An unbanked curve has a radius of $60\,m$. The maximum speed at which a car can make a turn if the coefficient of static friction is $0.75$,is ...... $m/s$.

An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 \, g/cm^3$) standing initially $20 \, cm$ from the bottom in each arm. An immiscible liquid of density $4.0 \, g/cm^3$ is added to one arm until a layer $5 \, cm$ high forms,as shown in the figure. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?

If $A=\left[\begin{array}{rr}i & -i \\ -i & i\end{array}\right]$ and $B=\left[\begin{array}{rr}1 & -1 \\ -1 & 1\end{array}\right]$,then find $A^8$. (in $B$)

If the foot of the perpendicular from $(0,0,0)$ to a plane is $(1,2,3)$,then the equation of the plane is

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=2x+3$ and $g(x)=x^2+7$,then the values of $x$ such that $g(f(x))=8$ are