GATE CE
Engineering Mathematics
Numerical Methods
Previous Years Questions

## Marks 1

The quadratic approximation of $$f\left( x \right) = {x^3} - 3{x^2} - 5\,\,$$ at the point $$x=0$$ is
The estimate of $$\int\limits_{0.5}^{1.5} {{{dx} \over x}} \,\,$$ obtained using Simpson's rule with three-point function evaluation exceeds the exact...
The Newton-Raphson iteration $${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {R \over {{x_n}}}} \right)$$ can be used to compute
The following equation needs to be numerically solved using the Newton $$-$$ Raphson method $${x^3} + 4x - 9 = 0.\,\,$$ The iterative equation for thi...
Given that one root of the equation $$\,{x^3} - 10{x^2} + 31x - 30 = 0\,\,$$ is $$5$$ then other roots are
Given $$a>0,$$ we wish to calculate it reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0.$$ The Newton - Raphson algor...
Let $$\,\,f\left( x \right) = x - \cos \,x.\,\,\,$$ Using Newton-Raphson method at the $$\,{\left( {n + 1} \right)^{th}}$$ iteration, the point $$\,{... Given the differential equation$${y^1} = x - y$$with initial condition$$y(0)=0.$$The value of$$y(0.1)$$calculated numerically upto the third pla... ## Marks 2 Consider the equation$${{du} \over {dt}} = 3{t^2} + 1$$with$$u=0$$at$$t=0.$$This is numerically solved by using the forward Euler method with a ... Newton-Raphson method is to be used to find root of equation$$\,3x - {e^x} + \sin \,x = 0.\,\,$$If the initial trial value for the root is taken as ... For step-size,$$\Delta x = 0.4,$$the value of following integral using Simpson's$$1/3$$rule is ______ In Newton-Raphson iterative method, the initial guess value$$\left( {{x_{ini}}} \right)$$is considered as zero while finding the roots of the equati... The quadratic equation$${x^2} - 4x + 4 = 0$$is to be solved numerically, starting with the initial guess$${x_0} = 3.$$The Newton- Raphson method i... The integral$$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,} $$with$${x_2} > {x_1} > 0$$is evaluated analytically as well as numerically using a singl... There is no value of$$x$$that can simultaneously satisfy both the given equations. Therefore, find the 'least squares error' solution to the two equ... The square root of a number$$N$$is to be obtained by applying the Newton$$-$$Raphson iteration to the equation$$\,{x^2} - N = 0.\,\,$$If$$i$$d... The table below gives values of a function$$f(x)$$obtained for values of$$x$$at intervals of$$0.25$$The value of the integral of the function... The area under the curve shown between$$x=1$$and$$x=5$$is to be evaluated using the trapezoidal rule. The following points on the curve are given ... If the interval of integration is divided into two equal intervals of width$$1.0,$$the value of the definite integral$$\,\,\int\limits_1^3 {\log _e...
Given $$a>0,$$ we wish to calculate its reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0.$$ For $$a=7$$ and starting ...
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