The ratio of angular speeds of the minute hand and the hour hand of a watch is

For $x \in \mathbb{R}$,the range of $3 \cos (4x - 5) + 4$ lies in the interval

If the excess pressure inside a soap bubble is balanced by an oil column of height $2\; mm$,then the surface tension of the soap solution will be ($r = 1\; cm$ and density $d = 0.8\; g/cm^3$).

Ethanol,when reacted with $PCl_5$,gives $A$,$POCl_3$,and $HCl$. $A$ reacts with silver nitrite to form $B$ (major product) and $AgCl$. $A$ and $B$ are respectively:

Two coherent point sources $S_1$ and $S_2$ vibrating in phase emit light of wavelength $\lambda$. The separation between them is $2 \lambda$ as shown in the figure. The first bright fringe is formed at $P$ due to interference on a screen placed at a distance $D$ from $S_1$ $(D >> \lambda)$. Then the distance $OP$ is:

The acceleration due to gravity on the moon is $\left(\frac{1}{6}\right)$ times the acceleration due to gravity on the earth. If the ratio of the density of the earth $\rho_{e}$ to the density of the moon $\rho_{m}$ is $\frac{5}{3}$,then the radius of the moon $R_{m}$ in terms of the radius of the earth $R_{e}$ is: