# 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.