Let $$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$ with $$n \ge 3$$ and
$${{a_{ij}} = i.j.}$$ Then the rank of $$A$$ is

Let $$A$$ be $$n \times n$$ real matrix such that $${A^2} = {\rm I}$$ and $$Y$$ be an $$n$$-diamensional vector. Then the linear system of equations $$Ax=y$$ has

For real $$x,$$ the maximum value of $${{{e^{Sin\,x}}} \over {{e^{Cos\,x}}}}\,\,$$ is

Consider the function $$\,\,f\left( x \right) = {\left| x \right|^3},\,\,\,$$ where $$x$$ is real. Then the function $$f(x)$$ at $$x=0$$ is

The value of $$\,\int\limits_0^\infty {\int\limits_0^\infty {{e^{ - {x^2}}}{e^{ - {y^2}}}} dx\,dy\,\,\,\,} $$ is

Assume that the duration in minutes of a telephone conversation follows the exponential distribution $$\,f\left( x \right) = {1 \over 5}{e^{ - x/5}},\,x \ge 0.\,\,\,$$ The probability that the conversation will exceed five minutes is

For the function $${{\sin z} \over {{z^3}}}$$ of a complex variable z, the point z = 0 is

Let $$j\, = \,\sqrt { - 1} $$. Then one value of $${j^j}$$ is

The polynomial $$\,p\left( x \right) = {x^5} + x + 2\,\,$$ has

Identity the Newton $$-$$ Raphson iteration scheme for the finding the square root of $$2$$