If the probability of hitting a target by a shooter, in any shot, is $${1 \over 3}$$, then the minimum number of independent shots at the target required by him so that the probability of hitting the target atleast once is greater than $${5 \over 6}$$ is :

The value of   $$\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {\left[ x \right] + \left[ {\sin x} \right] + 4}}} ,$$  where [t] denotes the greatest integer less than or equal to t, is

The tangent to the curve, y = xe^x2 passing through the point (1, e) also passes through the point

Let S = $$\left\{ {\left( {x,y} \right) \in {R^2}:{{{y^2}} \over {1 + r}} - {{{x^2}} \over {1 - r}}} \right\};r \ne \pm 1.$$ Then S represents :