2025
GATE CE 2025 Set 2GATE CE 2025 Set 12024
GATE CE 2024 Set 2GATE CE 2024 Set 12023
GATE CE 2023 Set 2GATE CE 2023 Set 12022
GATE CE 2022 Set 2GATE CE 2022 Set 12018
GATE CE 2018 Set 2GATE CE 2018 Set 12017
GATE CE 2017 Set 2GATE CE 2017 Set 12016
GATE CE 2016 Set 2GATE CE 2016 Set 12015
GATE CE 2015 Set 1GATE CE 2015 Set 22014
GATE CE 2014 Set 2GATE CE 2014 Set 12013
GATE CE 20132012
GATE CE 20122011
GATE CE 20112010
GATE CE 20102009
GATE CE 20092008
GATE CE 20082007
GATE CE 20072006
GATE CE 20062005
GATE CE 20052004
GATE CE 20042003
GATE CE 20032002
GATE CE 20022001
GATE CE 20012000
GATE CE 20001999
GATE CE 19991998
GATE CE 19981997
GATE CE 19971996
GATE CE 19961995
GATE CE 19951994
GATE CE 19941993
GATE CE 19931992
GATE CE 19921991
GATE CE 19911990
GATE CE 19901989
GATE CE 19891988
GATE CE 19881987
GATE CE 1987GATE CE 2014 Set 2
Paper was held on Thu, Jan 1, 1970 12:00 AM
1
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 the density function given as: $$f\left( x \right) = {1 \over {\sqrt {2\pi * b} }}{e^{ - {1 \over 2}{{\left( {{{x - a} \over b}} \right)}^2}}}$$ where $$'a'$$ and $$'b'$$ are the statistical attributes of the random variable $$\left\{ x \right\}$$. The value of the integral $$\int\limits_{ - \infty }^a {{1 \over {\sqrt {2\pi * b} }}{e^{ - {1 \over 2}{{\left( {{{x - a} \over b}} \right)}^2}}}} dx\,\,\,$$ is
2
$$z = {{2 - 3i} \over { - 5 + i}}$$ can be expressed as
3
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 $$5$$m at the beginning and $$1$$m at the end. If the governing equation of flow in the soil strip is $$\,\,{{{d^2}H} \over {d{x^2}}} = 0\,\,$$ (where $$x$$ is the distance along the soil strip), the value of $$H$$ (in m) at the middle of the strip is _______.
4
The integrating factor for the differential equation $${{dP} \over {dt}} + {k_2}\,P = {k_1}{L_0}{e^{ - {k_1}t}}\,\,$$ is
5
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 arriving over a $$30$$-second time interval is _______.
6
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'' when the coin is tossed again is
7
The expression $$\mathop {Lim}\limits_{a \to 0} \,{{{x^a} - 1} \over a}\,\,$$ is equal to
8
The rank of the matrix $$\left[ {\matrix{
6 & 0 & 4 & 4 \cr
{ - 2} & {14} & 8 & {18} \cr
{14} & { - 14} & 0 & { - 10} \cr
} } \right]$$ is
9
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
10
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 is
classified as
11
A certain soil has the following properties: Gs = 2.71, n = 40% and w = 20%. The degree of saturation of the soil (rounded off to the nearest percent) is _________
12
The modulus of elasticity, E = 5000$$\sqrt{{\mathrm f}_\mathrm{ck}}$$ where fck is the characteristic compressive strength
of concrete, specified in IS:456-2000 is based on
13
The target mean strength fcm for concrete mix design obtained from the characteristic strength
(fck) and standard deviation $$\sigma$$, as defined in IS:456-2000, is
14
The flexural tensile strength of M25 grade of concrete, in N/mm2, as per IS:456-2000 is
__________.
15
The axial load (in $$kN$$) in the member $$PQ$$ for the arrangement/assembly shown in the figure given below is ___________

16
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 __________
17
The beam of an overall depth $$250$$ $$mm$$ (shown below) is used in a building subjected to two different thermal environments. The temperatures at the top and bottom surfaces of the beam are $${36^ \circ }C$$ and $${72^ \circ }C$$ respectively. Considering coefficient of thermal expansion $$\left( \alpha \right)$$ as $$1.50 \times {10^{ - 5}}\,\,$$ per$${}^ \circ C,$$ the vertical deflection of the beam (in $$mm$$) at its mid-span due to temperature gradient is ______________

18
The first moment of area about the axis of bending for a beam cross-section is
19
The values of axial stress $$\left( \sigma \right)$$ in $$kN/{m^2},$$ bending moment $$(M)$$ in $$kNm,$$ and shear force $$(V)$$ in $$kN$$ acting at point $$P$$ for the arrangement shown in the figure are respectively.

20
For the state of plane stress (in $$MPa$$) shown in the figure below, the maximum shear stress (in $$MPa$$) is ___________

21
A prismatic beam (as shown below) has plastic moment capacity of $${{M_P}}$$, then the collapse load $$P$$ of the beam is

22
Considering the symmetry of a rigid frame as shown below, the magnitude of the bending moment (in $$kN$$-$$m$$) at $$P$$ (preferably using the moment distribution method) is

23
The tension (in $$kN$$) in a $$10$$ $$m$$ long cable, shown in the figure, neglecting its self-weight is

24
The static indeterminacy of the two-span continuous beam with an internal hinge, shown
below, is ______________.


25
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 (in
m) required for safe vehicular movement is