GATE CE 2014 Set 1

## GATE CE

Given the matrices $$J = \left[ {\matrix{
3 & 2 & 1 \cr
2 & 4 & 2 \cr
1 & 2 & 6 \c

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The sum of Eigen values of the matrix, $$\left[ M \right]$$
is where $$\left[ M \right] = \left[ {\matrix{
{215} &am

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With reference to the conventional Cartesian $$(x,y)$$ coordinate system, the vertices of a triangle have the following

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$$\,\,\mathop {Lim}\limits_{x \to \infty } \left( {{{x + \sin x} \over x}} \right)\,\,$$ equal to

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A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2$

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The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by
$$$f\left( E

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A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of

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A straight 100 m long raw water gravity main is to carry water from an intake structure to the
jack well of a water trea

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Some of the nontoxic metals normally found in natural water are

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For a sample of water with the ionic composition shown in the figure below, the carbonate and noncarbonate
hardness conc

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The dimension for kinematic viscosity is

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Three rigid buckets, shown as in the figures (1), (2) and (3), are of identical heights and base areas.
Further, assume

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For a beam of cross-section, width $$= 230$$ $$mm$$ and effective depth $$= 500$$ $$mm,$$ the number of rebars of $$12$$

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In a reinforced concrete section, the stress at the extreme fibre in compression is $$5.80$$ $$MPa.$$ The depth of neutr

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A rectangular beam of width $$(b)$$ $$230$$ $$mm$$ and effective depth $$(d)$$ $$450$$ $$mm$$ is reinforced with four ba

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While designing, for a steel column of $$Fe250$$ grade, a base plate resting on a concrete pedestal of $$M20$$ grade, th

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The tension and shear force (both in $$kN$$) in each bolt of the joint, as shown below, respectively are

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A steel section is subjected to a combination of shear and bending actions. The applied shear force is $$V$$ and the she

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A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are
coplanar, the magnitude a

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The possible location of shear center of the channel section, shown below, is

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For the cantilever beam of span $$3$$ $$m$$ (shown below), a concentrated load of $$20$$ $$kN$$ applied at the free end

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If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown i

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The degree of static indeterminacy of a rigid jointed frame PQR supported as shown in the figure is

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In a beam of length $$L,$$ four possible influence line diagrams for shear force at a section located at a distance of $

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For the truss shown below, the member $$PQ$$ is short by $$3$$ $$mm.$$ The magnitude of vertical displacement of joint $

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The ultimate collapse load $$(P)$$ in terms of plastic moment $${M_P}$$ by kinematic approach for a propped cantilever o

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Match the information given in Group $$-$$ $${\rm I}$$ with those in Group $$-$$ $${\rm II}.$$

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Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of $

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The perception-reaction time for a vehicle travelling at 90 km/h, given the coefficient of
longitudinal friction of 0.35

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