Two tangent galvanometers $A$ and $B$ have coils of radii $8 \, cm$ and $16 \, cm$ respectively and resistance $8 \, \Omega$ each. They are connected in parallel with a cell of emf $4 \, V$ and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $30°$ and $60°$ respectively. If $A$ has $2$ turns, then $B$ must have: (in $turns$)

The mass of oxygen gas occupying a volume of $11.2 \text{ litres}$ at a temperature $27^{\circ}C$ and a pressure of $760 \text{ mm}$ of mercury in kilograms is $[$Molecular weight of oxygen $= 32]$

If $\frac{3x}{(x-a)(x-b)} = \frac{2}{x-a} + \frac{1}{x-b}$,then $a:b$ is equal to

As shown in the figure,two particles each of mass $m$ tied at the ends of a light string of length $2 a$ are kept on a frictionless horizontal surface. When the mid-point $(P)$ of the string is pulled vertically upwards with a small but constant force $F$,the particles move towards each other on the surface. The magnitude of acceleration of each particle,when the separation between them becomes $2 x$,is:

The figure shows a transparent sphere of radius $R$ and refractive index $\mu$. An object $O$ is placed at a distance $x$ from the pole of the first surface so that a real image is formed at the pole of the exactly opposite surface. If $x = \infty$,then the value of $\mu$ is

The air density at Mount Everest is less than that at sea level. Mountaineers find that for one trip lasting a few hours,the extra oxygen needed corresponds to $30,000 \ cc$ at sea level (pressure $1 \ atm$,temperature $27^{\circ}C$). Assuming that the temperature around Mount Everest is $-73^{\circ}C$ and that the oxygen cylinder has a capacity of $5.2 \ L$,the pressure at which $O_2$ must be filled in the cylinder is ..... $atm$.