$$\mathop {\lim }\limits_{x \to 0} \left( {{{{e^{5x}} - 1} \over x}} \right)$$ is equal to ________.

A normal random variable $$X$$ has the following probability density function $$${f_x}\left( x \right) = {1 \over {\sqrt {8\pi } }}e{}^{ - \left\{ {{{{{\left( {x - 1} \right)}^2}} \over 8}} \right\}}, - \infty < x < \infty $$$
Then $$\,\int\limits_1^\infty {{f_x}\left( x \right)dx = } $$

A fair coin is tossed $$N$$ times. The probability that head does not turn up in any of the tosses is

To solve the equation $$2sinx=x$$ by Newton- Raphson method, the initial guess was chosen to be $$x=2.0.$$ Consider $$x$$ in radian only. The value of $$x$$ (in radian) obtained after one iteration will be closest to