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)

In a new system of units,the unit of mass is $a \ kg$,and the units of length and time are $b \ m$ and $c \ s$,respectively. What is the magnitude of $6 \ W$ of power in this system?

Assertion $(A)$: Energy per unit volume and angular momentum can be added dimensionally.
Reason $(R)$: Physical quantities having same dimensions can be added or subtracted.

The energy $(E)$,angular momentum $(L)$,and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of the universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity $X$ as follows: $[position] = [X^\alpha]$; $[speed] = [X^\beta]$; $[acceleration] = [X^p]$; $[linear momentum] = [X^q]$; $[force] = [X^r]$. Then -
$(A)$ $\alpha + p = 2\beta$
$(B)$ $p + q - r = \beta$
$(C)$ $p - q + r = \alpha$
$(D)$ $p + q + r = \beta$

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a \sin(ct) + b \cos(dx)$. Then the dimension of $a/b$ is: