List of top Engineering Mathematics Questions asked in Andhra Pradesh Post Graduate Engineering Common Entrance Test

Starting from \( x_0 = 1 \), one step Newton-Raphson method in solving the equation \( x^3 + 3x - 7 = 0 \) gives the next value as
The values of \( \mu \) which satisfy the equation \( A^{100} \vec{x} = \mu \vec{x} \), where \( A = \begin{bmatrix} 2 & -1 \\ 0 & -2 \\ 1 & 1 \end{bmatrix} \) are
The value of \( \int_0^3 \int_0^0 (x^2 + 3y^2) \, dy \, dx \) is
Complete integral of the partial differential equation \( 2\frac{\partial^2 f}{\partial q^2} + 3\frac{\partial f}{\partial q} = 6x + 2y \) is
The radius of convergence of Taylor's series expansion of \( f(z) = \frac{1}{(z - 1)^2} \) in powers of \( (z - 1) \) is ...
Evaluate \( \int_C \frac{dz}{z^2 + 9} \), where \( C \) is \( |z - 3| = 4 \)
A solution of the ODE \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = 0 \) is such that \( y(0) = 2 \) and \( y'(0) = 3 \). The value of \( y''(0) \) is
A die is thrown at random, find the probability of getting 5 or a number greater than 2 and is even
For any two arbitrary events \( A \) and \( B \), which of the following is true?
The matrix \( A = \begin{bmatrix} 3 & -1 & 1 \\ 1 & -5 & 1 \\ 1 & -1 & 3 \end{bmatrix} \) has eigenvalues 2, 3, 6 then the eigenvalues of \( A^4 \) are
Determine the value of \( p \) such that the rank of matrix \( A \) is 2:
\[ A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 0 & 2 & p \\ 1 & 0 & p & 7 \end{bmatrix} \]