2025
GATE CE 2025 Set 2GATE CE 2025 Set 12024
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GATE CE 1987GATE CE 2017 Set 1
Paper was held on Thu, Jan 1, 1970 12:00 AM
1
The activity details of a project are given below:
The estimated minimum time (in days) for the completion of the project will be________

2
Consider the following second $$-$$order differential equation : $$\,y''\,\, - 4y' + 3y = 2t - 3{t^2}\,\,\,$$
The particular solution of the differential equation is
The particular solution of the differential equation is
3
Consider the equation $${{du} \over {dt}} = 3{t^2} + 1$$ with $$u=0$$ at $$t=0.$$ This is numerically solved by using the forward Euler method with a step size. $$\,\Delta t = 2.$$ The absolute error in the solution at the end of the first time step is __________
4
Consider the following partial differential equation: $$\,\,3{{{\partial ^2}\phi } \over {\partial {x^2}}} + B{{{\partial ^2}\phi } \over {\partial x\partial y}} + 3{{{\partial ^2}\phi } \over {\partial {y^2}}} + 4\phi = 0\,\,$$ For this equation to be classified as parabolic, the value of $${B^2}$$ must be ____________.
5
The solution of the equation $$\,{{dQ} \over {dt}} + Q = 1$$ with $$Q=0$$ at $$t=0$$ is
6
For the function $$\,f\left( x \right) = a + bx,0 \le x \le 1,\,\,$$ to be a valid probability density function, which one of the following statements is correct?
7
The number of parameters in the univariate exponential and Gaussian distributions, respectively, are
8
Let $$x$$ be a continuous variable defined over the interval $$\left( { - \infty ,\infty } \right)$$, and $$f\left( x \right) = {e^{ - x - {e^{ - x}}}}.$$
The integral $$g\left( x \right) = \int {f\left( x \right)dx\,\,} $$ is equal to
The integral $$g\left( x \right) = \int {f\left( x \right)dx\,\,} $$ is equal to
9
$$\mathop {Lim}\limits_{x \to 0} \left( {{{\tan x} \over {{x^2} - x}}} \right)$$ is equal to _________.
10
The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the following options is correct?
11
Consider the matrix $$\left[ {\matrix{
5 & { - 1} \cr
4 & 1 \cr
} } \right].$$ Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?
12
A particle of mass 2 kg is traveling at a velocity of 1.5 m/s. A force f(t)=3t2 (in N) is applied
to it in the direction of motion for a duration of 2 seconds, where t denotes time in seconds.
The velocity (in m/s, up to one decimal place) of the particle immediately after the removal of
the force is________
13
A pre-tensioned rectangular concrete beam $$150$$ $$mm$$ wide and $$300$$ $$mm$$ depth is prestressed with three straight tendones, each having a cross-sectional area of $$50$$ $$m{m^2},$$ to an initial stress of $$1200$$ $$N/m{m^2}.$$ The tendons are located at $$100$$ $$mm$$ from the soffit of the beam. If the modular ratio is $$6,$$ the loss of prestressing force (in $$kN,$$ up to one decimal place) due to the elastic deformation of concrete only is ________
14
According to $$IS$$ $$456$$- $$2000,$$ which one of the following statements about the depth of natural axis $${x_u},\,\,bal$$ for a balanced reinforced concrete section is correct?
15
A column is subjected to a load through a bracket as shown in figure

The resultant force (in $$kN,$$ up to one decimal place) in the bolt $$1$$ is _______________
16
Consider the stepped bar made with a linear elastic material and subjected to an axial load of $$1$$ $$kN$$, as shown in the figure

Segment $$1$$ and $$2$$ have cross-sectional area of $$100\,\,m{m^2}$$ and $$60\,\,m{m^2}$$, Young's modulus of $$2 \times {10^5}\,\,MPa$$ and $$3 \times {10^5}\,\,MPa,$$ and length of $$400$$ $$mm$$ and $$900$$ $$mm,$$ respectively. The strain energy (in $$N$$-$$mm,$$ up to one decimal place) in the bar due to the axial load is _________
17
Consider two axially loaded columns, namely. $$1$$ and $$2,$$ made of a linear elastic material with Young's modulus $$2 \times {10^5}\,\,MPa,$$ square cross-section with side $$10$$ $$mm$$, and length $$1$$ $$m.$$ For Column $$1,$$ one end is fixed and the other end is free. For column $$2,$$ one end is fixed and the other end is pinned. Based on the Euler's theory, the ratio (up to one decimal place) of the buckling load of Column $$2$$ to the buckling load of column $$1$$ is ___________
18
A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true?
19
An elastic bar of length L, uniform cross sectional area A, coefficient of thermal expansion
a, and Young’s modulus E is fixed at the two ends. The temperature of the bar is increased
by T, resulting in an axial stress $$\sigma$$. Keeping all other parameters unchanged, if the length of
the bar is doubled, the axial stress would be
20
The value of $$M$$ in the beam $$ABC$$ shown in the figure is such that the joint $$B$$ does not rotate.

The value of support reaction (in $$kN$$) at $$B$$ should be equal to _____________
21
The figure shows a two $$-$$hinged parabolic arch of span $$L$$ subjected to a uniformly distributed load of intensity $$q$$ per unit length.

The maximum bending moment in the arch is equal to
22
Consider the beam $$ABCD$$ shown in figure

For a moving concentrated load of $$50$$ $$kN$$ on the beam, the magnitude of the maximum bending moment (in $$kN$$-$$m$$) obtained at the support $$C$$ will be equal to _________
23
A planar truss tower structure is shown in the figure:
Consider the following statements about the external and internal determinacies of the truss.
(P) Externally Determinate
(Q) External Static Indeterminacy = 1
(R) External Static Indeterminacy = 2
(S) Internally Determinate
(T) Internal Static Indeterminacy = 1
(U) Internal Static Indeterminacy = 2
Which one of the following options is correct?

(P) Externally Determinate
(Q) External Static Indeterminacy = 1
(R) External Static Indeterminacy = 2
(S) Internally Determinate
(T) Internal Static Indeterminacy = 1
(U) Internal Static Indeterminacy = 2
Which one of the following options is correct?
24
A super-elevation e is provided on a circular horizontal curve such that a vehicle can be
stopped on the curve without sliding. Assuming a design speed v and maximum coefficient of
side friction fmax, which one of the following criteria should be satisfied?