GATE Civil Engineering 2020 SET-2

Question 1
The ordinary differential equation \frac{d^2u}{dx^2}-2x^2u+\sin x=0 is
A
linear and homogeneous
B
linear and nonhomogeneous
C
nonlinear and homogeneous
D
nonlinear and nonhomogeneous
Engineering Mathematics   Ordinary Differential Equation
Question 1 Explanation: 
Its solution is of the type u=f(x), i.e., dependent variable is u.
Hence, given equation is Linear and Non-Homogeneous.
Question 2
The value of \lim_{x \to \infty } \frac{\sqrt{9x^2+2020}}{x+7} is
A
\frac{7}{9}
B
1
C
3
D
Indeterminable
Engineering Mathematics   Calculus
Question 2 Explanation: 
\lim_{x \to \infty }\frac{3x \sqrt{1+\frac{2020}{x^2}}}{x\left ( 1+\frac{7}{x} \right )}=3
Question 3
The integral
\int_{0}^{1}(5x^3+4x^2+3x+2)dx

is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson's rules with a common step size. In this context, which one of the following statement is TRUE?
A
Simpsons rule as well as rectangular rule of estimation will give NON-zero error.
B
Simpson's rule, rectangular rule as well as trapezoidal rule of estimation will give NON-zero error.
C
Only the rectangular rule of estimation will given zero error.
D
Only Simpson's rule of estimation will give zero error.
Engineering Mathematics   Numerical Methods
Question 3 Explanation: 
Because integral is a polynomial of 3rd degree so Simpson's rule will give error free answer.
Question 4
The following partial differential equation is defined for u:u(x,y)

\frac{\partial u}{\partial y}=\frac{\partial^2 u}{\partial x^2}; \; \; y\geq 0;\;x_1\leq x\leq x_2

The set of auxiliary conditions necessary to solve the equation uniquely, is
A
three initial conditions
B
three boundary conditions
C
two initial conditions and one boundary condition
D
one initial condition and two boundary conditions
Engineering Mathematics   Ordinary Differential Equation
Question 4 Explanation: 
Given: DE is \frac{\partial u}{\partial y}=\frac{\partial^2 u}{\partial x^2}; \; y\geq 0;\; x_1 \leq x\leq x_2
\because y is given as \geq 0 so we take it as time. Hence, above equation is nothing but one-D heat equation which requires one initial condition and two boundary condition.
Question 5
The ratio of the plastic moment capacity of a beam section to its yield moment capacity is termed as
A
aspect ratio
B
load factor
C
shape factor
D
slenderness ratio
Design of Steel Structures   Plastic Analysis
Question 5 Explanation: 
Ratio of \frac{M_p}{M_y}= Shape factor
Question 6
The state of stress represented by Mohr's circle shown in the figure is
A
uniaxial tension
B
biaxial tension of equal magnitude
C
hydrostatic stress
D
pure shear
Solid Mechanics   Properties of Metals, Stress and Strain
Question 6 Explanation: 
In pure shear condition, Mohr's circle has its center at origin.
Question 7
A weightless cantilever beam of span L is loaded as shown in the figure. For the entire span of the beam, the material properties are identical and the cross-section is rectangular with constant width.

From the flexure-critical perspective, the most economical longitudinal profile of the beam to carry the given loads amongst the options given below, is
A
A
B
B
C
C
D
D
Solid Mechanics   Shear Force and Bending Moment
Question 7 Explanation: 


(-PL) + (PL) + (-M_A) = 0
M_A = 0

For most economical,
Maximum cross-section is given where maximum bending moment occurs.

Question 8
As per IS 456:2000, the pH value of water for concrete mix shall NOT be less than
A
4.5
B
5
C
5.5
D
6
RCC Structures   Working Stress and Limit State Method
Question 8 Explanation: 
1. Minimum pH value of water for concrete = 6.0
As per IS code provision no. 5.4.2, the pH value of water shall not less than 6.0.
Question 9
The traffic starts discharging from an approach at an intersection with the signal turning green. The constant headway considered from the fourth or fifth headway position is referred to as
A
discharge headway
B
effective headway
C
intersection headway
D
saturation headway
Transportation Engineering   Traffic Engineering
Question 10
Soil deposit formed due to transportation by wind is termed as
A
aeolian deposit
B
alluvial deposit
C
estuarine deposit
D
lacustrine deposit
Geotechnical Engineering   Properties of Soils
Question 10 Explanation: 
Soil deposited by wind is Aeolian soil.
There are 10 questions to complete.

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