$A$ metal wire has mass $(0.4 \pm 0.002) \, g$,radius $(0.3 \pm 0.001) \, mm$ and length $(5 \pm 0.02) \, cm$. The maximum possible percentage error in the measurement of density will nearly be $.......\%$

The period of oscillation of a simple pendulum is $T = 2\pi(L/g)^{1/2}$. Measured value of $L$ is $10 \text{ cm}$ known to $1 \text{ mm}$ accuracy and time for $100$ oscillations is $50 \text{ s}$, using a watch of $1 \text{ s}$ resolution. The percentage error in the measurement of $g$ is (in $\%$)

Two intervals of time are measured as $\Delta t_1 = (2.00 \pm 0.02) \ s$ and $\Delta t_2 = (4.00 \pm 0.02) \ s$. The value of $\sqrt{(\Delta t_1)(\Delta t_2)}$ with correct significant figures and error is

The percentage error in the measurement of mass and speed are $3\%$ and $2\%$ respectively. Then,the percentage error in kinetic energy will be .......... $\%$

The current-voltage relation of a diode is given by $I = (e^{1000V/T} - 1) \text{ mA}$,where the applied voltage $V$ is in volts and the temperature $T$ is in Kelvin. If a student makes an error of $\pm 0.01 \text{ V}$ while measuring the voltage to obtain a current of $5 \text{ mA}$ at $300 \text{ K}$,what will be the error in the value of current in $\text{mA}$?

$A$ quantity $Q$ is formulated as $Q = X^{-2} Y^{\frac{3}{2}} Z^{-\frac{2}{5}}$. $X, Y$ and $Z$ are independent parameters which have fractional errors of $0.1, 0.2$ and $0.5$,respectively,in measurement. The maximum fractional error of $Q$ is: