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

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 $0^{\circ}$:

$A$ physical quantity $X$ is given by $X = \frac{2k^3l^2}{m\sqrt{n}}$. The percentage errors in the measurements of $k, l, m$ and $n$ are $1\%, 2\%, 3\%$ and $4\%$ respectively. The value of $X$ is uncertain by .......... $\%$

Explain uncertainty or error in a given measurement with a suitable example.

$A$ physical quantity $X$ is related to four measurable quantities $a, b, c$ and $d$ as follows: $X = a^2b^3c^{\frac{5}{2}}d^{-2}$. The percentage errors in the measurement of $a, b, c$ and $d$ are $1\%$,$2\%$,$3\%$ and $4\%$ respectively. What is the percentage error in quantity $X$? If the value of $X$ calculated on the basis of the above relation is $2.763$,to what value should you round off the result?

When two resistors of resistances $R_1=(200 \pm 2) \Omega$ and $R_2=(400 \pm 4) \Omega$ are connected in series,then the equivalent resistance of the combination is