Mathematics Mock Test - 11

Let $L$ be a line that is perpendicular to the plane $x-3y+2z=k$ and passes through the point $(1,2,-2)$. The point on the line $L$ that is nearest to the $y$ -axis is:

Let $P$ be the plane passing through the intersection of planes $P_1:x+y+z-6=0$ and $P_2:2x+3y+4z+5=0$. If the plane $P$ contains the origin, then the equation of the plane $P$ is:

The reflection of the origin in the plane $P_2:2x+3y+4z+5=0$ is:

The unit vector perpendicular to line $L$ (DRs: $1,-3,2$) and the normal to the plane $P_1:x+y+z-6=0$ is:

If the probability of $A$ to fail in an examination is $0.2$ and that for $B$ is $0.3$, then the probability that either $A$ or $B$ fails (meaning exactly one of them fails) is: