Identify the incorrect statement in the following.

The vectors $3\,i + j - 5\,k$ and $a\,i + b\,j - 15\,k$ are collinear,if

The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index $1.5$. When the telescope is adjusted to infinity,the separation between the two lenses is $16 ~cm$. If the space between the lenses is now filled with water (refractive index $4/3$) and the telescope is again adjusted for infinity,then the present separation between the lenses is: (in $~cm$)

If $A$ and $B$ are two independent events such that $P(B)=\frac{2}{7}$ and $P(A \cup B^c)=0.8$,then $P(A)$ is equal to:

The pair of straight lines is represented by the equation $3dx^2 - 5xy + (d^2 - 2)y^2 = 0$. If the lines are perpendicular to each other,for how many values of $d$ will this condition be satisfied?

In the equation $log S = log C + Z log A$,what does $S$ represent?