A target is to be destroyed in a bombing exercise and there is a $75 \%$ chance that a bomb will hit the target. Assuming that two direct hits are required to destroy the target completely, the minimum number of bombs to be dropped in order that the probability of destroying the target is not less than $99 \%$, is

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$, then $P(X \leq 3)=$

If $A=(1,2), B=(2,1)$ and $P$ is any point satisfying the condition $P A+P B=3$, then the equation of the locus of $P$ is

Let $C$ be a curvea $x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ in a cartesian plane. By rotating the coordinate axes through an angle $\frac{\pi}{4}$ in the positive direction, if the transformed equation of $C$ is $Y^2+X Y-X=0$, then $\left(h^2-a b\right)-2 g f=$