Which of the following relations can be derived using dimensional analysis?

The equation of the stationary wave is $y = 2A \sin \left( \frac{2\pi ct}{\lambda} \right) \cos \left( \frac{2\pi x}{\lambda} \right)$. Which statement is not true?

The characteristic distance at which quantum gravitational effects are significant,the Planck length,can be determined from a suitable combination of the fundamental physical constants $G, h$ and $c$. Which of the following correctly gives the Planck length?

$L$, $C$, and $R$ represent the physical quantities inductance, capacitance, and resistance, respectively. The dimensional formula $ML^2T^{-4}A^{-2}$ corresponds to . . . . . . .

Given that $v$ is speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

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 -
$(A)$ $\alpha + p = 2\beta$
$(B)$ $p + q - r = \beta$
$(C)$ $p - q + r = \alpha$
$(D)$ $p + q + r = \beta$