The condition for which the eigenvalues of the matrix $$A = \left[ {\matrix{ 2 & 1 \cr 1 & k \cr } } \right]$$ are positive, is

The values of $$x$$ for which the function $$f\left( x \right) = {{{x^2} - 3x - 4} \over {{x^2} + 3x - 4}}$$ is NOT continuous are

The probability that a screw manufactured by a company is defective is $$0.1$$. The company sells screws in packets containing $$5$$ screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________.

Numerical integration using trapezoidal rule gives the best result for a single variable function, which is