GATE CE 2015 Set 1
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## GATE CE

The smallest and largest Eigen values of the following matrix are : $$\left[ {\matrix{ 3 &amp; { - 2} &amp; 2 \cr View Question For what value of$$'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
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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)\
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The quadratic equation $${x^2} - 4x + 4 = 0$$ is to be solved numerically, starting with the initial guess $${x_0} = 3. View Question The integral$$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,} $$with$${x_2} &gt; {x_1} &gt; 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. .tg {border-collapse:collapse;border-spacing:0;m 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 $$\left( {1/k} \right)\left( {\phi {\sigma _s View Question A bracket plate connected to a column flange transmits a load of$$100kN$$as shown in the following figure. The ma View Question Two triangular wedges are glued together as shown in the following figure. The stress acting normal to the interface,$$ 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
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