A physical quantity is $A = P^2/Q^3.$ The percentage error in measurement of $P$ and $Q$ is $x$ and $y$ respectively. Maximum error in measurement of $A$ is

If the random error in the arithmetic mean of $50$ observations is $\alpha$, then the random error in the arithmetic mean of $150$ observations would be

A physical quantity is given by $X = {M^a}{L^b}{T^c}$. The percentage error in measurement of $M,L$ and $T$ are $\alpha ,\beta $ and $\gamma $ respectively. Then maximum percentage error in the quantity X is

Error in the measurement of radius of a sphere is $1\%$. The error in the calculated value of its volume is  ......... $\%$

The energy of a system as a function of time $t$ is given as $E(t)=A^2 \exp (-\alpha t)$, where $\alpha=0.2 s ^{-1}$. The measurement of $A$ has an error of $1.25 \%$. If the error in the measurement of time is $1.50 \%$, the percentage error in the value of $E(t)$ at $t=5 s$ is

Quantity $Z$ varies with $x$ and $y$ , according to given equation $Z = x^2y - xy^2$ , where $x = 3.0 \pm 0.1$ and $y = 2.0 \pm 0.1$ . The value of $Z$ is