Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. The first guest to arrive is given a room which is a prime number. The probability that the second guest to arrive is given a room which is a prime number is

Negation of the statement : $$3+6>8$$ and $$2+3<6$$ is

If $$f(x)=\operatorname{cosec}^{-1}\left[\frac{10}{6 \sin \left(2^x\right)-8 \cos \left(2^x\right)}\right]$$, then $$f^{\prime}(x)=$$

The area bounded by the parabola $$y^2=4 a x$$ and its latus-rectum $$x=a$$ is