$A$ set of defective observation weights is used by a student to find the mass of an object using a physical balance. $A$ large number of readings will reduce:

The energy of a system is given as $E(t) = \alpha^3 e^{-\beta t}$,where $t$ is the time and $\beta = 0.3 \ s^{-1}$. The errors in the measurement of $\alpha$ and $t$ are $1.2 \%$ and $1.6 \%$,respectively. At $t = 5 \ s$,the maximum percentage error in the energy is: (in $\%$)

$A$ physical quantity $S$ is related to four observables $a, b, c$, and $d$ as $S = \frac{\sqrt{a} b}{c^3 d^4}$. If the percentage errors of measurement in $a, b, c$, and $d$ are $2 \%$, $1 \%$, $1 \%$, and $1 \%$ respectively, then the percentage error in the quantity $S$ is: (in $\%$)

$A$ physical quantity $P$ is related to four observables $a, b, c$ and $d$ as $P = \frac{\sqrt{a b} \cdot d^\alpha}{\sqrt{c}}$ (where $\alpha$ is a constant). The percentage errors in $a, b, c$ and $d$ are $0.5 \%$ each. If the percentage error in $P$ is $2 \%$,then the value of $\alpha$ is:

The percentage error in the measurement of mass and speed of a particular body is $3 \%$ and $4 \%$ respectively. The percentage error in the measurement of kinetic energy is (in $\%$)

Using the expression $2 d \sin \theta = \lambda$,one calculates the values of $d$ by measuring the corresponding angles $\theta$ in the range $0^{\circ}$ to $90^{\circ}$. The wavelength $\lambda$ is exactly known and the error in $\theta$ is constant for all values of $\theta$. As $\theta$ increases from $0^{\circ}$: