GATE 2014 Civil Engineering

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

With reference to the conventional Cartesian $$(x,y)$$ coordinate system, the vertices of a triangle have the following coordinates: $$\,\left( {{x_1},{y_1}} \right) = \left( {1,0}...

Given the matrices $$J = \left[ {\matrix{ 3 & 2 & 1 \cr 2 & 4 & 2 \cr 1 & 2 & 6 \cr } } \right]$$ and $$K = \left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right],\,\,$$ the product $...

The perception-reaction time for a vehicle travelling at 90 km/h, given the coefficient of longitudinal friction of 0.35 and the stopping sight distance of 170 m (assume g = 9.81 m...

The sum of Eigen values of the matrix, $$\left[ M \right]$$ is where $$\left[ M \right] = \left[ {\matrix{ {215} & {650} & {795} \cr {655} & {150} & {835} \cr {485} & {355} & {550}...

In a reinforced concrete section, the stress at the extreme fibre in compression is $$5.80$$ $$MPa.$$ The depth of neutral axis in the section is $$58$$ $$mm$$ and the grade of con...

A steel section is subjected to a combination of shear and bending actions. The applied shear force is $$V$$ and the shear capacity of the section is $${V_s}.$$ For such a section,...

A traffic office imposes on an average $$5$$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Pois...

A particle moves along a curve whose parametric equations are: $$\,x = {t^3} + 2t,\,y = - 3{e^{ - 2t}}\,\,$$ and $$z=2$$ $$sin$$ $$(5t),$$ where $$x, y$$ and $$z$$ show variations...

The probability density function of evaporation $$E$$ on any day during a year in a watershed is given by $$$f\left( E \right) = \left\{ {\matrix{ {{1 \over 5}} & {0 \le E \le 5\,m...

A straight 100 m long raw water gravity main is to carry water from an intake structure to the jack well of a water treatment plant. The required flow through this water main is 0....

While designing, for a steel column of $$Fe250$$ grade, a base plate resting on a concrete pedestal of $$M20$$ grade, the bearing strength of concrete (in $$N/m{m^2}$$) in limit st...

A rectangular beam of width $$(b)$$ $$230$$ $$mm$$ and effective depth $$(d)$$ $$450$$ $$mm$$ is reinforced with four bars of $$12$$ $$mm$$ diameter. The grade of concrete is $$M20...

For a beam of cross-section, width $$= 230$$ $$mm$$ and effective depth $$= 500$$ $$mm,$$ the number of rebars of $$12$$ $$mm$$ diameter required to satisfy minimum tension reinfor...

Some of the nontoxic metals normally found in natural water are

The dimension for kinematic viscosity is

Water is following at a steady rate through a homogeneous and saturated horizontal soil strip of $$10$$m length. The strip is being subjected to a constant water head $$(H)$$ of $$...

The rank of the matrix $$\left[ {\matrix{ 6 & 0 & 4 & 4 \cr { - 2} & {14} & 8 & {18} \cr {14} & { - 14} & 0 & { - 10} \cr } } \right]$$ is

A road is being designed for a speed of 110 km/hr on a horizontal curve with a super elevation of 8%. If the coefficient of side friction is 0.10, the minimum radius of the curve (...

A certain soil has the following properties: G s = 2.71, n = 40% and w = 20%. The degree of saturation of the soil (rounded off to the nearest percent) is _________

The target mean strength f cm for concrete mix design obtained from the characteristic strength (f ck ) and standard deviation $$\sigma$$, as defined in IS:456-2000, is

The modulus of elasticity, E = 5000$$\sqrt{{\mathrm f}_\mathrm{ck}}$$ where f ck is the characteristic compressive strength of concrete, specified in IS:456-2000 is based on

The flexural tensile strength of M25 grade of concrete, in N/mm 2 , as per IS:456-2000 is __________.

If $$\left\{ x \right\}$$ is a continuous, real valued random variable defined over the interval $$\left( { - \infty ,\,\, \pm \infty } \right)$$ and its occurrence is defined by t...

A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes; (i) Head, (ii) Head, (III) Head, (iv) Head. The probability of obtaining a ''Tail...

The expression $$\mathop {Lim}\limits_{a \to 0} \,{{{x^a} - 1} \over a}\,\,$$ is equal to

The determinant of matrix $$\left[ {\matrix{ 0 & 1 & 2 & 3 \cr 1 & 0 & 3 & 0 \cr 2 & 3 & 0 & 1 \cr 3 & 0 & 1 & 2 \cr } } \right]$$ is

The integrating factor for the differential equation $${{dP} \over {dt}} + {k_2}\,P = {k_1}{L_0}{e^{ - {k_1}t}}\,\,$$ is

$$z = {{2 - 3i} \over { - 5 + i}}$$ can be expressed as

An observer counts $$240$$veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed, the probability of having one vehicle arrivi...

The survey carried out to delineate natural features, such as hills, rivers, forests and manmade features, such as towns, villages, buildings, roads, transmission lines and canals...

The first moment of area about the axis of bending for a beam cross-section is

Polar moment of inertia $$\left( {{{\rm I}_p}} \right),$$ in $$c{m^4},$$ of a rectangular section having width, $$b=2$$ $$cm$$ and depth $$d=6$$ $$cm$$ is __________