Mathematics Mock Test - 7

If from a point $P(a,b,c)$, perpendiculars $PA$ and $PB$ are drawn to the $yz$ and $zx$ planes respectively, then the equation of the plane $OAB$ (where $O$ is the origin) is:

The ratio in which the plane $x-2y+3z=17$ divides the line joining the points $(-2,4,7)$ and $(3,-5,8)$ is:

If $73\equiv x(\mathrm{mod}13)$, what is the value of $x$ if $50<x<65$?

Maximize $Z=5x+8y$, subject to $2x+3y\ge 10$, $5x+2y\ge 14$, and $x,y\ge 0$. For this LPP:

A die is thrown 3 times. Let Event A be "4 on the 3rd throw" and Event B be "6 on the 1st and 5 on the 2nd throw". What is the probability of A given that B has already occurred?