If $|\overline{\mathrm{a}}|=2,|\overline{\mathrm{~b}}|=3$ and $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ are mutually perpendicular vectors, then the area of the triangle whose vertices are $0, a+2 b, a-2 b$ is

If $y$ is a function of $x$ and $\log (x+y)=2 x y$, then the value of $y^{\prime}(0)$ is

A random variable X has the following probability distribution

For the events $\mathrm{E}=\{\mathrm{X}$ is prime number $\}$

$$\mathrm{F}=\{\mathrm{X}<4\}$$

Then $P(E \cup F)=$

If $y=a x^{n+1}+b x^{-n}$, then $x^2 \frac{d^2 y}{d x^2}=$