Table below is shows the relation between three variables \(P\), \(Q\) and \(R\).

Given that \(P\) varies directly as \(Q\) and varies inversely as \(R\).

\(\begin {array}{|c|c|c|} \hline \,\,P\,\,&\,\,Q\,\,&\,\,R\,\, \\\hline 2 & x & 3 \\\hline 4 & 10 & 5 \\\hline \end {array}\)

Find the value of \(x\).

(A)  \(2\)

(B)  \(3\)

(C)  \(4\)

(D)  \(6\)

(A)  \(x=-\dfrac1{27}\)

(B)  \(x=-\dfrac1{3}\)

(C)  \(x=-\dfrac1{9}\)

(D)  \(x=-\dfrac4{9}\)

The refractive index, \(n\) of medium varies directly as the real depth, \(H\)

and inversely as the apparent depth, \(h\).

It is given that \(n=4.0\), \(H=16.0\) and \(h=4.0\).

Find the value of \(H\) when \(n=1.64\) and \(h=3.2\).

(A)  \(H=0.513\)

(B)  \(H=1.951\)

(C)  \(H=5.248\)

(D)  \(H=3.451\)

The momentum, \(p\), of a particle varies directly as its mass, \(m\)

and as its velocity, \(v\).

\(p=5\) when \(m=\dfrac13\) and \(v=15\).

Calculate the value of \(p\)

when \(m=3.6\) and \(v=5\).

(A)  \(p=15.00\)

(B)  \(p=18.00\)

(C)  \(p=1.39\)

(D)  \(p=0.72\)

The table shows two sets of values of \(A\), \(B\) and \(C\) which satisfy 

\(A\propto BC^2\).

\(\begin{array}{|c|c|c|} \hline \quad\textbf{A}\quad&\quad24\quad&\quad72\quad\\ \hline \quad\textbf{B}\quad&\quad3\quad&\quad1\quad\\ \hline \quad\textbf{C}\quad&\quad2\quad&\quad x\quad\\ \hline \end{array}\)

Calculate the value of \(x\).

(A)  \(x=3\)

(B)  \(x=4\)

(C)  \(x=5\)

(D)  \(x=6\)