1

GATE CE 2015 Set 1

MCQ (Single Correct Answer)

+2

-0.6

The integral $$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,} $$ with $${x_2} > {x_1} > 0$$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $${\rm I}$$ is the exact value of the integral obtained analytically and $$J$$ is the approximate value obtained using the trapezoidal rule, which of the following statements is correct about their relationship?

2

GATE CE 2015 Set 2

Numerical

+2

-0

For step-size, $$\Delta x = 0.4,$$ the value of following integral using Simpson's $$1/3$$ rule is ______

Your input ____

3

GATE CE 2015 Set 2

Numerical

+2

-0

In Newton-Raphson iterative method, the initial guess value $$\left( {{x_{ini}}} \right)$$ is considered as zero while finding the roots of the equation: $$\,f\left( x \right) = - 2 + 6x - 4{x^2} + 0.5{x^3}.\,\,\,$$ The correction, $$\Delta x,$$ to be added to $${{x_{ini}}}$$ in the first iteration is __________.

Your input ____

4

GATE CE 2013

Numerical

+2

-0

There is no value of $$x$$ that can simultaneously satisfy both the given equations. Therefore, find the 'least squares error' solution to the two equations, i.e., find the value of $$x$$ that minimizes the sum of squares of the errors in the two equations

$$2x=3$$

$$4x=1$$

$$2x=3$$

$$4x=1$$

Your input ____

Questions Asked from Numerical Methods (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CE Subjects

Engineering Mechanics

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude