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




There are 5 questions to complete.

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