GATE PI
Engineering Mathematics
Numerical Methods
Previous Years Questions

## Marks 1

To solve the equation $$2sinx=x$$ by Newton- Raphson method, the initial guess was chosen to be $$x=2.0.$$ Consider $$x$$ in radian only. The value o...
In numerical integration using Simpson's rule, the approximating function in the interval is a
Using the Simpson's $$1/{3^{rd}}$$ rule, the value of $$\,\int {ydx} \,\,$$ computed, for the data given below, is ...
If the equation $$sin(x)$$ $$\, = {x^2}$$ is solved by Newton Raphson's method with the initial guess of $$x=1,$$ then the value of $$x$$ after $$2$$ ...
During the numerical solution of a first order differential equation using the Euler (also known as Euler Cauchy) method with step size $$h,$$ the loc...
For solving algebraic and transcendental equation which one of the following is used?
Newton $$-$$ Raphson formula to find the roots of an equation $$f(x)=0$$ is given by

## Marks 2

The following algorithm computes the integral $$\,J = \int\limits_a^b {f\left( x \right)dx\,\,\,}$$ from the given values $${f_j} = f\left( {{x_j}} \... Matching exercise choose the correct one out of the alternatives$$A, B, C, D$$Group$$-{\rm I}P.{2^{nd}}$$order differential equati... The real root of the equation$$x{e^x} = 2$$is evaluated using Newton$$-$$Raphson's method. If the first approximation of the value of$$x$$is$$...
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