GATE AE (Aerospace Engineering) Numerical Methods previous year questions from the Engineering Mathematics section, with figures and the official answer key where available.
Engineering Mathematics - Numerical Methods
An approximate solution of the equation $x^3 - 17 = 0$ is to be obtained using the Newton-Raphson method. If the initial guess is $x_o = 2$, the value at the end of the first iteration is $x_1 =$ _____ (rounded off to two decimal places).
Official answer: 2.75
Engineering Mathematics - Numerical Methods
Using Trapezoidal rule with one interval, the approximate value of the definite integral: $$\int_1^2 \dfrac{dx}{1+x^2}$$ is _____ (rounded off to 2 decimal places).
Official answer: 0.35
Engineering Mathematics - Numerical Methods
If a monotonic and continuous function $y = f(x)$ has only one root in the interval $x_1 < x < x_2$, then
Official answer: C
Engineering Mathematics - Numerical Methods
Use Newton-Raphson method to solve the equation: $xe^x = 1$. Begin with the initial guess $x_0 = 0.5$. The solution after one step is $x =$ _________.
Official answer: 0.56 to 0.58