# 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