GATE ME
Engineering Mathematics
Numerical Methods
Previous Years Questions

## Marks 1

The root of the function $$f\left( x \right) = {x^3} + x - 1$$ obtained after first iteration on application of Newton-Raphson scheme using an initial...
Numerical integration using trapezoidal rule gives the best result for a single variable function, which is
The real root of the equation $$5x-2cosx=0$$ (up to two decimal accuracy) is
Using the trapezoidal rule, and dividing the interval of integration into three equal sub-intervals, the definite integral $$\,\,\int\limits_{ - 1}^{... Match the CORRECT pairs. ... The integral$$\,\int\limits_1^3 {{1 \over x}\,\,dx\,\,\,} $$when evaluated by using simpson's$$1/{3^{rd}}$$rule on two equal sub intervals each of... Starting from$$\,{x_0} = 1,\,\,$$one step of Newton - Raphson method in solving the equation$${x^3} + 3x - 7 = 0$$gives the next value$${x_1}$$a... The order of error in the simpson's rule for numerical integration with a step size$$h$$is Given the differential equation$${y^1} = x - y$$with initial condition$$y(0)=0.$$The value of$$y(0.1)$$calculated numerically upto the third pla... Simpson's rule for integration gives exact result when$$f(x)$$is a polynomial function of degree less than or equal to ________. ## Marks 2$$\,\,P\,\,\,\left( {0,3} \right),\,\,Q\,\,\,\left( {0.5,4} \right),\,\,$$and$$\,\,R\,\,\,\left( {1,5} \right)\,\,\,$$are three points on the curv... The error in numerically computing the integral$$\,\int\limits_0^\pi {\left( {\sin \,x + \cos \,x} \right)dx\,\,\,} $$using the trapezoidal rule wi... Solve the equation$$x = 10\,\cos \,\left( x \right)$$using the Newton-Raphson method. The initial guess is$$x = {\pi \over 4}.$$The value of the ... Gauss-Seidel method is used to solve the following equations (as per the given order).$$${x_1} + 2{x_2} + 3{x_3} = 5$2{x_1} + 3{x_2} + {x_3} =...
Newton-Raphson method is used to find the roots of the equation, $${\,{x^3} + 2{x^2} + 3x - 1 = 0}$$ If the initial guess is $${x_0} = 1,$$ then the ...
Using a unit step size, the value of integral $$\int\limits_1^2 {x\,\ln \,xdx\,\,\,}$$ by trapezoidal rule is ___________.
The values of function $$(x)$$ at $$5$$ discrete points are given below: Using Trapezodial rule with step size of $$0.1,$$ the value of $$\,\int\lim... Simpson's$${1 \over 3}$$rule is used to integrate the function$$f\left( x \right) = {3 \over 5}{x^2} + {9 \over 5}\,\,$$between$$x=0$$and$$x=1\$...
Consider an ordinary differential equation $${{dx} \over {dt}} = 4t + 4.\,\,$$ If $$x = {x_0}$$ at $$t=0,$$ the increment in $$x$$ calculated using R...
The value of $$\int\limits_{2.5}^4 {\ln \left( x \right)}$$ calculated using the Trapezoidal rule with five sub-intervals is
The definite integral $$\,\int\limits_1^3 {{1 \over x}} dx\,\,$$ is evaluated using Trapezoidal rule with a step size of $$1.$$ The correct answer is
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