The dimensional formula for a physical quantity $x$ is $[M^{-1} L^{3} T^{-2}]$. The errors in measuring the quantities $M, L$ and $T$ respectively are $2\%, 3\%$ and $4\%$. The maximum percentage of error that occurs in measuring the quantity $x$ is (in $\%$)

$A$ physical quantity $z$ depends on four observables $a, b, c$ and $d$ as $z = \frac{a^2 b^{2/3}}{\sqrt{c} d^3}$. The percentage errors in the measurement of $a, b, c$ and $d$ are $2\%, 1.5\%, 4\%$ and $2.5\%$ respectively. The percentage error in $z$ is $......\%$. (in $.5$)

When a wave traverses a medium, the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$, where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?

If force $F$,length $L$,and time $T$ are taken as the fundamental quantities,then what will be the dimension of density?

Due to an explosion underneath water, a bubble started oscillating. If this oscillation has a time period $T$, which is proportional to $p^\alpha S^\beta E^\gamma$, where $p$ is static pressure, $S$ is the density of water, and $E$ is the total energy of the explosion, determine $\alpha, \beta$, and $\gamma$.

Consider two physical quantities $A$ and $B$ related to each other as $E = \frac{B - x^2}{At}$,where $E, x,$ and $t$ have dimensions of energy,length,and time respectively. The dimension of $AB$ is