 2015 Set 1

## GATE CE

The smallest and largest Eigen values of the
following matrix are : $$\left[ {\matrix{
3 & { - 2} & 2 \cr

View Question For what value of $$'p'$$ the following set of equations will have no solutions?
$$$2x+3y=5$$$
$$$3x+py=10$$$

View Question The directional derivative of the field $$u(x, y, z)=$$ $${x^2} - 3yz$$ in the direction of the vector $$\left( {\wideh

View Question Consider the following probability mass function (p.m.f) of a random variable $$X.$$
$$$p\left( {x,q} \right) = \left\{

View Question Consider the following differential equation
$$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$
$$\

View Question The quadratic equation $${x^2} - 4x + 4 = 0$$ is to be solved numerically, starting with the initial guess $${x_0} = 3.$

View Question The integral $$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,} $$ with $${x_2} > {x_1} > 0$$ is evaluated analytically as wel

View Question Consider the following complex function $$f\left( z \right) = {9 \over {\left( {z - 1} \right)\left( {z + 2} \right)}}.$

View Question In a catchment, there are four rain-gauge stations, P, Q, R, and S. Normal annual precipitation
values at these stations

View Question The two columns below show some parameters and their possible values.
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View Question Workability of concrete can be measured using slump, compaction factor and Vee bee time.
Consider the following statemen

View Question Consider the following statements for air-entrained concrete:
(i) Air-entrainment reduces the water demand for a given l

View Question The composition of an air-entrained concrete is given below:
Water : 184 kg /m3
Ordinary Portland Cement(OPC) : 368 kg

View Question Consider the singly reinforced beam section given below (left figure). The stress block parameters for the cross-section

View Question Consider the singly reinforced beam shown in the figure below:
At cross-section $$XX,$$ which of the following statem

View Question The development length of a deformed reinforcement bar can be expressed as $$\left( {1/k} \right)\left( {\phi {\sigma _s

View Question A bracket plate connected to a column flange transmits a load of $$100$$ $$kN$$ as shown in the following figure. The ma

View Question Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, $$

View Question A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform
circular rod of diameter

View Question Two beams are connected by a linear spring as shown in the following figure. For a load $$P$$ as shown in the figure, th

View Question For the $$2D$$ truss with the applied loads shown below, the strain energy in the member $$XY$$ is _______________ $$kN$

View Question For the beam shown below, the value of the support moment
$$M$$ is ____________ $$KN$$-$$m$$.

View Question For formation of collapse mechanism in the following figure, the minimum value of $${{P_u}}$$ is $$c{M_P}/L.$$ $${M_P}$$

View Question For the beam shown below, the stiffness coefficient $${K_{22}}$$ can be written as

View Question