List of top Engineering Mathematics Questions on Numerical Methods asked in GATE BT

Consider a nonlinear algebraic equation, \( e^x - 2 = 0 \). Using the Newton-Raphson method, with the initial guess of \( x_0 = 1 \), the approximated value of the root of the equation after one iteration is ________.
The value of \( k \), for which the linear equations \( 2x + 3y = 6 \) and \( 4x + 6y = 3k \) have at least one solution, is ________. (Answer in integer)
Consider a nonlinear algebraic equation, \( e^x - 2 = 0 \). Using the Newton-Raphson method, with the initial guess of \( x_0 = 1 \), the approximated value of the root of the equation after one iteration is ________.

The value of \( k \), for which the linear equations \( 2x + 3y = 6 \) and \( 4x + 6y = 3k \) have at least one solution, is ________. (Answer in integer)