GATE CE 2015 Set 1
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GATE CE

For what value of $$'p'$$ the following set of equations will have no solutions? $$$2x+3y=5$$$ $$$3x+py=10$$$
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The smallest and largest Eigen values of the following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr
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The directional derivative of the field $$u(x, y, z)=$$ $${x^2} - 3yz$$ in the direction of the vector $$\left( {\wideh
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Consider the following probability mass function (p.m.f) of a random variable $$X.$$ $$$p\left( {x,q} \right) = \left\{
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Consider the following differential equation $$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$ $$\
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The integral $$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,} $$ with $${x_2} > {x_1} > 0$$ is evaluated analytically as wel
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The quadratic equation $${x^2} - 4x + 4 = 0$$ is to be solved numerically, starting with the initial guess $${x_0} = 3.$
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Consider the following complex function $$f\left( z \right) = {9 \over {\left( {z - 1} \right)\left( {z + 2} \right)}}.$
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In a catchment, there are four rain-gauge stations, P, Q, R, and S. Normal annual precipitation values at these stations
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The two columns below show some parameters and their possible values. .tg {border-collapse:collapse;border-spacing:0;m
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Workability of concrete can be measured using slump, compaction factor and Vee bee time. Consider the following statemen
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Consider the following statements for air-entrained concrete: (i) Air-entrainment reduces the water demand for a given l
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The composition of an air-entrained concrete is given below: Water : 184 kg /m3 Ordinary Portland Cement(OPC) : 368 kg
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Consider the singly reinforced beam section given below (left figure). The stress block parameters for the cross-section
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Consider the singly reinforced beam shown in the figure below: At cross-section $$XX,$$ which of the following statem
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The development length of a deformed reinforcement bar can be expressed as $$\left( {1/k} \right)\left( {\phi {\sigma _s
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A bracket plate connected to a column flange transmits a load of $$100$$ $$kN$$ as shown in the following figure. The ma
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Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface, $$
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A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform circular rod of diameter
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Two beams are connected by a linear spring as shown in the following figure. For a load $$P$$ as shown in the figure, th
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For the $$2D$$ truss with the applied loads shown below, the strain energy in the member $$XY$$ is _______________ $$kN$
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For the beam shown below, the value of the support moment $$M$$ is ____________ $$KN$$-$$m$$.
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For formation of collapse mechanism in the following figure, the minimum value of $${{P_u}}$$ is $$c{M_P}/L.$$ $${M_P}$$
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For the beam shown below, the stiffness coefficient $${K_{22}}$$ can be written as
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