If the equation $y = x^2 r + M^1 L^1 T^{-2}$ is dimensionally correct,find the dimensional formula of $x^2$. (Here,$r$ represents displacement.)

In an electromagnetic system,the quantity representing the ratio of electric flux and magnetic flux has dimensions of $M^{P} L^{Q} T^{R} A^{S}$. The values of $Q$ and $R$ are:

Planck's constant $h$,speed of light $c$,and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are):
$(A)$ $M \propto \sqrt{c}$
$(B)$ $M \propto \sqrt{G}$
$(C)$ $L \propto \sqrt{h}$
$(D)$ $L \propto \sqrt{G}$

If the orbital velocity of a planet is given by $v = G^a M^b R^c$,then:

Given that the displacement of an oscillating particle is given by $y = A \sin(Bx + Ct + D)$. The dimensional formula for $ABCD$ is: (Here $x$ is position,$t$ is time)

$A$ quantity $f$ is given by $f = \sqrt{\frac{hc^5}{G}}$,where $c$ is the speed of light,$G$ is the universal gravitational constant,and $h$ is Planck's constant. The dimension of $f$ is that of: