GATE EE
Engineering Mathematics
Numerical Methods
Previous Years Questions

## Marks 1

If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of the following statements is TRU...
The function $$f\left( x \right) = {e^x} - 1\,\,$$ is to be solved using Newton $$-$$ Raphson method. If the initial value of $${x_0}$$ is taken $$1.0... When the Newton-Raphson method is applied to solve the equation$$\,\,f\left( x \right) = {x^3} + 2x - 1 = 0,\,\,$$the solution at the end of the fi... Let$$\,{x^2} - 117 = 0.\,\,$$The iterative steps for the solution using Newton -Raphson's method is given by Equation$${e^x} - 1 = 0\,\,$$is required to be solved using Newton's method with an initial guess$$\,\,{x_0} = - 1.\,\,$$Then after one step of N... Given the differential equation$${y^1} = x - y$$with initial condition$$y(0)=0.$$The value of$$y(0.1)$$calculated numerically upto the third pla... ## Marks 2 Solution, the variable$${x_1}$$and$${x_2}$$for the following equations is to be obtained by employing the Newton$$-$$Raphson iteration method e... A differential equation$${{dx} \over {dt}} = {e^{ - 2t}}\,\,u\left( t \right)\,\,$$has to be solved using trapezoidal rule of integration with a st... The value of$$\,\,\,\int\limits_1^2 {{1 \over x}\,\,\,dx\,\,\,\,} $$computed using simpson's rule with a step size of$$h=0.25 is
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